Relevant bibliographies by topics / Discrete-to-continuum limit

Academic literature on the topic 'Discrete-to-continuum limit'

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Published: 14 March 2023

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Journal articles on the topic "Discrete-to-continuum limit"

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Müller, Stefan, and Anja Schlömerkemper. "Discrete-to-continuum limit of magnetic forces." Comptes Rendus Mathematique 335, no. 4 (January 2002): 393–98. http://dx.doi.org/10.1016/s1631-073x(02)02494-9.

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Cesana, Pierluigi, and Patrick van Meurs. "Discrete-to-continuum limits of planar disclinations." ESAIM: Control, Optimisation and Calculus of Variations 27 (2021): 23. http://dx.doi.org/10.1051/cocv/2021025.

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In materials science, wedge disclinations are defects caused by angular mismatches in the crystallographic lattice. To describe such disclinations, we introduce an atomistic model in planar domains. This model is given by a nearest-neighbor-type energy for the atomic bonds with an additional term to penalize change in volume. We enforce the appearance of disclinations by means of a special boundary condition. Our main result is the discrete-to-continuum limit of this energy as the lattice size tends to zero. Our proof relies on energy relaxation methods. The main mathematical novelty of our proof is a density theorem for the special boundary condition. In addition to our limit theorem, we construct examples of planar disclinations as solutions to numerical minimization of the model and show that classical results for wedge disclinations are recovered by our analysis.
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LING, YI. "DISCRETE GRAVITY AND ITS CONTINUUM LIMIT." Modern Physics Letters A 20, no. 03 (January 30, 2005): 213–25. http://dx.doi.org/10.1142/s0217732305015793.

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Recently Gambini and Pullin proposed a new consistent discrete approach to quantum gravity and applied it to cosmological models. One remarkable result of this approach is that the cosmological singularity can be avoided in a general fashion. However, whether the continuum limit of such discretized theories exists is model dependent. In the case of massless scalar field coupled to gravity with Λ=0, the continuum limit can only be achieved by fine tuning the recurrence constant. We regard this failure as the implication that cosmological constant should vary with time. For this reason we replace the massless scalar field by Chaplygin gas which may contribute an effective cosmological constant term with the evolution of the universe. It turns out that the continuum limit can indeed be reached in this case.
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Español, Malena I., Dmitry Golovaty, and J. Patrick Wilber. "Euler elastica as a Γ-limit of discrete bending energies of one-dimensional chains of atoms." Mathematics and Mechanics of Solids 23, no. 7 (May 26, 2017): 1104–16. http://dx.doi.org/10.1177/1081286517707997.

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In the 1920s, Hencky proposed a discrete elastica model describing a chain of identical rigid bars connected by torsional springs. Hencky observed that this discrete elastica model converges to Euler’s elastica as the number of bars increases while their lengths decrease, and Hencky’s bar-chain model has been used primarily as an approximation of Euler’s elastica. A Hencky-type bar-chain model can also be incorporated into a Frenkel–Kontorova-type discrete atomistic model, where the joints and bars represent the atoms and interatomic bonds, respectively, while the entire chain of atoms interacts with either a substrate or other chains. The energy of a continuum system corresponding to this Frenkel–Kontorova-type model can then be recovered by taking an appropriate discrete-to-continuum limit. Developing a correct limiting procedure for the discrete elastica establishes the bending component of this continuum energy. In this paper we use Γ-convergence to rigorously show that as the bar length in the discrete elastica model we consider goes to 0, the bending energies of the chain Γ-converge to the continuum bending energy associated with Euler’s elastica.
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REQUARDT, MANFRED. "THE CONTINUUM LIMIT OF DISCRETE GEOMETRIES." International Journal of Geometric Methods in Modern Physics 03, no. 02 (March 2006): 285–313. http://dx.doi.org/10.1142/s0219887806001156.

