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1
Kellermann, David Conrad Mechanical & Manufacturing Engineering Faculty of Engineering UNSW. "Strongly orthotropic continuum mechanics." Publisher:University of New South Wales. Mechanical & Manufacturing Engineering, 2008. http://handle.unsw.edu.au/1959.4/41454.
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The principal contribution of this dissertation is a theory of Strongly Orthotropic Continuum Mechanics that is derived entirely from an assertion of geometric strain indeterminacy. Implementable into the finite element method, it can resolve widespread kinematic misrepresentations and offer unique and purportedly exact strain-induced energies by removing the assumptions of strain tensor symmetry. This continuum theory births the proposal of a new class of physical tensors described as the Intrinsic Field Tensors capable of generalising the response of most classical mechanical metrics, a number of specialised formulations and the solutions shown to be kinematically intermediate. A series of numerical examples demonstrate Euclidean objectivity, material frame-indifference, patch test satisfaction, and agreement between the subsequent Material Principal Co-rotation and P??I??C decomposition methods that produce the intermediary stress/strain fields. The encompassing theory has wide applicability owing to its fundamental divergence from conventional mechanics, it offers non-trivial outcomes when applied to even very simple problems and its use of not the Eulerian, Lagrangian but the Intrinsic Frame generates previously unreported results in strongly orthotropic continua.
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Menzel, Andreas. "Frontiers in inelastic continuum mechanics." Kaiserslautern Techn. Univ., Lehrstuhl für Techn. Mechanik, 2007. http://d-nb.info/99794563X/34.
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Popovic, Marko. "Continuum mechanics of developing epithelia:." Doctoral thesis, Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2017. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-227283.
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Developing tissues are out-of-equilibrium systems that grow and reshape to form organs in adult animals. They are typically composed of a large number of cells. The constitutive cells of a tissue perform different roles in tissue development and contribute to the overall tissue shape changes.
In this thesis, we construct a hydrodynamic theory of developing epithelial tissues. We use it to investigate the developing wing of the fruit fly Drosophila melanogaster. This theory relates the coarse-grained cell scale properties to the large-scale tissue flows. We explicitly account for the active cellular processes in the tissue that drive tissue flows. In our description of the tissue, we also include the memory effects that are necessary to account for the experimental observations. These memory effects have a significant influence on the tissue rheology.
Using this hydrodynamic theory we analyze shear flow in a developing fruit fly wing tissue. We find that the active cellular processes contribute to overall tissue flows and that memory effects are present in the wing tissue. We investigate consequences of these findings on the rheology of tissue shear flow. We find that the memory effects give rise to an inertial response that leads to oscillations in the tissue but it does not stem from the wing mass. Finally, we describe how the tissue rheology is affected by different boundary conditions.
We then investigate the area changes during the pupal wing development and we construct a mechanosensitive model for the cell extrusion rate in the pupal wing. Analysis of cell extrusions in the context of this model also allows us to extract information about the cell division properties.
Boundary connections between the wing tissue and surrounding cuticle are crucial for the proper development of the pupal wing. A dumpy mutant wing is strongly misshaped during the pupal wing morphogenesis. We use a simple model for the wing to show that the dumpy mutant wing can be described as a wild type wing with compromised boundary conditions.
Finally, we analyze cell properties and tissue flows in a developing wing disc epithelium. Motivated by the observation of radially oriented active T1 transitions in the wing disc epithelium, we use the hydrodynamic theory to investigate the influence of such T1 transitions on stresses in the tissue. We show that sufficiently strong radially oriented active T1 transitions can contribute to the control of the tissue size.
Results obtained in this thesis extend our understanding of the fly wing tissue rheology and the role of internal and external forces in the proper shaping of the wing epithelium. The hydrodynamic theory we use to describe the fly wing development provides a set of phenomenological parameters that characterize the tissue mechanics and can be experimentally measured. Therefore, we expect that future research will include and extend the hydrodynamic theory presented in this thesis.
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Borrvall, Thomas. "Computational topology optimization in continuum mechanics /." Linköping : Univ, 2002. http://www.bibl.liu.se/liupubl/disp/disp2002/tek744s.pdf.
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Nyman, Ulf. "Continuum mechanics modelling of corrugated board /." Lund : Univ, 2004. http://www.byggmek.lth.se/.
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Wei, Zhiyan. "Studies in discrete and continuum mechanics." Thesis, Harvard University, 2014. http://dissertations.umi.com/gsas.harvard:11582.
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We have used a combination of theory and computation to investigate collective aspects of discrete mechanical systems. The analysis involves considerations from geometry, elasticity and hydrodynamics. We have developed continuum theories to describe these systems, in the spirit of compressing information by mathematical abstraction from the discrete description.Engineering and Applied Sciences
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Alruwaili, Khalid Mohammed M. "Continuum and combined continuum-discontinuum analysis of wellbore mechanics and stimulation response." Thesis, Heriot-Watt University, 2016. http://hdl.handle.net/10399/3195.
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Wellbore drilling and stimulation activities are interlinked processes within the task of borehole construction. Before drilling a well, the initial stress state in the rock can be defined by three principal stresses, with a typical assumption that these consist of the vertical stress (σv), the maximum horizontal stress (σH) and the minimum horizontal stress (σh). After drilling, the stress state changes around the created borehole. The fundamental engineering problem then is to calculate the stresses around the created borehole and/or at the borehole’s wall. Numerous analytical and numerical models exist to estimate the stresses around a circular hole, but these models cannot explain the observed phenomena either in the field or the lab. Attention here is focused on models that are commonly used to predict the stress state around a circular opening. These models do not account for the sequence of the physical processes, leading to an inadequate stress state estimation. This research investigates the 2D classical analytical method, along with a comparison of that approach against numerical methods. This investigation reveals that the models are not equivalent. This is not because of mathematical issues, but is due to the fact that the mechanical systems expressed by these models are not equivalent. The drilling model captures the physics of the real process which makes it possible to explain some phenomena observed in field and laboratory tests. The drilling model approach is applied for several sedimentary rock examples. The combined continuum-discontinuum method reveals its capability in calculating rock failure and deformation that is comparable to some published laboratory drilling tests. Also, the simulation results shed light into the complex fracture growth regime around the wellbore. Drilling and Hydraulic fracture simulation is carried out for Berea sandstone using both the continuum and the combined continuum-discontinuum methods. The results are in good agreement which identifies a practical engineering method for larger models. The fracturing initiates in Mode II (shear) near the circumference of the wellbore aligned with the maximum stress. At later stages, Mode I (tensile) fractures also develop and propagate the fracture parallel to the maximum horizontal stress. This fracturing mechanism continues for as long as the pressure is applied.
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Thellner, Mikael. "Multi-parameter topology optimization in continuum mechanics /." Linköping : Dept. of Mechanical Engineering, Univ, 2005. http://www.bibl.liu.se/liupubl/disp/disp2005/tek934s.pdf.
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Rahimi, Mohammad. "Hybrid Molecular Dynamics – Continuum Mechanics for Polymers." Phd thesis, TU Darmstadt, 2012. https://tuprints.ulb.tu-darmstadt.de/3292/1/Final.pdf.
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The interaction of polymers and a solid surface modifies the polymer properties near the surface (the
so-called interphase) in comparison to those of the bulk polymers. A clear explanation of the origin of
this modification in the polymer properties is still missing. The aim of my PhD thesis has been the
study of the mechanical properties of nanocomposite materials and the analysis of the behavior of
polymers in the interphase region under deformation. Coarse-grained simulations have been performed
for a model system of silica nanoparticles (NPs) embedded in atactic polystyrene (PS). In this case
molecular details are important only in a small spatial region of the interphase. The rest of the polymer
has bulk-like behavior which can be described by continuum mechanics. Therefore, it is convenient to
simulate the region of interest by molecular dynamics (MD) and to treat the rest of the nanocomposite
by continuum mechanics methods. To fulfill this we developed a new hybrid molecular – continuum
simulation method for polymers. In our model the center of the simulation box is treated by MD. This
region is surrounded by a continuum domain which is described by a finite element approach. To the
best of our knowledge, the present work is the first attempt to use simultaneously MD and FE methods
in simulations of polymers. It has been the main motivation of this work to develop a new hybrid
scheme for polymers. Coupling a MD to a FE method requires a lot of modifications in both the MD
and FE domains. The introduction of my thesis contains a short review on the existing hybrid schemes
and modifications needed to couple the two domains. Difficulties to couple them such as transferring
the information between two domains and equilibrating the continuum domain are explained. Different
methods and techniques to overcome these difficulties as well as the advantages and disadvantages of
each method are described briefly. These methods, however, are limited to liquid and crystalline solid
materials. They have to be modified to be capable of simulating polymers. In the present PhD thesis
we have explained the technical difficulties to couple a MD to a FE model for polymers in the MD
domain and how we tackled these problems. Modifications in the FE domain have been done by
researchers in the Applied Mechanics Department of the University of Erlangen. The current work has
involved a strong collaboration with them to integrate a modified MD domain into a FE domain.
