Relevant bibliographies by topics / Deformations (Mechanics) – Mathematical models

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Deformations (Mechanics) – Mathematical models'

Author: Grafiati
Published: 4 June 2021
Last updated: 4 February 2022

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Journal articles on the topic "Deformations (Mechanics) – Mathematical models"

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Faddeev, Alexander O., Svetlana A. Pavlova, and Tatiana M. Nevdakh. "Mathematical Models and Evaluation Software for Stress-Strain State of the Earth’s Lithosphere." Engineering Technologies and Systems, no. 1 (March 29, 2019): 51–66. http://dx.doi.org/10.15507/2658-4123.029.201901.051-066.

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Introduction. For the purposes of this article, geodeformation processes mean processes associated with deformations arising from the movement of species and blocks of the lithosphere at various depths, including surfaces. The objective is to reconstruct geodynamic stress fields, which cause modern shifts and deformations in the Lithosphere. A mathematical model and software for estimating the stress-strain state of the Earth Lithosphere are considered. Materials and Methods.For mathematical modeling of stresses, isostatically reduced data on abnormal gravitation field were used. The methods of continuum mechanics and methods of the theory of differential equations were used to design a model for estimating the stressstrain state of the Earth Lithosphere. For processing input, intermediate and outcoming data, the Fourier transform method of spectral analysis for constructing grid functions and spectral-temporal method were used. To model for the stress-strain state of the Lithosphere globally, stress calculation was corrected on the basis of sputnik-derived velocity data at the surface of the earth crust. The data on the rates of horizontal and vertical movements at the surface of the Earth crust were processed to obtain a distribution of velocities in the uniform grid embracing longitudes and latitudes. The processing procedure was carried out on the basis of the Kraiging method. The software was developed in Borland Delphi 7.0 programming environment. Results. Based on the data on the abnormal gravitation field in isostatic reduction and information on the distribution of velocities of horizontal motions on the surface of the Earth crust, a mathematical model of the stress-strain state of the Lithosphere was constructed. With the help of the obtained mathematical model and software complex, the stress-strain state of the Lithosphere was calculated at various depth using elastic and elastic-viscous models, and maps of equipotential distribution of shear elastic-viscous deformations in the lithosphere at the depth of 10 km were constructed. Discussion and Conclusion. The presented mathematical model and software allow restoring fields of both elastic and elastic-viscous deformations that is fundamental for quantification of elastic-viscous shear stresses deep in the Earth Lithosphere.
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Petrushin, G. D., and A. G. Petrushina. "Determination of the area of mechanical hysteresis loop using mathematical models." Industrial laboratory. Diagnostics of materials 86, no. 5 (May 22, 2020): 59–64. http://dx.doi.org/10.26896/1028-6861-2020-86-5-59-64.

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A method of the hysteresis loop relates to the direct methods for determination of the energy dissipation and studying the inelasticity in the material. The method is based on the direct formation of the mechanical hysteresis loop by static loading and unloading of the sample and measuring of the corresponding deformations. The relative energy dissipation is defined as the ratio of the hysteresis loop area to the elastic energy corresponding to the maximum amplitude of strain. Construction of the hysteresis loop is performed on the installation «torsional pendulum for determination of the mechanical properties of materials» which can work as a device for measuring internal energy dissipation by damped oscillations, and as a precision torsion test machine using a deforming device. The aim of this work is to determine the area of the static hysteresis loop through the choice of the mathematical models of loading and unloading curves with subsequent numerical integration using the ordinate values at equidistant points. The analysis of using polynomials of the second or third degree was carried out according to the criterion of the smallest sum of squared deviations between the empirical and calculated values of the function. The experimentally obtained coordinates of the points of the deformation diagram of the sample during loading and unloading were used as initial data for estimation of regression coefficients in polynomial equations. A distinctive feature of the proposed method is that analytical dependences between stresses and strains obtained by N. N. Davidenkov and containing hard-to-determine geometric parameters of the loop, which must be pre-set from the known values of the logarithmic decrement of oscillations obtained from the experiment are not used in the developed method to calculate the area of the static hysteresis loop. It is shown that a comparative assessment of the relative energy scattering in the ferrite gray iron performed by the direct method of determining the area of the mechanical hysteresis loop at different amplitudes of shear deformation, is in good agreement with the data obtained by the indirect method of damped oscillations on an installation of the similar class.
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SACHSE, FRANK B., GUNNAR SEEMANN, MATTHIAS B. MOHR, and ARUN V. HOLDEN. "MATHEMATICAL MODELING OF CARDIAC ELECTRO-MECHANICS: FROM PROTEIN TO ORGAN." International Journal of Bifurcation and Chaos 13, no. 12 (December 2003): 3747–55. http://dx.doi.org/10.1142/s0218127403008910.