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In various areas of modern physics and in particular in quantum gravity or foundational space–time physics, it is of great importance to be in the possession of a systematic procedure by which a macroscopic or continuum limit can be constructed from a more primordial and basically discrete underlying substratum, which may behave in a quite erratic and irregular way. We develop such a framework within the category of general metric spaces by combining recent work of our own and ingeneous ideas of Gromov et al. developed in pure mathematics. A central role is played by two core concepts. For one, the notion of intrinsic scaling dimension of a (discrete) space or, in mathematical terms, the growth degree of a metric space at infinity, on the other hand, the concept of a metrical distance between general metric spaces and an appropriate scaling limit (called by us a geometric renormalization group) performed in this metric space of spaces. In doing this, we prove a variety of physically interesting results about the nature of this limit process, properties of the limit space, e.g., what preconditions qualify it as a smooth classical space–time and, in particular, its dimension.
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Kevrekidis, P. G., and D. E. Pelinovsky. "Discrete vector on-site vortices." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 462, no. 2073 (April 4, 2006): 2671–94. http://dx.doi.org/10.1098/rspa.2006.1693.

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We study discrete vortices in coupled discrete nonlinear Schrödinger equations. We focus on the vortex cross configuration that has been experimentally observed in photorefractive crystals. Stability of the single-component vortex cross in the anti-continuum limit of small coupling between lattice nodes is proved. In the vector case, we consider two coupled configurations of vortex crosses, namely the charge-one vortex in one component coupled in the other component to either the charge-one vortex (forming a double-charge vortex) or the charge-negative-one vortex (forming a, so-called, hidden-charge vortex). We show that both vortex configurations are stable in the anti-continuum limit, if the parameter for the inter-component coupling is small and both of them are unstable when the coupling parameter is large. In the marginal case of the discrete two-dimensional Manakov system, the double-charge vortex is stable while the hidden-charge vortex is linearly unstable. Analytical predictions are corroborated with numerical observations that show good agreement near the anti-continuum limit, but gradually deviate for larger couplings between the lattice nodes.
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ANGUIGE, K. "A one-dimensional model for the interaction between cell-to-cell adhesion and chemotactic signalling." European Journal of Applied Mathematics 22, no. 4 (February 10, 2011): 291–316. http://dx.doi.org/10.1017/s0956792511000040.

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We develop and analyse a discrete, one-dimensional model of cell motility which incorporates the effects of volume filling, cell-to-cell adhesion and chemotaxis. The formal continuum limit of the model is a non-linear generalisation of the parabolic-elliptic Keller–Segel equations, with a diffusivity which can become negative if the adhesion coefficient is large. The consequent ill-posedness results in the appearance of spatial oscillations and the development of plateaus in numerical solutions of the underlying discrete model. A global-existence result is obtained for the continuum equations in the case of favourable parameter values and data, and a steady-state analysis, which, amongst other things, accounts for high-adhesion plateaus, is carried out. For ill-posed cases, a singular Stefan-problem formulation of the continuum limit is written down and solved numerically, and the numerical solutions are compared with those of the original discrete model.
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MIRONOV, A., and S. PAKULIAK. "ON THE CONTINUUM LIMIT OF THE CONFORMAL MATRIX MODELS." International Journal of Modern Physics A 08, no. 18 (July 20, 1993): 3107–37. http://dx.doi.org/10.1142/s0217751x93001247.

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The double scaling limit of a new class of the multi-matrix models proposed in Ref. 1, which possess the W-symmetry at the discrete level, is investigated in detail. These models are demonstrated to fall into the same universality class as the standard multi-matrix models. In particular, the transformation of the W-algebra at the discrete level into the continuum one of the papers2 is proposed and the corresponding partition functions compared. All calculations are demonstrated in full in the first nontrivial case of W(3)-constraints.
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BAKER, GEORGE A., and JAMES P. HAGUE. "RISE OF THE CENTRIST: FROM BINARY TO CONTINUOUS OPINION DYNAMICS." International Journal of Modern Physics C 19, no. 09 (September 2008): 1459–75. http://dx.doi.org/10.1142/s0129183108013023.