In the second chapter of the thesis, the mechanical properties of a pure polystyrene matrix as well as a
polystyrene matrix filled with bare silica nanoparticles are investigated by MD simulations at the
coarse-grained level. The stress-strain curve of polystyrene has been computed for a range of
temperatures below and above the glass transition. The Young’s modulus of polystyrene obtained from
the stress-strain curve has been compared to experimental and atomistic simulation data. By studying
the local segmental orientation and the local structure of the polymer near the nanoparticle surface under deformation, we have found that the segments close to the silica nanoparticle surface are stiffer
than those in the bulk. The thickness of the interphase has been estimated. We have shown that the
Young’s modulus of the studied nanocomposite increases by increasing the volume fraction of the
nanoparticle. The results of interphase studies under deformation as described in this section are
important input parameters for the FE simulations in the present hybrid scheme; this will explained in
chapter four.
In hybrid simulations the usual periodic boundary conditions of MD cannot be used as the MD domain
is surrounded by a FE domain. In hybrid schemes boundary conditions should allow an information
transfer through the boundary region between two domains. Therefore, I developed new non-periodic
boundary conditions, so-called stochastic boundary conditions (SBC), which are able to transfer
information (forces and deformations) between the two domains and to minimize the artifacts in the
dynamics. In the SBC ensemble we have defined a set of auxiliary particles, so-called anchor points, in
the boundary region. The anchor points are harmonically coupled to the MD particles. They play an
important role to transfer the information between the MD and FE domains. Particles in the boundary
region are forced to mimic the bulk behavior by employing a stochastic dynamics in the boundary
region. This minimizes the artificial influence of the anchor points and the vacuum on the polymers in
the center of the box. The SBCs are explained in more detail in the third chapter. We have validated
these boundary conditions by comparing the results of coarse-grained polystyrene melts under nonperiodic
and regular periodic boundary conditions. Excellent agreement is found for thermodynamic,
structural, and dynamic properties.
The new hybrid molecular – continuum method for polymers is explained in more detail in chapter
four. Due to the significant difference between the time steps in the two domains, we employed a
staggered coupling procedure in which the continuum domain has been described as a static region
while the MD domain has been treated dynamically. The Arlequin method has been used for the static
coupling of the MD to the FE domain. The information transfer between them has been realized in a
coupling region which contains the above mentioned anchor points. In this region two descriptions are
valid, i.e., the particle and the continuum one. The total energy is blended by a weighting factor.
Atactic PS and a PS silica nanocomposite have been simulated in a coarse-grained representation to
validate the new hybrid scheme. The deviations between data from the hybrid method and pure FE
simulations have been computed for quantities such as reaction forces and the Cauchy stress. The
sources of the observed deviations are discussed in some detail.
Finally, the fifth chapter summarizes the results obtained in this PhD work, and discusses possibilities
to extend the current hybrid model to new problems such as larger deformations.
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Sakatani, Yuho. "Relativistic viscoelastic fluid mechanics and the entropic formulation of continuum mechanics." 京都大学 (Kyoto University), 2012. http://hdl.handle.net/2433/157762.
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Sears, Aaron Thomas. "Carbon Nanotube Mechanics: Continuum Model Development from Molecular Mechanics Virtual Experiments." Diss., Virginia Tech, 2006. http://hdl.handle.net/10919/29959.
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Carbon Nanotubes (CNTs) hold great promise as an important engineering material for future applications. To fully exploit CNTs to their full potential, it is important to characterize their material response and ascertain their material properties. We have used molecular mechanics (MM) simulations to conduct virtual experiments on single-wall and multi-wall carbon nanotubes (SWNTs and MWNTs respectively) similar to those performed in the mechanics of materials laboratory on a continuum structure. The output (energy and deformation rather than the load and deflection) is used to understand the material response and formulate macroscopic constitutive relations.
From results of MM simulations of axial and torsional deformations on SWNTs, Young's modulus, the shear modulus and the wall thickness of an equivalent continuum tube made of a linear elastic isotropic material were found. These values were used to compare the response of the continuum tube, modeled as an Euler-Bernoulli beam, in bending and buckling with those obtained from the MM simulations.
MM simulations have been carried out to find energetically favorable double-walled carbon nanotube (DWNT) configurations, and analyze their responses to extensional, torsional, radial expansion/contraction, bending, and buckling deformations. Loads were applied either to one wall or simultaneously to both walls of an open-ended DWNT. These results were compared against SWNT results. It was found that for simple tension and torsional deformations, results for a DWNT can be derived from those for its constituent SWNTs within 3% error. Radial deformations of a SWNT were achieved by considering a DWNT with the SWNT as one of its walls and moving radially through the same distance all atoms of the other wall of the DWNT thereby causing a pseudo-pressure through changes in the cumulative van der Waals forces which deform the desired wall. Results of radial expansion/contraction of a SWNT were used to deduce an expression for the van der Waals forces, and find through-the-thickness elastic moduli (Young's modulus in the radial direction, Er, and Poisson's ratio ?r?) of the SWNT. We have found four out of the five elastic constants of a SWNT taken to be transversely isotropic about a radial line.
MWNTs were studied using the same testing procedures as those used SWNTs. Based on the results from those simulations a continuum model is proposed for a MWNT whose response to mechanical deformations is the same as that of the MWNT. The continuum structure is comprised of concentric cylindrical tubes interconnected by truss elements. Young's modulus, Poisson's ratio, the thickness of each concentric tube, and the stiffness of the truss elements are given. The proposed continuum model is validated by studying its bending and buckling deformations and comparing these results to those from MM simulations.
The major contributions to the field on nanotubes and the scientific literature is a simple and robust continuum model for nanotubes. This model can be used to study both SWNTs and MWNTs in either global or local responses by applying different analytic techniques. This model was developed using a consistent engineering methodology that mimicked traditional engineering testing, assumptions and constraints.Ph. D.
12
Wiker, Niclas. "Optimization in Continuum Flow Problems." Doctoral thesis, Linköpings universitet, Mekanik, 2008. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-14857.
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The work presented in this dissertation was carried out at the Division ofMechanics, Department of Management and Engineering at Link¨oping University,between 2003 and 2008. It was supervised by Prof. Anders Klarbring,head of the division, and financially supported by the National GraduateSchool of Scientific Computing (NGSSC) and the Swedish Research Council(VR). There are many people to whom I would like to express my gratitude: firstand foremost I would like to thank my supervisor Prof. Anders Klarbring forhis help, support and endless patience during our discussions, and for alwayshaving time to read and comment on the numerous drafts that eventually ledto the research manuscripts presented in this thesis. I would also like to thankmy co–supervisor Dr. Thomas Borrvall for all his help regarding numericalissues, especially with the implementation of the models. Moreover, I wouldlike to thank present and former colleagues for their inspiration and assistanceduring my time as a graduate student at the division. Last but not least, I am very grateful for having a family that has alwaysbeen there to support me, and for all my friends who enrich my life outsidethe office walls in more ways then I can say.
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Menzel, Andreas [Verfasser]. "Frontiers in inelastic continuum mechanics / von Andreas Menzel." Kaiserslautern : Techn. Univ., Lehrstuhl für Techn. Mechanik, 2007. http://d-nb.info/99794563X/34.
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Ranft, Jonas M. "Mechanics of Growing Tissues: A Continuum Description Approach." Doctoral thesis, Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2013. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-105479.