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Mathematical models of cardiac anatomy and physics provide information, which help to understand structure and behavior of the heart. Miscellaneous cardiac phenomena can only be adequately described by combination of models representing different aspects or levels of detail. Coupling of these models necessitates the definition of appropriate interfaces. Adequateness and efficiency of interfaces is crucial for efficient application of the combined models. In this work an integrated model is presented consisting of several models interconnected by interfaces. The integrated model allows the reconstruction of macroscopic electro-mechanical processes in the heart. The model comprises a three-dimensional are of left ventricular anatomy represented as truncated ellipsoid. The integrated model includes electrophysiological, tension development and elastomechanical models of myocardium at levels of single cell, proteins, and tissue patches, respectively. The model is exemplified by simulations of extracorporated left ventricle of small mammals. These simulations yield temporal distributions of electrophysiological parameters as well as descriptions of electrical propagation and mechanical deformation. The simulations show characteristic macroscopic ventricular function resulting from the interplay between cellular electrophysiology, electrical excitation propagation, tension development, and mechanical deformation.
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Ivanov, Evgeny, Olaf Lechtenfeld, and Stepan Sidorov. "Deformed N = 8 Supersymmetric Mechanics." Symmetry 11, no. 2 (January 26, 2019): 135. http://dx.doi.org/10.3390/sym11020135.

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We give a brief review of deformed N = 8 supersymmetric mechanics as a generalization of SU(2|1) mechanics. It is based on the worldline realizations of the supergroups SU(2|2) and SU(4|1) in the appropriate N = 8 , d = 1 superspaces. The corresponding models are deformations of the standard N = 8 mechanics models by a mass parameter m.
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Taghizadeh, D. M., and H. Darijani. "Mechanical Behavior Modeling of Hyperelastic Transversely Isotropic Materials Based on a New Polyconvex Strain Energy Function." International Journal of Applied Mechanics 10, no. 09 (November 2018): 1850104. http://dx.doi.org/10.1142/s1758825118501041.

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In this paper, the mechanical behavior of incompressible transversely isotropic materials is modeled using a strain energy density in the framework of Ball’s theory. Based on this profound theory and with respect to physical and mathematical aspects of deformation invariants, a new polyconvex constitutive model is proposed for the mechanical behavior of these materials. From the physical viewpoint, it is assumed that the proposed model is additively decomposed into three parts nominally representing the energy contributions from the matrix, fiber and fiber–matrix interaction where each of the parts should be presented in terms of the invariants consistent with the physics of the deformation. From the mathematical viewpoint, the proposed model satisfies the fundamental postulates on the form of strain energy density, specially polyconvexity and coercivity constraints. Indeed, polyconvexity ensures ellipticity condition, which in turn provides material stability and in combination with coercivity condition, guarantees the existence of the global minimizer of the total energy. In order to evaluate the performance of the proposed strain energy density function, some test data of incompressible transverse materials with pure homogeneous deformations are used. It is shown that there is a good agreement between the test data and the obtained results from the proposed model. At the end, the performance of the proposed model in the prediction of the material behavior is evaluated rather than other models for two representative problems.
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Moerman, Kevin M., Behrooz Fereidoonnezhad, and J. Patrick McGarry. "Novel hyperelastic models for large volumetric deformations." International Journal of Solids and Structures 193-194 (June 2020): 474–91. http://dx.doi.org/10.1016/j.ijsolstr.2020.01.019.