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We propose a model that extends the binary "united we stand, divided we fall" opinion dynamics of Sznajd-Weron to handle continuous and multi-state discrete opinions on a linear chain. Disagreement dynamics are often ignored in continuous extensions of the binary rules, so we make the most symmetric continuum extension of the binary model that can treat the consequences of agreement (debate) and disagreement (confrontation) within a population of agents. We use the continuum extension as an opportunity to develop rules for persistence of opinion (memory). Rules governing the propagation of centrist views are also examined. Monte Carlo simulations are carried out. We find that both memory effects and the type of centrist significantly modify the variance of average opinions in the large timescale limits of the models. Finally, we describe the limit of applicability for Sznajd-Weron's model of binary opinions as the continuum limit is approached. By comparing Monte Carlo results and long time-step limits, we find that the opinion dynamics of binary models are significantly different to those where agents are permitted more than 3 opinions.
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Schlömerkemper, Anja, and Bernd Schmidt. "Discrete-to-Continuum Limit of Magnetic Forces: Dependence on the Distance Between Bodies." Archive for Rational Mechanics and Analysis 192, no. 3 (July 25, 2008): 589–611. http://dx.doi.org/10.1007/s00205-008-0134-4.

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Dissertations / Theses on the topic "Discrete-to-continuum limit"

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Ruf, Matthias [Verfasser], Marco [Akademischer Betreuer] [Gutachter] Cicalese, Antoine [Gutachter] Gloria, and Andrea [Gutachter] Braides. "Discrete-to-continuum limits and stochastic homogenization of ferromagnetic surface energies / Matthias Ruf ; Gutachter: Antoine Gloria, Marco Cicalese, Andrea Braides ; Betreuer: Marco Cicalese." München : Universitätsbibliothek der TU München, 2017. http://d-nb.info/1137323493/34.

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Books on the topic "Discrete-to-continuum limit"

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Mann, Peter. Near-Integrable Systems. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0024.

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This chapter extends the now familiar Lagrangian formulation to a field theory and covers elementary material in this new setting. The motion of systems with a very large number of degrees of freedom makes it necessary to specify an almost infinite number of discrete coordinates. It is possible to simplify the situation by taking the continuum limit, which replaces the individual coordinates with a continuous function that describes a displacement field, which assigns a displacement vector to each position the system could occupy relative to an equilibrium configuration. The field thus takes a point in the spacetime manifold and assigns it a value corresponding to whatever the field represents. In this chapter, many interdisciplinary examples are solved and pedagogical models are discussed. The chapter also discusses Lagrange density, the Lagrange field equation, instantons, the Klein–Gordon equation, Fourier transforms and the Korteweg–de Vries equation.
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Tiwari, Sandip. Electromechanics and its devices. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198759874.003.0005.

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Electromechanics—coupling of mechanical forces with others—exhibits a continuum-to-discrete spectrum of properties. In this chapter, classical and newer analysis techniques are developed for devices ranging from inertial sensors to scanning probes to quantify limits and sensitivities. Mechanical response, energy storage, transduction and dynamic characteristics of various devices are analyzed. The Lagrangian approach is developed for multidomain analysis and to bring out nonlinearity. The approach is extended to nanoscale fluidic systems where nonlinearities, fluctuation effects and the classical-quantum boundary is quite central. This leads to the study of measurement limits using power spectrum and, correlations with slow and fast forces. After a diversion to acoustic waves and piezoelectric phenomena, nonlinearities are explored in depth: homogeneous and forced conditions of excitation, chaos, bifurcations and other consequences, Melnikov analysis and the classic phase portaiture. The chapter ends with comments on multiphysics such as of nanotube-based systems and electromechanobiological biomotor systems.
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Book chapters on the topic "Discrete-to-continuum limit"

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Braides, Andrea, and Margherita Solci. "Discrete-to-Continuum Limits of Planar Lattice Energies." In Geometric Flows on Planar Lattices, 31–51. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-69917-8_3.