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During development, higher organisms grow from a single fertilized egg cell to the adult animal. The many processes that lead to the eventual shape of the developed organism are subsumed as morphogenesis, which notably involves the growth of tissues by repeated rounds of cell division. Whereas coordinated tissue growth is a prerequisite for animal development, excessive cell division in adult animals is the key ingredient to cancer. In this thesis, we investigate the collective organization of cells by cell division and cell death. The multicellular dynamics of growing tissues is influenced by mechanical conditions and can give rise to cell rearrangements and movements. We develop a continuum description of tissue dynamics, which describes the stress distribution and the cell flow field on large scales. Cell division and apoptosis introduce stress sources that, in general, are anisotropic. By combining cell number balance with dynamic equations for the stress source, we show that the tissue effectively behaves as a viscoelastic fluid with a relaxation time set by the rates of division and apoptosis. If the tissue is confined in a fixed volume, it reaches a homeostatic state in which division and apoptosis balance. In this state, cells undergo a diffusive random motion driven by the stochasticity of division and apoptosis. We calculate the effective diffusion coefficient as a function of the tissue parameters and compare our results concerning both diffusion and viscosity to simulations of multicellular systems. Introducing a second material component that accounts for the extracellular fluid, we show that a finite permeability of the tissue gives rise to additional mechanical effects. In the limit of long times, the mechanical response of the tissue to external perturbations is confined to a region of which the size depends on the ratio of tissue viscosity and cell-fluid friction. The two-component description furthermore allows to clearly distinguish the different contributions to the isotropic part of the mechanical stress, i.e., the fluid pressure and the stress exerted by cells. Last but not least, we study the propagation of an interface between two different cell populations within a tissue driven by differences in the mechanical control of the rates of cell division and apoptosis. Combining simple analytical limits and numerical simulations, we distinguish two different modes of propagation of the more proliferative population: a diffusive regime in which relative fluxes dominate the expansion, and a propulsive regime in which the proliferation gives rise to dominating convective flowsDie Entwicklung höherer Organismen beginnt mit einer einzelnen befruchteten Eizelle und endet beim erwachsenen Tier. Die vielen Prozesse, die zur endgültigen Form des entwickelten Organismus führen, werden als Morphogenese zusammengefasst; diese umfasst insbesondere das Wachstum von Geweben durch wiederholte Zellteilungszyklen. Während koordiniertes Gewebewachstum eine Voraussetzung normaler Entwicklung ist, führt übermäßige, unkontrollierte Zellteilung letztlich zu Krebs. In dieser Arbeit untersuchen wir den Einfluss von Zellteilung und Zelltod auf die Organisation von Zellen in Geweben. Die Dynamik wachsender Gewebe wird durch mechanische Bedingungen beeinflusst, die u.a.~Anlass zu Zellbewegungen sein können. Wir entwickeln eine Kontinuumsbeschreibung der Gewebedynamik, die die mechanischen Spannungen und das Zellströmungsfeld auf großen Skalen beschreibt. Zellteilung und Apoptose wirken als Spannungsquellen, die in der Regel anisotrop sind. Indem wir die Erhaltungsgleichung für die Zellanzahldichte mit dynamischen Gleichungen für die Spannungsquellen kombinieren, zeigen wir, dass sich das Gewebe effektiv wie eine viskoelastische Flüssigkeit verhält, deren Relaxationszeit von Zellteilungs- und Apoptose-Raten abhängt. Wenn das Gewebe in einem gegebenen Volumen eingeschlossen ist, erreicht es einen homöostatischen Zustand, in dem Zellteilung und der Apoptose im Gleichgewicht sind. In diesem Zustand unterliegen die Zellen einer diffusiven Bewegung aufgrund der Stochastizität von Zellteilung und Apoptose. Wir berechnen den effektiven Diffusionskoeffizienten als Funktion der Gewebeparameter und vergleichen unsere Ergebnisse sowohl hinsichtlich der Diffusion und als auch der Viskosität mit numerischen Simulationen solcher vielzelliger Systeme. Die Berücksichtigung der extrazellulären Flüssigkeit als einer zweiten Materialkomponente erlaubt uns zu zeigen, dass eine endliche Permeabilität des Gewebes zusätzliche mechanische Effekte bedingt. Auf langer Zeitskalen bleibt die mechanische Reaktion des Gewebes auf externe Störungen auf einen Bereich beschränkt, dessen Größe vom Verhältnis der Gewebeviskosität zum Permeabilitätskoeffizienten abhängt. Die Zweikomponenten-Beschreibung erlaubt darüber hinaus eine klare Unterscheidung der verschiedenen Beiträge zum isotropen Teil der mechanischen Spannung, d.h., des hydrodynamischen und des von Zellen ausgeübten Drucks. Zuletzt untersuchen wir die Dynamik einer Grenzfläche zwischen zwei verschiedenen Zellpopulationen innerhalb eines Gewebes, die durch Unterschiede in der mechanischen Kontrolle der effektiven Zellteilungsraten angetrieben wird. Mithilfe der Kombination einfacher analytischer Grenzfälle und numerischer Simulationen zeigen wir, dass zwei unterschiedliche Ausbreitungsmodi unterschieden werden können: ein diffusives Regime, in dem relative Flüsse die Expansion der stärker wachsenden Zellpopulation dominieren, sowie ein Regime, in dem die Grenzfläche durch konvektive Strömungen angetrieben wird
Les organismes supérieurs se développent à partir d\'une seule cellule fécondée jusqu\'à l\'animal adulte. Les nombreux processus qui conduisent à la forme finale de l\'organisme sont connus sous le nom de morphogenèse, qui comprend notamment la croissance des tissus par des cycles répétés de division cellulaire. Alors que la croissance coordonnée des tissus est une condition nécessaire au développement des animaux, la division cellulaire excessive chez les animaux adultes est l\'ingrédient clé du cancer. Dans cette thèse, nous étudions l\'organisation collective des cellules par division et mort cellulaire. La dynamique multicellulaire des tissus en croissance est influencée par des conditions mécaniques et peut donner lieu à des réarrangements ainsi qu\'à des mouvements cellulaires. Nous élaborons une description continue de la dynamique des tissus qui décrit la distribution des contraintes et le champ d\'écoulement des cellules sur de grandes échelles. La division cellulaire et l\'apoptose introduisent des sources de contraintes qui, en général, sont anisotropes. En combinant l\'équation de conservation du nombre de cellules avec des équations dynamiques des sources de contraintes, nous montrons que le tissu se comporte de manière effective comme un fluide viscoélastique avec un temps de relaxation fixé par les taux de division et d\'apoptose. Si le tissu est confiné dans un volume donné, il atteint un état homéostatique dans lequel division et apoptose s\'équilibrent. Dans cet état, les cellules subissent un mouvement diffusif aléatoire dû à la stochasticité de la division et de l\'apoptose. Nous calculons le coefficient de diffusion effectif en fonction des paramètres du tissu et comparons nos résultats concernant à la fois la diffusion et la viscosité à des simulations numériques de tels systèmes multicellulaires. En introduisant un deuxième composant qui représente le liquide extracellulaire, nous montrons qu\'une perméabilité finie du tissu donne lieu à des effets mécaniques supplémentaires. Dans la limite des temps longs, la réponse mécanique du tissu à des perturbations extérieures est confinée à une région dont la taille dépend du rapport entre la viscosité tissulaire et le coefficient de frottement entre les cellules et le liquide extracellulaire. La description à deux composants permet en outre de distinguer clairement les différentes contributions à la partie isotrope de la contrainte mécanique, c\'est-à-dire la pression du fluide et la contrainte exercée par les cellules. Finalement, nous étudions la propagation d\'une interface entre deux populations de cellules différentes, due à des différences dans le contrôle mécanique des taux de division et de mort cellulaire. En combinant de simples limites analytiques et des simulations numériques, nous distinguons deux modes de propagation différents de la population cellulaire la plus proliférante : un régime diffusif dans lequel les flux relatifs dominent l\'expansion, et un régime de propulsion dans lequel la prolifération domine et entraine des flux convectifs
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Lupoli, Christopher. "Some problems of spatial behaviour in continuum mechanics." Thesis, Heriot-Watt University, 1995. http://hdl.handle.net/10399/759.
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Ranft, Jonas. "Mechanics of Growing Tissues : A Continuum Description Approach." Paris 6, 2012. http://www.theses.fr/2012PA066273.