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Bobkov, S. P., and I. V. Polishchuk. "Simulation and visualization of solid deformation upon impact." Vestnik IGEU, no. 2 (2020): 51–57. http://dx.doi.org/10.17588/2072-2672.2020.2.051-057.

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The use of adequate mathematical models to study the process of deformation of solids is an urgent issue for industrial engineering. It is known that under mechanical action the bodies are deformed and mechanical stresses arise in them, which, in turn, lead to destruction. Therefore, the simulation of deformation processes can be useful both in studying the issues of strength and reliability of equipment and for solving problems of fine grinding of solid fuels. Classical continuum models of continuum mechanics are useful for studying mechanical stresses in idealized environments and for bodies of regular shape. Their application in the analysis of heterogeneous structures and objects of complex shape encounters significant difficulties. In such cases, a number of simplifying assumptions have to be introduced, which reduces the adequacy of the models. A discrete model which considers a solid body as a set of local elements connected by elastic bonds is used in the research. A significant difference between the proposed approach and the one previously used is the following. In previous models, the separate local element of unit mass was a discretization step of space. In the new interpretation, the discretization step is consistent with the behavior of a system (set) of several interacting unit masses. An improved approach to the analysis of the process of deformation of a solid has been investigated. A model that allows studying not only axial deformations (compression – tension) but also the effects of changes in transverse dimensions (shear) has been proposed. It has been established that this approach to modeling can significantly simplify the visualization of the process at each step of the discrete time. The obtained results have made it possible to improve discrete approaches to simulation of solids deformation process. At the same time, it has become possible to model not only axial deformations (compression – tension), but also the effects of changes in transverse dimensions (shear). The discrete approach to modeling has enabled to significantly simplify the visualization of the process at each step of the discrete time. The study has shown that the discrete approach allows analyzing the stress state and visualizing the propagation of deformation waves in solids at free impact. The data on the propagation of elastic waves obtained by computer simulation coincide with the results of preceding physical experiments. The discrete approach does not create difficulties in analyzing the behavior of heterogeneous bodies of complex shape, since the design features are considered at the local level and do not require adjustment of the modeling algorithm.
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Consuegra, Franklin, Antonio Bula, Wilson Guillín, Jonathan Sánchez, and Jorge Duarte Forero. "Instantaneous in-Cylinder Volume Considering Deformation and Clearance due to Lubricating Film in Reciprocating Internal Combustion Engines." Energies 12, no. 8 (April 15, 2019): 1437. http://dx.doi.org/10.3390/en12081437.

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A new methodology for predicting the real instantaneous in-cylinder volume in the combustion chamber of a reciprocating internal combustion engine is implemented. The mathematical model developed as part of this methodology, takes into consideration the deformations due to pressure and inertial forces, via a deformation constant adjusted through ANSYS®, using a high-precision CAD model of a SOKAN SK-MDF300 engine. The deformation constant was obtained from the CAD model using the computational tool ANSYS® and the pressure data was obtained from the engine running at three regimes: 1500, 2500, and 3500 rpm. The results were compared with previous models reported in the literature, showing that the deformation constant obtained has a smaller variation among cycles, which leads to a more precise value of the mechanical deformations. Furthermore, to have a more accurate model of the instantaneous volume variation, a factor taking into consideration the lubricant film behavior is introduced to calculate volumetric variation due to geometrical clearances. The influence of the introduced volumetric variation was evaluated through a process of combustion diagnosis, evidencing the improvement in the predictive capacity of thermodynamic modeling and, therefore, the correct prediction of heat release rate.
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Bulucea, Cornelia A., Constantin Brindusa, Doru A. Nicola, Nikos E. Mastorakis, Carmen A. Bulucea, and Philippe Dondon. "Evaluating through mathematical modelling the power equipment busbars electrodynamic strength under sudden short-circuit conditions." MATEC Web of Conferences 210 (2018): 02004. http://dx.doi.org/10.1051/matecconf/201821002004.