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van Meurs, Patrick. "Convergence Rates for Discrete-to-Continuum Limits in 1D Particle Systems." In Mathematical Analysis of Continuum Mechanics and Industrial Applications II, 181–93. Singapore: Springer Singapore, 2017. http://dx.doi.org/10.1007/978-981-10-6283-4_15.

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Zinn-Justin, Jean. "The random walk: Universality and continuum limit." In From Random Walks to Random Matrices, 1–12. Oxford University Press, 2019. http://dx.doi.org/10.1093/oso/9780198787754.003.0001.

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The first chapter discusses the asymptotic properties at large time and space of the familiar example of the random walk. The universality of a large scale behaviour and, correspondingly, the existence of a macroscopic continuum limit emerge as collective properties of systems involving a large number of random variables whose individual distribution is sufficiently localized. These properties, as well as the appearance of an asymptotic Gaussian distribution when the random variables are statistically independent, are illustrated with the simple example of the random walk with discrete time steps. The emphasis here is on locality, universality, continuum limit, path integral, Brownian motion, Gaussian distribution and scaling. These properties are first derived from an exact solution and then recovered by renormalization group (RG) methods. This makes it possible to introduce all the RG terminology.
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Dimitri, Rossana, and Giorgio Zavarise. "Numerical Study of Discrete Masonry Structures under Static and Dynamic Loading." In Computational Modeling of Masonry Structures Using the Discrete Element Method, 254–91. IGI Global, 2016. http://dx.doi.org/10.4018/978-1-5225-0231-9.ch011.

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Much of the world's architectural heritage consists of Unreinforced Masonry (URM) structures whose preservation is a topical subject. To prevent possible collapse of multi-block systems in hazardous conditions, a promising tool to investigate their structural response is represented by numerical modelling with the Discrete Element Method (DEM). Gothic buttresses of trapezoidal and stepped shapes are first analysed comparatively under static loading, defining the optimal configurations. Numerical results are verified against the analytical predictions of overturning and sliding resistances, based on a continuum approximation of masonry. The DEM is then successfully adopted to assess the first-order seismic behavior of arches and buttressed arches with different shapes as compared to predictions based on limit analysis. A systematic investigation on dynamic behavior failure domains and on modes of collapse of URM structures is finally performed for varying input parameters, as needed to gain more confidence on the numerical results.
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Reccia, Emanuele, Antonella Cecchi, and Gabriele Milani. "FEM/DEM Approach for the Analysis of Masonry Arch Bridges." In Computational Modeling of Masonry Structures Using the Discrete Element Method, 367–92. IGI Global, 2016. http://dx.doi.org/10.4018/978-1-5225-0231-9.ch014.

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The problem of masonry arch bridges load carrying capacity is studied by means of a coupled FEM/DEM 2D approach. The numerical model relies into a triangular discretization of the domain with embedded crack elements that activate whenever the peak strength is reached. The proposed approach can be regarded as a combination between Finite Elements allowing for the reproduction of elastic strain into continuum and DEM, suitable to model frictional cohesive behavior exhibited by masonry structures even at very low levels of external loads. The aforementioned numerical approach is applied to masonry arch bridges interacting with infill. A preliminary validation of the procedure is addressed for the prediction of the masonry arches limit state behavior where the stones are supposed infinite resistant and plastic hinges can occur exclusively on mortar joints, modeled as cohesive frictional interfaces. The sensitivity of the infill role varying mechanical properties of the infill is extensively discussed.
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Conference papers on the topic "Discrete-to-continuum limit"

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Li, Husheng. "Entropy analysis of CPS with application in smart grids: From discrete network to continuum limit." In 2015 IEEE International Conference on Smart Grid Communications (SmartGridComm). IEEE, 2015. http://dx.doi.org/10.1109/smartgridcomm.2015.7436384.