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Dans cette thèse, nous étudions l'organisation collective des cellules par division et mort cellulaire. La dynamique multicellulaire des tissus en croissance est influencée par des conditions mécaniques et peut donner lieu à des mouvements cellulaires. Nous élaborons une description continue de la dynamique des tissus qui décrit les contraintes et le champ d'écoulement sur de grandes échelles. La division cellulaire et l'apoptose introduisent des sources de contraintes qui, en général, sont anisotropes. Nous montrons que le tissu se comporte comme un fluide viscoélastique avec un temps de relaxation fixé par les taux de division et d'apoptose. Dans un état dans lequel division et apoptose s'équilibrent, les cellules subissent un mouvement aléatoire dû à la stochasticité de la division et de l'apoptose. Nous calculons le coefficient de diffusion et comparons nos résultats à des simulations numériques. En introduisant un deuxième composant qui représente le liquide extracellulaire, nous montrons qu'une perméabilité finie du tissu donne lieu à des effets supplémentaires. Dans la limite des temps longs, la réponse mécanique du tissu à des perturbations est confinée à une région de taille finie. Cette description permet en outre de distinguer la pression du fluide et la contrainte exercée par les cellules. Finalement, nous étudions la propagation d'une interface entre deux populations de cellules différentes. Nous distinguons deux modes de propagation de la population cellulaire la plus proliférante : un régime diffusif dans lequel les flux relatifs dominent l'expansion, et un régime de propulsion dans lequel la prolifération domine et entraine des flux convectifsIn this thesis, we investigate the collective organization of cells by cell division and cell death. The multicellular dynamics of growing tissues is influenced by mechanical conditions and can give rise to cell movements. We develop a continuum description of tissue dynamics, which describes the stress distribution and the cell flow field on large scales. Cell division and apoptosis introduce stress sources that, in general, are anisotropic. We show that the tissue effectively behaves as a viscoelastic fluid with a relaxation time set by the rates of division and apoptosis. If the tissue is confined in a fixed volume, it reaches a state in which division and apoptosis balance. In this state, cells undergo a diffusive motion driven by the stochasticity of division and apoptosis. We calculate the diffusion coefficient and compare our results concerning both diffusion and viscosity to simulations of multicellular systems. Introducing a second material component that accounts for the extracellular fluid, we show that a finite permeability of the tissue gives rise to additional mechanical effects. In the limit of long times, the mechanical response of the tissue to external perturbations is confined to a region of which the size depends on the ratio of tissue viscosity and cell-fluid friction. Last but not least, we study the propagation of an interface between two different cell populations within a tissue. We distinguish two different modes of propagation of the more proliferative population: a diffusive regime in which relative fluxes dominate the expansion, and a propulsive regime in which the proliferation gives rise to dominating convective flows
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Hall, Cameron Luke. "Modelling of some biological materials using continuum mechanics." Thesis, Queensland University of Technology, 2008. https://eprints.qut.edu.au/37244/1/Cameron_Hall_Thesis.pdf.
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Continuum mechanics provides a mathematical framework for modelling the physical stresses experienced by a material. Recent studies show that physical stresses play an important role in a wide variety of biological processes, including dermal wound healing, soft tissue growth and morphogenesis. Thus, continuum mechanics is a useful mathematical tool for modelling a range of biological phenomena. Unfortunately, classical continuum mechanics is of limited use in biomechanical problems. As cells refashion the �bres that make up a soft tissue, they sometimes alter the tissue's fundamental mechanical structure. Advanced mathematical techniques are needed in order to accurately describe this sort of biological `plasticity'. A number of such techniques have been proposed by previous researchers. However, models that incorporate biological plasticity tend to be very complicated. Furthermore, these models are often di�cult to apply and/or interpret, making them of limited practical use. One alternative approach is to ignore biological plasticity and use classical continuum mechanics. For example, most mechanochemical models of dermal wound healing assume that the skin behaves as a linear viscoelastic solid. Our analysis indicates that this assumption leads to physically unrealistic results. In this thesis we present a novel and practical approach to modelling biological plasticity. Our principal aim is to combine the simplicity of classical linear models with the sophistication of plasticity theory. To achieve this, we perform a careful mathematical analysis of the concept of a `zero stress state'. This leads us to a formal de�nition of strain that is appropriate for materials that undergo internal remodelling. Next, we consider the evolution of the zero stress state over time. We develop a novel theory of `morphoelasticity' that can be used to describe how the zero stress state changes in response to growth and remodelling. Importantly, our work yields an intuitive and internally consistent way of modelling anisotropic growth. Furthermore, we are able to use our theory of morphoelasticity to develop evolution equations for elastic strain. We also present some applications of our theory. For example, we show that morphoelasticity can be used to obtain a constitutive law for a Maxwell viscoelastic
uid that is valid at large deformation gradients. Similarly, we analyse a morphoelastic model of the stress-dependent growth of a tumour spheroid. This work leads to the prediction that a tumour spheroid will always be in a state of radial compression and circumferential tension. Finally, we conclude by presenting a novel mechanochemical model of dermal wound healing that takes into account the plasticity of the healing skin.
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Bosia, Stefano. "On some multi-phase problems in continuum mechanics." Palaiseau, Ecole polytechnique, 2013. https://pastel.hal.science/docs/00/92/36/91/PDF/Bosia_-_pastel.pdf.
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Ce travail de thèse affronte l'étude de divers problèmes surgissant de la mécanique du milieu continu. La première partie du manuscrit est dédiée à l'étude mathématique de certains modèles à interfaces diffuses qui décrivent la séparation de phase de mixtures binaires (par exemple, le grossissement de la taille des grains dans un alliage ou bien l'écoulement des fluides polymériques bistables). La seconde partie examine le fonctionnement de certains dispositifs électroniques, comme les jonctions p-n, sous l'effet de déformations mécaniques. La troisième partie présente un model pour la prédiction de la durée de vie pour des métaux polycristallins en régime de chargement cyclique. Un modèle typique de séparation de phase est le modèle H, qui est constitué d'une équation de Cahn-Hilliard convective couplée avec le système de Navier-Stokes par la force dite de Korteweg. On considère des variations de ce modèle qui tiennent compte, par exemple, d'une viscosité du fluide dépendante du cisaillement ou de constituants réagissant chimiquement entre eux. Tout d'abord, on étudie des questions de base comme l'existence, l'unicité et la régularité des solutions. Par la suite, on analyse le comportement asymptotique des systèmes dynamiques infini-dimensionnels générés par les systèmes étudiés. Plus précisément, on démontre l'existence d'attracteurs globaux, d'attracteurs exponentiels, d'attracteurs pullback et d'attracteurs de trajectoires pour les systèmes dynamique correspondants. On discute aussi la robustesse de ces ensembles invariants par rapport à des perturbations de certains paramètres du modèle. Nos résultats constituent une extension naturelle des propriétés connues pour le cas de l'écoulement d'un fluide simple qui représentent le cas de référence pour toute nouvelle technique proposée en littérature. Enfin, comme description plus précise des phénomènes de séparation de phase, on considère une équation de Cahn-Hilliard modélisant des interactions non-locales à travers un noyau singulier. En ce cas, des résultats d'existence et de régularité sont donnés. La seconde partie de cette thèse est dédiée à l'étude des effets de couplage entre les propriétés mécaniques et électroniques des semi-conducteurs. La modélisation des dispositifs électroniques choisie se base sur le modèle de diffusion et transport pour les électrons et les trous. Le dispositif est décrit comme un continu macroscopique standard avec, pour objectif, la compréhension des effets des déformations sur les propriétés électroniques du semi-conducteur et, en particulier, sur la caractéristique d'une jonction p-n. Ceci permet de proposer une formulation variationelle du système classique de diffusion et transport et de dériver un modèle thermodynamiquement consistent pour les effets électromécaniques couplés. Les déformations ont des effets en particulier sur les coefficients de mobilité et sur le terme de génération et recombinaison des porteurs. Deux solutions approximées sont étudiées : une développé à partir d'hypothèses physiques et l'autre qui comporte une expansion asymptotique. Ces résultats constituent une étape préalable pour la compréhension des dispositifs électroniques flexibles. La dernière partie de la thèse présente une application de la théorie des systèmes dynamiques à la prédiction de la durée de vie des métaux polycristallins sous chargement périodique pour grand nombre de cycle de chargement. Un nouveaux model est proposé et ses prévisions comparées avec les résultats connus dans la littératureThis work discusses a series of modelling problems in continuum mechanics. The first part is devoted to the mathematical analysis of some diffuse interface models in phase separation of binary mixtures (e. G. , coarsening of alloys or bistable polymeric fluids). The second part discusses the function of electronic devices (in particular p-n junctions) under mechanical deformations. The third part presents a model for lifetime predictions in polycrystalline metals under periodic loading. A typical phase separation model is the well-known model H, constructed by coupling the convective Cahn-Hilliard equation with the Navier-Stokes system through the so-called Korteweg force. Here we consider some variants of the model which account, e. G. , for shear dependent viscosity or chemically reacting components. We first study basic issues like existence, uniqueness and regularity of solutions. Then we analyze the long-time behaviour of the infinite dimensional dissipative dynamical systems generated by the systems studied. More precisely, we prove the existence of global attractors, exponential attractors, pullback attractors and trajectories attractors for the corresponding dynamical systems. Also, we discuss the robustness of such invariant sets with respect to perturbations of some parameters of the model. The results obtained represent natural extensions of the properties known for single fluid flows, whose features are considered a benchmark for all new techniques proposed in the literature. Finally, as a more realistic description of phase separation phenomena, we introduce a Cahn-Hilliard equation accounting for nonlocal interactions through a singular kernel. In this case some well-posedness and regularity results are demonstrated. The second part of this work is devoted to the study of the coupling effects between mechanical and electronic properties in semiconductors. The modelling of the electronic device is based on the drift-diffusion model for electrons and holes. The device is viewed as a standard macroscopic continuum and the objective is to understand the effects of mechanical strain on the electronic properties of the semiconductor and in particular its effects on the characteristic curve of a p-n junction. This permits to propose a variational formulation of the classical drift-diffusion system and to derive a thermodynamically consistent model for the coupled electromechanical phenomena. The strain mainly influences the mobility coefficients and the generation/recombination term. Two approximate solutions are discussed, one based on only physical assumptions and one involving asymptotic expansions. This part of the work is a preliminary step towards the understanding of the properties of flexible electronic devices. The final part of the thesis presents an application of the theory of dynamical systems to predict the lifetime of polycrystalline metals undergoing a high cycle fatigue regime. A new model is proposed and compared with the existing literature
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Fougeron, Gabriel. "Contribution to the improvement of meshless methods applied to continuum mechanics." Thesis, Université Paris-Saclay (ComUE), 2018. http://www.theses.fr/2018SACLC068/document.