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Tavarez, Federico A., and Michael E. Plesha. "Discrete Element Method for Modeling Penetration." In ASME/JSME 2004 Pressure Vessels and Piping Conference. ASMEDC, 2004. http://dx.doi.org/10.1115/pvp2004-3045.

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The Discrete Element Method (DEM) discretizes a material using rigid elements of simple shape. Each element interacts with neighboring elements through appropriate interaction laws. The number of elements is typically large and is limited by computer speed. The method has seen widespread applications to modeling particulate media and more recently to modeling solids such as concrete, ceramic, and metal. For problems with severe damage, DEM offers a number of attractive features over continuum based numerical methods, with the primary feature being a seamless transition from solid phase to particulate phase. This study illustrates the potential of DEM for modeling penetration and briefly points out its numerous advantages. A weakness of DEM is that its convergence properties are not understood. The crucial question is whether convergence is obtained as DEM element size vanishes in the limit of model refinement. The major focus of our investigation will be a careful study of convergence for modeling the degradation of a solid into fragments. Our results show that indeed convergence is obtained in several specific test problems. Moreover, elastic interelement stiffness and damping properties were proven to be particle size-independent. However, convergence in material failure due to crack growth is obtained only if the interparticle potentials are properly constructed as functions of DEM element size and bulk material properties such as elastic modulus and fracture toughness.
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Takezawa, Akihiro, Shinji Nishiwaki, Kazuhiro Izui, and Masataka Yoshimura. "Structural Topology Optimization Using Function-Oriented Elements Based on the Concept of First Order Analysis." In ASME 2003 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2003. http://dx.doi.org/10.1115/detc2003/dac-48773.

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Computer Aided Engineering (CAE) has been successfully utilized in mechanical industries, but few mechanical design engineers use CAE tools that include structural optimization, since the development of such tools has been based on continuum mechanics that limit the provision of useful design suggestions at the initial design phase. In order to mitigate this problem, a new type of CAE based on classical structural mechanics, First Order Analysis (FOA), has been proposed. This paper presents the outcome of research concerning the development of a structural topology optimization methodology within FOA. This optimization method is constructed based on discrete and function-oriented elements such as beam and panel elements, and sequential convex programming. In addition, examples are provided to show the utility of the methodology presented here for mechanical design engineers.
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Xu, Jianfeng, Basel Abdalla, Ayman Eltaher, and Paul Jukes. "Permafrost Thawing-Pipeline Interaction Advanced Finite Element Model." In ASME 2009 28th International Conference on Ocean, Offshore and Arctic Engineering. ASMEDC, 2009. http://dx.doi.org/10.1115/omae2009-79554.

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The increasing energy demand has promoted the interest in exploration and field development in the Arctic waters, which holds one quarter of the world’s petroleum reserves. The harsh conditions and fragile environment in the arctic region introduce many challenges to a sustainable development of these resources. One of the key challenges is the engineering consideration of warm pipelines installed in permafrost areas; found mainly in shallow waters and shore crossings. Evaluations have to be made during the pipeline design to avoid significant thaw settlement and large-scale permafrost degrading. In this paper, a three-dimensional (3D) finite element (FE) model was developed to study the interaction between buried pipelines transporting warm hydrocarbons and the surrounding permafrost. This interaction is a combination of several mechanisms: heat transfer from the pipeline, results in permafrost thawing and formation of thaw bulb around the pipeline. Consequently, the thaw settlement of soil beneath the pipeline base results in bending strains in the pipe wall. For safe operations, the pipe should be designed so that the induced strains do not exceed the ultimate limit state conditions. The developed model helps in accurate prediction of pipe strains by using finite element continuum modeling method as opposed to the more commonly used discrete (springs) modeling and hand calculations. It also assesses the real size of the thaw bulb and the corresponding settlement at any time, thus preventing an over-conservative design.
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Schafer, Nicholas P., Radu Serban, and Dan Negrut. "Implicit Integration in Molecular Dynamics Simulation." In ASME 2008 International Mechanical Engineering Congress and Exposition. ASMEDC, 2008. http://dx.doi.org/10.1115/imece2008-66438.