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Cette thèse présente un cadre général pour l’étude de schémas de discrétisation nodaux sans maillageformulé en termes d’opérateurs discrets définis sur un nuage de points : intégration volumique et de bord, gradientet opérateur de reconstruction. Ces définitions dotent le nuage de points d’une structure plus faible que celledéfinie par un maillage, mais partageant avec elle certain concepts fondamentaux. Le plus important d’entre euxest la condition de compatibilité intégro-différentielle. Avec la consistance linéaire du gradient discret, cet analoguediscret de la formule de Stokes constitue une condition nécessaire à la consistance linéaire des opérateurs elliptiquesen formulation faible. Sa vérification, au moins de manière approchée, permet d’écrire des discrétisations dont le tauxde convergence est optimal. La construction d’opérateurs discrets compatibles est si difficile que nous conjecturons– sans parvenir à le démontrer – qu’elle nécessite soit la résolution d’un système linéaire global, soit la constructiond’un maillage : c’est "la malédiction sans-maillage". Trois grandes approches pour la construction d’opérateursdiscrets compatibles sont étudiées. Premièrement, nous proposons une méthode de correction permettant de calculerl’opérateur gradient compatible le plus proche – au sens des moindres carrés – sans mettre à mal la consistancelinéaire. Dans le cas particulier des gradients DMLS, nous montrons que le gradient corrigé est en réalité globalementoptimal. Deuxièmement, nous adaptons l’approche SFEM au cadre opérateur et constatons qu’elle définit desopérateurs consistants à l’ordre un et compatibles. Nous proposons une méthode d’intégration discrète exploitantla relation topologique entre les cellules et les faces d’un maillage qui préserve ces caractéristiques. Troisièmement,nous montrons qu’il est possible de générer tous les opérateurs sans maillage rien qu’avec la donnée d’une formuled’intégration volumique nodale en exploitant la dépendance fonctionnelle des poids volumiques nodaux par rapportà la position des noeuds du nuage, l’espace continu sous-jacent et le nombre de noeuds. Les notions de consistance desdifférents opérateurs sont caractérisées en termes des poids volumiques initiaux, formant un jeu de recommandationpour la mise au point de bonnes formules d’intégration. Dans ce cadre, nous réinterprétons les méthodes classiquesde stabilisation de la communauté SPH comme cherchant à annuler l’erreur sur la formule de Stokes discrète.L’exemple des opérateurs SFEM trouve un équivalent en formulation volume, ainsi que la méthode d’intégrationdiscrète s’appuyant sur un maillage. Son écriture nécessite toutefois une description très précise de la géométriedes cellules du maillage, en particulier dans le cas où les faces ne sont pas planes. Nous menons donc à bienune caractérisation complète de la forme de telles cellules uniquement en fonction de la position des noeuds dumaillage et des relations topologiques entre les cellules, permettant une définition sans ambigüité de leur volume etcentre de gravité. Enfin, nous décrivons des schémas de discrétisation d’équations elliptiques utilisant les opérateurssans-maillage et proposons plusieurs possibilités pour traiter les conditions au bord tout en imposant le moinsde contraintes sur la position des noeuds du nuage de points. Nous donnons des résultats numériques confirmantl’importance capitale de vérifier les conditions de compatibilité, au moins de manière approchée. Cette simple recommandation permet dans tous les cas d’obtenir des discrétisations dont le taux de convergence est optimalThis thesis introduces a general framework for the study of nodal meshless discretization schemes. Itsfundamental objects are the discrete operators defined on a point cloud : volume and boundary integration, discretegradient and reconstruction operator. These definitions endow the point cloud with a weaker structure than thatdefined by a mesh, but share several fundamental concepts with it, the most important of them being integrationdifferentiationcompatibility. Along with linear consistency of the discrete gradient, this discrete analogue of Stokes’sformula is a necessary condition to the linear consistency of weakly discretized elliptic operators. Its satisfaction, atleast in an approximate fashion, yields optimally convergent discretizations. However, building compatible discreteoperators is so difficult that we conjecture – without managing to prove it – that it either requires to solve a globallinear system, or to build a mesh. We dub this conjecture the "meshless curse". Three main approaches for theconstruction of discrete meshless operators are studied. Firstly, we propose a correction method seeking the closestcompatible gradient – in the least squares sense – that does not hurt linear consistency. In the special case ofMLS gradients, we show that the corrected gradient is globally optimal. Secondly, we adapt the SFEM approachto our meshless framework and notice that it defines first order consistent compatible operators. We propose adiscrete integration method exploiting the topological relation between cells and faces of a mesh preserving thesecharacteristics. Thirdly, we show that it is possible to generate each of the meshless operators from a nodal discretevolume integration formula. This is made possible with the exploitation of the functional dependency of nodal volumeweights with respect to node positions, the continuous underlying space and the total number of nodes. Consistencyof the operators is characterized in terms of the initial volume weights, effectively constituting guidelines for thedesign of proper integration formulae. In this framework, we re-interpret the classical stabilization methods of theSPH community as actually seeking to cancel the error on the discrete version of Stokes’s formula. The example ofSFEM operators has a volume-based equivalent, and so does its discrete mesh-based integration. Actually computingit requires a very precise description of the geometry of cells of the mesh, in particular in the case where its facesare not planar. We thus fully characterize the shape of such cells, only as a function of nodes of the mesh andtopological relations between cells, allowing unambiguous definition of their volumes and centroids. Finally, wedescribe meshless discretization schemes of elliptic partial differential equations. We propose several alternatives forthe treatment of boundary conditions with the concern of imposing as few constraints on nodes of the point cloudas possible. We give numerical results confirming the crucial importance of verifying the compatibility conditions,at least in an approximate fashion. This simple guideline systematically allows the recovery of optimal convergencerates of the studied discretizations
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Fusco, Amintore. "Continuum mechanics and finite element numerical solutions in geotechnique." Thesis, University of Ottawa (Canada), 1985. http://hdl.handle.net/10393/4571.
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Jones, R. "Numerical optimisation techniques applied to problems in continuum mechanics." Thesis, University of Nottingham, 1987. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.378760.
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Lahiri, Sudeep Kumar. "Variationally consistent methods for Lagrangian dynamics in continuum mechanics." Thesis, Massachusetts Institute of Technology, 2006. http://hdl.handle.net/1721.1/39597.
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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2006.Includes bibliographical references (p. 135-143).
Rapid dynamics are commonly encountered in industrial applications such as forging, crash tests and many others. These problems are typically non-linear due to large deformations and/or non-linear constitutive relations. Such problems are typically modelled from a Lagrangian viewpoint, where the mesh is attached to the body; hence, large deformations lead to large distortions in the mesh. Explicit numerical methods are considered to be efficient in these cases where large meshes and small time-steps are employed for spatial and temporal resolution. However, incompressible and nearly incompressible materials pose a problem as the timestep stability restriction in explicit methods becomes increasingly severe. Most of the numerical methods employed for such simulations, are developed from discretization of the equations of motion. Recently, Variational Integrators have been developed where the numerical time integration scheme is developed from a variational principle based on Hamilton's principle of stationary action. Such methods ensure conservation of linear and angular momentum, which lead to more physically consistent simulations.
(cont.) In this research, numerical methods addressing incompressibility and mesh distortions have been developed under a variational framework. A variational formulation for mesh adaptation procedures, involving local mesh changes for triangular meshes, is presented. Such procedures are very well suited for explicit methods, without significant expense. Conservation properties of such methods are proved and demonstrated. Further, a Fractional Time-Step method is developed, from a variational framework, for incompressible and nearly incompressible problems. Algorithmic details are presented, followed by examples demonstrating the performance of the method.
by Sudeep K. Lahiri.
Ph.D.
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PIRULLI, MARINA. "Numerical modelling of landslide runout. A continuum mechanics approach." Doctoral thesis, Politecnico di Torino, 2005. http://hdl.handle.net/11583/2499763.
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Increasing population density and development of mountainous terrains bring human settlements within reach of landslide hazards. Perhaps the most serious threat arises from small, high frequency landslides such as debris flows and debris avalanches. On the other hand, large and relatively rare rock avalanches also constitute a significant hazard, due to their prodigious capacity for destruction. Such landslides involve the spontaneous failure of entire mountain slopes, involving volumes measured in tens or hundreds million m3 and travel distances of several kilometres.
Flow-like movements of rocks can be identified among the most dangerous and damaging of all landslide phenomena. Since it often proves impossible to mitigate their destructive potential by stabilising the area of origin, risk analyses, including predictions of runout, have to be performed. With these predictions losses can be reduced, as they provide means to define the hazardous areas, estimate the intensity of the hazard, and work out the parameters for the identification of appropriate protective measures. At the same time, reliable predictions of runout can help to avoid exceedingly conservative decisions regarding the development of hazardous areas.
Risk evaluation of these events requires the comprehension of two fundamental problems: the initiation and the runout. Even though the specification of the initial conditions is also a primarily problem, which is not yet resolved, the runout, that is the flowing and stopping phases of the mass, is here analysed.
Numerical simulation should provide a useful tool for investigating, within realistic geological contexts, the dynamics of these flows and of their arrest phase.
In the 1970’s the most widely used and perhaps earliest model proposed for the analysis of rockslides and similar phenomena was that of a rigid block on an inclined plane. In recent years, new and more sophisticated models based on a continuum mechanics approach have emerged. Together with continuum mechanics models, a noteworthy type of modelling is that based on a discontinuum mechanics approach, in which the run out mass is modelled as an assembly of particles moving down along a surface.
It is probably fair to state that Savage and Hutter in 1989 developed the first continuum mechanical theory capable of describing the evolving geometry of a finite mass of a granular material and the associated velocity distribution as an avalanche slides down inclined surfaces. Their model provided a more complete analysis of such flows than previous models had done, and its extension as well as comparison with laboratory experiments demonstrated it to be largely successful.
A continuum mechanics approach assumes that during an avalanche, the characteristic length in the flowing direction is generally much larger than the vertical one, e.g. the avalanche thickness. Such a long-wave scaling argument has been widely used in derivation of continuum flow models. This leads to depth-averaged models governed by generalized Saint Venant equations.
Nowadays, these models provide a fruitful tool for investigating the dynamics and extent of avalanches.
Anyway, whatever the applied analytical model, results of a numerical simulation depend on the value assigned to the constitutive parameter of the assumed rheology.
The aim of the dissertation is the development and validation of a three dimensional numerical model able to run analyses of propagation on a complex topography and the setting of a procedure direct to define some reference values for characteristic parameters of an assumed rheology. Case histories having a different runout path and material type are analysed and compared, the obtained values could be considered useful guidelines to study a potential landslide.
The choice of a certain approach rather than another is the result of a careful analysis of advantages and disadvantages of each existing method. All choices are made never forgetting to remain focused on real problems and real behaviour of a mass. By consequence, each problem tackled and solved is directed to guarantee more
realistic results.
Whatever the chosen numerical approach, it is fundamental to know in detail the type of phenomenon that will be studied. In this sense, it is important to learn from past events and to always have on mind that each analysed problem is not abstract but it is linked to a real site.
In the present work, a continuum mechanics approach has been followed.
The original version (SHWCIN) of the implemented three dimensional code was developed at the Institut de Physique du Globe de Paris but before using it to run analysis of propagation on a complex topography many fundamental changes are necessary.
Trying to reduce the uncertainty range of values to be assigned in prediction to rheological parameters, the numerical code DAN (Hungr, 1995) is applied to back analyse a set of case histories of landslides selected from literature.
For prediction, the main limitation of DAN is due to the fact that it reduces a complex and heterogeneous 3D problem into an extremely simple formulation and the width of propagation is a part of the input data. But, when a back analysis is run, the geometry of propagation is already known. Therefore, the limits of DAN in some way disappear. Also, cases for which a DEM (Digital Elevation Model) is not available can be analysed. Moreover, advantages in using this code are mainly due to its simplicity, it makes possible an immediate and rapid numerical simulation of many real cases.
The methodology here proposed consists in using DAN to run back analyses of as many case histories as possible and the new three dimensional code to predict propagation of a mass on a complex topography.
It is important to underline that when values obtained from back analyses are used to simulate a potential landslide, only cases having similar characteristics (e.g. run out area shape, material type) can be compared.
To guarantee correctness of this approach it is necessary to verify that DAN results, if used as input data in a three dimensional numerical code, give approximately the same solution. Cases for which a DEM pre-collapse is available are analysed with both DAN and the new code.
After a critic overview of landslide classifications and a detailed description of those phenomena known as rock avalanches (Ch. 2), a description of existing propagation methods has been done, underlining advantages and disadvantages of each considered approach (Ch. 3). On the basis of possibility of application on analysis of real cases a continuum mechanics approach has then been followed, two numerical codes have been analysed: SHWCIN and DAN (Ch. 4).
The SHWCIN code was originally used to carry out simple numerical simulations of a mass released from a gate or from a hemi-spherical cap on an inclined plane and results were analysed considering the centre line section.
To simulate the movement on a complex three dimensional topography, the code has been numerically implemented allowing to: reduce mesh-dependency effects on results of propagation by using an irregular mesh, change gravity components as a function of the considered topography, change earth pressure coefficients in a condition of anisotropy of normal stresses, take into account both different constitutive laws and pore water effects. Each of these changes has been carefully validated. Once the final version of the code was obtained it has been tested through numerical analysis of laboratory tests and back analysis of case histories obtained from
literature (Ch. 5).
In order to create a database of well described phenomena and rheological parameters, that can be useful guidelines when prediction is the aim of an analysis, case histories have been analysed with DAN following a procedure that gives the possibility of calibrating the model in order to obtain the best value for each of the parameters required by the assumed rheology (Ch. 6).
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Smith, Matthew Ross. "Hybrid methods in near continuum flows /." [St. Lucia, Qld], 2004. http://www.library.uq.edu.au/pdfserve.php?image=thesisabs/absthe18282.pdf.
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Fallqvist, Björn. "On the mechanics of actin and intermediate filament networks and their contribution to cellular mechanics." Doctoral thesis, KTH, Hållfasthetslära (Inst.), 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-175748.
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The mechanical behaviour of cells is essential in ensuring continued physiological function, and deficiencies therein can result in a variety of diseases. Also, altered mechanical response of cells can in certain cases be an indicator of a diseased state, and even actively promoting progression of pathology. In this thesis, methods to model cell and cytoskeletal mechanics are developed and analysed. In Paper A, a constitutive model for the response of transiently cross-linked actin networks is developed using a continuum framework. A strain energy function is proposed and modified in terms of chemically activated cross-links. In Paper B, a finite element framework was used to assess the influence of numerous geometrical and material parameters on the response of cross-linked actin networks, quantifying the influence of microstructural properties and cross-link compliance. Also, a micromechanically motivated constitutive model for cross-linked networks in a continuum framework was proposed. In Paper C, the discrete model is extended to include the stochastic nature of cross-links. The strain rate dependence observed in experiments is suggested to depend partly on this. In Paper D, the continuum model for cross-linked networks is extended to encompass more composite networks. Favourable comparisons to experiments indicate the interplay between phenomenological evolution laws to predict effects in biopolymer networks. In Paper E, experimental and computational techniques are used to assess influence of the actin cytoskeleton on the mechanical response of fibroblast cells. The influence of cell shape is assessed, and experimental and computational aspects of cell mechanics are discussed. In Paper F, the filament-based cytoskeletal model is extended with an active response to predict active force generation. Importantly, experimentally observed stiffening of cells with applied stress is predicted.QC 20151209
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Fu, Kaibin. "Applications of a new theory extending continuum mechanics to the nanoscale." Texas A&M University, 2005. http://hdl.handle.net/1969.1/2708.
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In this dissertation, we present the Slattery-Oh-Fu theory extending continuum
mechanics to the nanoscale and its applications.
We begin with an analysis of supercritical adsorption of argon, krypton, and
methane on Graphon before we fully develop the theory. We compare our results
both with existing experimental data and with prior molecular-based theories.