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Molecular Dynamics (MD) simulation is a versatile methodology that has found many applications in materials science, chemistry and biology. In biology, the models employed range from mixed quantum mechanical and fully atomistic to united atom and continuum mechanical. These systems are evolved in discrete time by solving Newton’s equations of motion at each time step. The numerical methods currently in use limit the step size of a typical all atom simulation to 1 femtosecond. This step size limitation means that many steps need to be taken in order to reach biologically relevant time scales. At each time step, an evaluation of the forces on each atom must be performed resulting in heavy computational loads. This work investigates the use of implicit integration methods in MD. Implicit integration methods have been proven superior to their explicit counterparts in classical mechanical simulation, with which MD has many similarities. Longer time steps reduce the number of force evaluations that must be performed and the corresponding computational load. Herein we present results that compare implicit integration techniques with the current standard for molecular dynamics, the explicit velocity Verlet integration scheme. Total energy conservation is used as a metric for evaluating the dependability of simulations in the microcanonical ensemble. In order to understand the nature of the problem, several long simulations were run and analyzed by performing a Fourier analysis on the position, velocity and acceleration signals. Lastly, several methods for improving the viability of implicit integration methods are considered including replacing the Jacobian used in the Quasi-Newton method with a constant, diagonal mass matrix, evaluating the Jacobian infrequently and finding a better prediction of the system configuration to improve the convergence of the Quasi-Newton method.
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Odina, Lanre, and Roger Tan. "Seismic Fault Displacement of Buried Pipelines Using Continuum Finite Element Methods." In ASME 2009 28th International Conference on Ocean, Offshore and Arctic Engineering. ASMEDC, 2009. http://dx.doi.org/10.1115/omae2009-79739.

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In deep waters, pipelines are usually installed exposed on the seabed, as burial is generally not required to ensure on-bottom stability. These exposed pipelines are nevertheless susceptible to seismic geohazards like slope instability at scarp crossings, soil liquefaction and fault movements which may result in failure events, although larger diameter pipelines are generally known to have good tolerances to ground deformation phenomena, provided the seismic magnitudes are not too onerous. Regardless of the pipeline size, these seismic geohazard issues are usually addressed during the design stage by routing the pipeline to avoid such hazardous conditions, where possible. However, extreme environmental conditions like hurricanes or tropical cyclones, which are typically experienced in the Gulf of Mexico and Asia-Pacific regions, are also factors which can cause exposed pipelines to be susceptible to large pipeline displacements and damage. Secondary stabilisation in the form of rock dump is sometimes employed to reduce the hydrodynamic loads from high turbidity currents acting on the pipeline. However, rock dumping (or burying the displaced pipeline) on a fault line could again pose a threat to its integrity following a seismic faulting event. The traditional method of assessment of a buried pipeline subjected to seismic faulting is initially carried out using analytical methods. Due to the limitations of these techniques for large deformation soil movement associated with fault displacement, non-linear finite element (FE) methods are widely used to assess the pipeline integrity. The FE analysis typically idealises the pipeline using discrete structural beam-type elements and the pipeline-soil interaction as discrete non-linear springs, based on the concept of subgrade reactions proposed by Winkler. Recent research from offshore pipeline design activities in the arctic environment for ice gouge events have however suggested that the use of the discrete Winkler element model leads to over-conservative results in comparison to the coupled continuum model. The principal reason for the conservatism is related to the poor modeling of realistic surrounding soil behaviour for large deformation events. This paper discusses the application of continuum FE methods to model the fully coupled seabed-buried pipeline interaction events subject to ground movements at active seismic faults. Using the continuum approach, a more realistic mechanical response of the pipeline is established and can be further utilised to confirm that calculated strains are within allowable limits.
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Srivastava, Nilabh, Yi Miao, and Imtiaz U. Haque. "Influence of Clearance on the Dynamics of Chain CVT Drives." In ASME 2006 International Mechanical Engineering Congress and Exposition. ASMEDC, 2006. http://dx.doi.org/10.1115/imece2006-14059.