Then, we present the general theory, which is based upon a long history of
important developments beginning with Hamaker (1937). In the context of continuum
mechanics, nanoscale problems always involve the immediate neighborhood of a phase
interface or the immediate neighborhood of a three-phase line of contact or common
line. We test this theory by using it to predict both the surface tensions of the
n-alkanes and the static contact angles for the n-alkanes on PTFE and for several
liquids on PDMS. For the contact angle predictions, the results are compatible with
previously published experimental data. The results for the contact angle analysis
also provide a successful test of a previously derived form of Young??s equation for the
true, rather than apparent, common line.
We also studied Mode I fracture at nanoscale. While we don??t have experimental
data to compare, we get reasonable crack configuration and avoid stress singularity at
the crack tip. Coalescence problems are revisited to explore the retardation effects in the computation of intermolecular forces. We get good agreement with experimental
results.
We conclude with a confidence that this theory can be used as a bridge between
continuum mechanics and other molecular-based methods.
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王軍 and Chun Wang. "Development of an anisotropic damage mechanics model in ductile fracture." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1987. http://hub.hku.hk/bib/B31231378.
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Wang, Chun. "Development of an anisotropic damage mechanics model in ductile fracture /." [Hong Kong : University of Hong Kong], 1987. http://sunzi.lib.hku.hk/hkuto/record.jsp?B12362864.
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Stewart, John. "Physical and analytical aspects of projection operators in non equilibrium statistical mechanics." Thesis, University of Strathclyde, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.248591.
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Patlolla, Kiran Kumar. "Free vibration analysis: comparison between continuum mechanics and molecular mechanics models a thesis presented to the faculty of the Graduate School, Tennessee Technological University /." Click to access online, 2009. http://proquest.umi.com/pqdweb?index=0&did=1786737281&SrchMode=1&sid=2&Fmt=6&VInst=PROD&VType=PQD&RQT=309&VName=PQD&TS=1268928551&clientId=28564.
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Chia, Julian Yan Hon. "A micromechanics-based continuum damage mechanics approach to the mechanical behaviour of brittle matrix composites." Thesis, University of Glasgow, 2002. http://theses.gla.ac.uk/2856/.
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The thesis describes the development of a new continuum damage mechanics (hereafter, CDM) model for the deformation and failure of brittle matrix composites reinforced with continuous fibres. The CDM model is valid over sizes scales large compared to the spacing of the fibres and the dimensions of the damage. The composite is allowed to sustain damage in the form of matrix micro-cracking, shear delamination, tensile delamination and fibre failure. The constitutive equations are developed by decomposing the composite compliance into terms attributable to the fibre and matrix, and modelling the competing failure modes by intersecting failure surfaces based on maximum stress theory. The fibres are treated as being weakly bonded to the matrix so that the fibres only transmit axial loads, and fail in tension. The matrix is modelled as isotropic linear elastic and is treated as transversely-isotropic after damage has initiated. The effect of multiple matrix cracking on the stiffness was determined from experimental data, while failure was modelled by a rapid decay in the load bearing capacity. Although the model is motivated largely to proportional loading, matrix unloading and damage closure has been modelled by damage elasticity. During compression, the matrix stiffness is identical to the undamaged state with the exception that the fibres are assumed not to transmit compressive loads. The model was implemented computationally through a FORTRAN subroutine interfaced with the ABAQUS/Standard finite element solver. The CDM model was validated by comparing experimental and computational results of test specimens with unidirectional and balanced 0°-90° woven fibres of a brittle matrix composite, fabricated from polyester fibres in a polyester matrix. This composite system exhibits low elastic mismatch between fibres and matrix, and has similar non-dimensionalised stress-strain response to a SiC/SiC composite proposed for the exhaust diffuser unit of the Rolls-Royce EJ200 aero-engine.
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Sayre, Eleanor C. "Plasticity: Resource Justification and Development." Fogler Library, University of Maine, 2007. http://www.library.umaine.edu/theses/pdf/SayreEC2007.pdf.
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Liu, Ming. "Multidimensional damage state identification using phase space warping /." View online ; access limited to URI, 2005. http://0-wwwlib.umi.com.helin.uri.edu/dissertations/dlnow/3188065.
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Lacy, Thomas E. Jr. "Distribution effects in damage mechanics." Diss., Georgia Institute of Technology, 1998. http://hdl.handle.net/1853/15937.
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Bandini, Chiara. "FE-numerical modelling of damage in wood using continuum damage mechanics." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2018.
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In this thesis, the mechanical behavior of a timber joint has been studied. The main task is to model the mechanical behavior of the joint as good as possible. To be able to solve the numerical instabilities of the timber joints, a deeper look needs to be done to the modelling of the wooden material and the steel wood contact. For this thesis a previously developed 3D numerical damage model of wood has been studied. This model has been elaborated by Sandhaas(2012) and it describes crack initiation and propagation of the material based on the concepts of continuum damage mechanics. The basic material model of wood has been implemented as a user material in the UMAT subroutine of ABAQUS. The developed model is giving some numerical instabilities due to the extreme distortion of the elements. During this thesis the model has been enhanced in order to be able to represent the mechanical behavior of wood as good as possible and solve the problem of the model. The modelling outcomes were compared to the results obtained by experimental tests (ref. to Sandaas,2012).The results showed that the first model, a tension test parallel-to grain, had been enhanced. Indeed the results got closer to the experimental value than the original model’s results did. The second model represented a timber joint with slotted-in steel plate with a dowel. The analysis were done with different wood spieces (spruce, beech and azobè). Regarding the spruce, the analysis reached fairly accurate results concerning the capacity load but they were less precise regarding the displacement and the stiffness. The prediction quality was rather poor for the other two species, beech and azobè. It is necessary to find other ways to further enhance the model.Even today a model that is able to represent all three fields (stiffness, capacity load and displacement) accurately doesn’t exist. Good results of one of these lead to bad results of the others. Modelling wood then still represents an evolving challenge.
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Alcazar, Hermann E. "Durability prediction of structural composites through a continuum damage mechanics approach." Morgantown, W. Va. : [West Virginia University Libraries], 2010. http://hdl.handle.net/10450/10868.
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Thesis (Ph. D.)--West Virginia University, 2010.Title from document title page. Document formatted into pages; contains xiv, 176 p. : ill. (some col.). Includes abstract. Includes bibliographical references (p. 119-125).
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Yu, Ligang. "Orthotropic damage models for fatigue crack initiation and propagation /." [Hong Kong : University of Hong Kong], 1993. http://sunzi.lib.hku.hk/hkuto/record.jsp?B13570377.
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Bai, Jie. "A homogenization based continuum plasticity-damage model for ductile fracture of materials containing heterogeneities." Columbus, Ohio : Ohio State University, 2008. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1211910660.
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Glass, Bradley Smyth. "Continuum mechanics approaches to the study of fracture and fatigue in metals." Faculty of Engineering, 2004. http://ro.uow.edu.au/theses/264.
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This thesis investigates continuum mechanics based means of metal failure assessment. A basic science approach was employed throughout the study to examine the fundamental relationships responsible for metal failure. The extension of previously existing continuum mechanics based theories to encompass a wider range of application was considered in this thesis. Research was conducted as two separate studies which examine specific aspects of the metal failure spectrum, namely failure due to monotonic loading, and fatigue failure due to cyclic loading. The failure due to monotonic loading research was conducted to examine the influence of hydrostatic stress on metal ductility. A fundamental relationship in the form of a monotonic failure criterion was proposed based on a relationship between equivalent plastic fracture strain and hydrostatic stress. An experimental program incorporating uniaxial tensile testing of notched specimens was conducted to examine the proposed relationship for the hydrostatic tensile stress range. Finite element analyses were produced to confirm the mechanical properties and obtain the stress-strain state present at specimen failure. A good correlation was established between the load-displacement results obtained from experiment and finite element analysis, providing confirmation of the stress-strain data. The stress-strain results confirmed the existence of a relationship between hydrostatic stress and ductility in the form of a monotonically decreasing value of equivalent plastic fracture strain with increasing hydrostatic tensile stress. The relationship determined was in accordance with the trend indicated by various researchers for the hydrostatic compressive stress range. The potential application of such a criterion to finite element methods was amply demonstrated from this research. The fatigue failure due to cyclic loading research examined the application of energy based methods to fatigue life characterisation. Based on the hypothesis that irreversible damage may be attributed entirely to plastic deformation, the application of the plastic strain energy approach to the entire fatigue life spectrum was pursued. For application to high cycle fatigue, a thermodynamic approach was developed to allow plastic strain energy determination beyond the range of application of conventional mechanical measurement. Thermodynamic models consisting of varying degrees of free surface contribution to heat dissipation were developed as possible representations of the high cycle fatigue damage process. An experimental program was conducted incorporating mechanical and thermodynamic means of measurement. Thermodynamic measurement was achieved via an experimental apparatus incorporating precision temperature measurement and thermal isolation at the specimen surface. Assuming an appropriate thermodynamic model, a finite difference analysis allowed a quantitative determination of plastic strain energy. Close agreement was indicated from comparison of the low cycle fatigue plastic strain energy results obtained from mechanical and thermodynamic measurement. A qualitative determination of plastic strain energy for high cycle fatigue was achieved, subject to confirmation of the thermodynamic model. The qualitative assessment verified the existence of measurable plastic strain energy during high cycle fatigue.
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Cardenas, Heliana [Verfasser], and Jürgen [Gutachter] Horbach. "Continuum Mechanics Studies on Glass-Forming Liquids / Heliana Cardenas ; Gutachter: Jürgen Horbach." Düsseldorf : Universitäts- und Landesbibliothek der Heinrich-Heine-Universität Düsseldorf, 2018. http://d-nb.info/1170388922/34.
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Chervova, O. "The massless Dirac equation from the continuum mechanics and microlocal analysis perspectives." Thesis, University College London (University of London), 2012. http://discovery.ucl.ac.uk/1362431/.
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The thesis is concerned with the study of the massless Dirac equation. In the first part we study the massless Dirac equation in dimension 1+3 in the stationary setting, i.e. when the spinor field oscillates harmonically in time. We suggest a new geometric interpretation for this equation. We think of our 3-dimensional space as an elastic continuum and assume that material points can experience no displacements, only rotations. This framework is a special case of the Cosserat theory of elasticity. Rotations of material points are described mathematically by attaching to each geometric point an orthonormal basis which gives a field of orthonormal bases called the coframe. As the dynamical variables we choose the coframe and a density. We choose a particular potential energy which is conformally invariant and then incorporate time into our action by subtracting kinetic energy. We prove that in the stationary setting our model is equivalent to a pair of massless Dirac equations. In the second part we consider an elliptic self-adjoint first order pseudodifferential operator acting on columns of m complex-valued half-densities over a compact n-dimensional manifold. The eigenvalues of the principal symbol are assumed to be simple but no assumptions are made on their sign, so the operator is not necessarily semi-bounded. We study the spectral function and derive a two-term asymptotic formula. We then restrict our study to the case when m=2, n=3, the operator is differential and has trace-free principal symbol, and address the question: is our operator a massless Dirac operator? We prove that it is a massless Dirac operator if and only if, at every point, a) the subprincipal symbol is proportional to the identity matrix and b) the second asymptotic coefficient of the spectral function is zero.
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Singh, Gaurav. "Discrete and continuum studies of some fundamental issues in brittle fracture mechanics." Thesis, Imperial College London, 2013. http://hdl.handle.net/10044/1/22184.
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This thesis addresses four fundamental, yet unresolved, issues in brittle fracture mechanics: (a) the validity of linear elasticity in the crack-tip region, (b) crack growth direction under mixed-mode loading, (c) the nature and impact of cohesive stresses, (d) the effect of crack-face friction on the crack growth criterion in Griffith's model for compressive failure. It is a well known fact that, according to classical elasticity, the stress in the near-tip region of the crack is singular, which has led to a debate over the validity of linear elasticity in this region. The strain, stress and elastic strain energy of a cracked silicon crystal in the crack-tip region is calculated, according to atomistic simulations, and compared to the classical elasticity solution. The classical continuum solution is found to have the ability to match the atomistic stresses and strains, very close to the crack tip. Multiple criteria have been proposed, inconsistent among themselves, to predict the direction of crack growth under mixed-mode loading, with no consensus as to which one is the most accurate. A new lattice spring model that simulates an isotropic elastic material is developed. A pre-cracked model is taken, and the crack is allowed to grow under the influence of mixed-mode loading, to calculate the direction of crack growth. The growth direction matches several well-known criteria in different ranges of loading. The theory of cohesive stresses has been used widely, specially in numerical simulations. However, there has been no concerted effort to explain the nature of this force, and its influence on stresses and deformations around crack. A clearer insight into the origins and impact of cohesive stress in cracks will lay down a solid foundation for its correct application in numerical simulations. An analytical method based on complex potentials has been employed to find the variation of crack aperture and stress in the crack plane in the presence of a cohesive stress. Friction has been incorporated into the Griffith crack theory for compressive loading for a long time. However, it has always been considered to be acting at its maximum value, and not as an inequality. In the present work, the latter treatment is made, in which the crack faces have variable slip-stick regions. Using this more accurate model for crack face friction, the condition for crack growth at the crack tip is re-visited.
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Ahonsi, Bright. "On the propagation of stress waves in viscoelastic rods for Hopkinson bar studies." Thesis, University of Aberdeen, 2011. http://digitool.abdn.ac.uk:80/webclient/DeliveryManager?pid=182239.
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The propagation of stress waves in long polymer rods forms the basis of two major experimental techniques. The first is a modified Split-Hopkinson pressure bar (SHPB) arrangement that employs polymer Hopkinson bars (as opposed to metallic bars) in order to determine the high strain-rate mechanical properties of soft materials. The second experimental technique consists of a group of methods for determining the viscoelastic properties of polymer rods within a frequency range of 20 Hz to 30 kHz. An experimental, analytical and finite element study of stress waves propagating in viscoelastic rods is reported. A propagation coefficient is used to account for the attenuation and dispersion of stress waves propagating in polymer rods. Through experimental investigations, an optimal experimental arrangement is used to determine the propagation coefficient of a PMMA rod with an improved level of accuracy in comparison with results available in the open literature. Analytical investigations show difficulties associated with experimental arrangements as well as the numerical procedure adopted which tend to reduce the accurate frequency range of the determined propagation coefficient. The FE analysis of stress waves propagating in polymer rods suggests end effects are important; these end effects are not accounted for in any analytical bar wave theory. The high strain-rate mechanical properties of Hydroxyl-terminated polybutadiene (HTPB) are measured via a viscoelastic SHPB set-up. A scheme for processing the strain signals from the tests that allows for large strain measurement (approximately 60%) is presented. The use of viscoelastic SHPB set-up is able to produce a more sensitive measurement when compared with test results in the literature which are obtained using conventional metallic bars. A Finite element model of a viscoelastic Hopkinson bar set-up is developed. The applicability of the model in viscoelastic SHPB testing is validated.
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劉英傑 and Yingjie Liu. "Damage characterization of multi-directional laminates with matrix cracks and delamination." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1996. http://hub.hku.hk/bib/B31235104.
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俞立剛 and Ligang Yu. "Orthotropic damage models for fatigue crack initiation andpropagation." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1993. http://hub.hku.hk/bib/B31233995.
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Liu, Ying-jie. "Damage characterization of multi-directional laminates with matrix cracks and delamination /." Hong Kong : University of Hong Kong, 1996. http://sunzi.lib.hku.hk/hkuto/record.jsp?B16504434.
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Steinhauer, Mark. "On analysis of some nonlinear systems of partial differential equations of continuum mechanics." Bonn : Mathematisches Institut der Universität, 2003. http://catalog.hathitrust.org/api/volumes/oclc/54890745.html.
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Gay, Anthony J. "Development of a Hybrid Particle Continuum Solver." DigitalCommons@CalPoly, 2021. https://digitalcommons.calpoly.edu/theses/2258.
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When simulating complex flows, there are some physical situations that exhibit large fluctuations in particle density such as: planetary reentry, ablation due to arcing, rocket exhaust plumes, etc. When simulating these events, a high level of physical accuracy can be achieved with kinetic methods otherwise known as particle methods. However, this high level of physical accuracy requires large amounts of computation time. If the simulated flow is in collisional equilibrium, then less computationally intensive continuum methods, otherwise known as fluid methods, can be utilized. Hybrid Particle-Continuum (HPC) codes attempt to blend particle and fluid solutions in order to reduce computation time for transitional flows that exhibit both continuum and rarefied flow in a single domain. This thesis details the development of an HPC code in OpenFoam for Cal Poly's Aerospace Engineering department. The primary benchmark for the solver, named hybridFoam, was to simulate a 1D sod-shock simulation. This primary goal was achieved and a collection of test simulations were conducted to map out the solvers current capabilities and identify where future development efforts should focus.
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Saha, Reema. "Investigation of a continuum damage model using experimental and numerical techniques." Diss., Georgia Institute of Technology, 1995. http://hdl.handle.net/1853/12542.
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Markert, Bernd [Verfasser]. "Weak or strong : on coupled problems in continuum mechanics / vorgelegt von Bernd Markert." Stuttgart : Inst. für Mechanik (Bauwesen), 2010. http://d-nb.info/1006417842/34.
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