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A continuously variable transmission (CVT) is an emerging automotive transmission technology that offers a continuum of gear ratios between desired limits. The present research focuses on developing models to understand the influence of clearance on the dynamic performance of a chain CVT drive. Clearances may arise in such a CVT during the assembly process or during extensive continual operation of the system, which further leads to wear and failure of the system. A detailed planar multibody model of a chain CVT is developed in order to accurately capture the dynamics characterized by the discrete structure of the chain, which causes polygonal excitations in the system. A suitable model for clearance between the chain links is embedded into this multibody model of the chain CVT. Friction between the chain link and the pulley sheaves is modeled using continuous Coulomb approximation theory. The mathematical models, the computational scheme, and the results corresponding to different loading scenarios are discussed. The results discuss the influence of clearance parameters on the dynamic performance, the axial force requirements, and the torque transmitting capacity of a chain CVT drive.
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SALVIATO, MARCO, SEAN E. PHENISEE, ANTONIO A. DELEO, DANIELE PELESSONE, and MARK FLORES. "A NOVEL DISCRETE, MESOSCALE MODELING FRAMEWORK FOR THE SIMULATION OF THE DAMAGING AND FRACTURING BEHAVIOR OF COMPOSITES." In Proceedings for the American Society for Composites-Thirty Seventh Technical Conference. Destech Publications, Inc., 2022. http://dx.doi.org/10.12783/asc37/36473.

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Unidirectional (UD) and 2D/3D textile composites are increasingly being employed in systems acrossed many industrial sectors including aerospace, automotive, and wind energy. This is due to the excellent specific mechanical properties and tailorability of composites, paving new avenues for structural optimization and weight savings. One of the challenges with the simulation of the mechanical response of composite materials is that their damage mechanisms depend strongly on the material micro- and mesostructures. Phenomena such as fiber micro-buckling and kinking in compression or fiber scissoring and matrix microcracking in shear in UD composites are only a few examples. Homogenized continuum models that describe these mechanisms are extremely mathematically complex, lack generality, and can only be used to fit experimental data. In fact, the constitutive equations compensate for not modeling fibers and matrix explicitly by introducing several complex equations and fitting parameters of unclear physical meaning. This makes model calibration extremely cumbersome and limits the predictive capability of the model. In reality, the modeling of damage and fracture in composite materials does not have to be complex if the physics of the micro-and mesostructures is simulated explicitly. This is the goal of the Discrete Model for Composites (DM4C), a novel discrete mesoscale modeling framework that simulates the mechanical behavior of UD and textile composites. Specifically, this framework is only based on physical laws and does not depend on element erosion to simulate fracture. As it will be shown in this presentation, in DM4C, fibers, groups of fibers, and tows are simulated explicitly as Timoshenko beam elements while the matrix is described by vectorial constitutive laws defined on the facets of a tetrahedral mesh anchored to the nodes of the beam elements. These vectorial laws describe both the elastic and inelastic behavior of the matrix, including the traction-separation laws governing the fracture process and the friction between facets governing the compressive behavior. Thanks to the facet-based formulation, fracture is modeled in a discrete way and the need for element erosion can be avoided. Furthermore, since fibers and matrix are now simulated explicitly, the constitutive laws of each material can be physics-based, simple, and with clearly defined material parameters. To demonstrate the predictive capability of the proposed framework, simulations of several typical damage mechanisms in composites will be compared to experimental data such as shear band formation in transverse compression, fiber micro-buckling and kinking in longitudinal compression, and sub-critical matrix microcraking in off-axis layers.
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