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The electrodynamic strength, as forces acting between the current-carrying electric circuits are exerted as long as the currents exist, and have the tendency of deformation and displacement of the circuits. In short-circuit regimes the strength in electrical equipment becomes severe. For instance, short-circuits highly affect power transformers connected to power transmission lines. The effects are also strong because of mechanical deformations occurring in the power transformer connection part. In line with this idea, in this paper it is made an analytical study upon the a.c. single-phase and a.c. three-phase electric circuits, taking into account the current instantaneous maximum value. The paper also entails numerical simulations of electrodynamic strength in power transformer busbars under short-circuit conditions. MATLAB software, with its specific extensions, enable simulation models to generate the charts of the electrodynamic forces in the power transformer connection bars.
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Clifton, R. J., and F. P. Chiang. "Experimental Mechanics." Applied Mechanics Reviews 38, no. 10 (October 1, 1985): 1279–81. http://dx.doi.org/10.1115/1.3143691.

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Mechanical failure of machine parts, structures, and microelectronic components has a strong negative impact on the safety, security, and productivity of our people. Prevention of these failures is a principal focus of solid mechanics, which uses analysis, experiment, and computation to provide the understanding necessary for failure reduction through improved design, fabrication, and inspection. Experimental mechanics plays a critical role in this effort since it provides the data base for the calculations and the means for testing the validity of proposed theoretical models of failure. Current trends in experimental mechanics show increased use of optical methods for monitoring the displacements, velocities, and strains of surfaces. This trend has gained impetus from the attractiveness of noncontact methods for hostile environments and dynamically loaded bodies. Advances in laser technology have enhanced the instrumentation associated with these methods. Another trend is the investigation of material behavior under more complex loading conditions, made possible by the availability of servo-controlled testing machines with computer interfaces. Still another trend is the increased attention given to defects, such as inclusions, cracks, and holes, because of their importance in failure mechanisms. Opportunities for future contributions from experimental mechanics appear to be great and to occur across a broad range of technological problems. A central theme of future research appears to be increased emphasis on measurements at the micron and submicron scale in order to advance the understanding of material response and failure at the micromechanical level. Increased attention will also be given to internal measurements of defects, deformations and residual stresses because of their importance in developing a fundamental understanding of failure. Automated data reduction and control of experiments will greatly increase the information obtained from experiments and its usefulness for the development of mathematical models. Other important research directions include improved methods for measurements of in situ stresses in rocks, improved measurements of displacements and physiological parameters in biological systems, capability for long-term monitoring of the integrity of structures, and improved sensors for feedback control of mechanical systems.
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Dissertations / Theses on the topic "Deformations (Mechanics) – Mathematical models"

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Beckham, Jon Regan. "Analysis of mathematical models of electrostatically deformed elastic bodies." Access to citation, abstract and download form provided by ProQuest Information and Learning Company; downloadable PDF file, 169 p, 2008. http://proquest.umi.com/pqdweb?did=1475178561&sid=27&Fmt=2&clientId=8331&RQT=309&VName=PQD.

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Miller, Matthew P. "Improved constitutive laws for finite strain inelastic deformation." Diss., Georgia Institute of Technology, 1993. http://hdl.handle.net/1853/16098.

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Gaballa, Mohamed Abdelrhman Ahmed. "Nonlinear multiphasic mechanics of soft tissue using finite element methods." Diss., The University of Arizona, 1989. http://hdl.handle.net/10150/184837.

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The purpose of the research was to develop a quantitative method which could be used to obtain a clearer understanding of the time-dependent fluid filteration and load-deformation behavior of soft, porous, fluid filled materials (e.g. biological tissues, soil). The focus of the study was on the development of a finite strain theory for multiphasic media and associated computer models capable of predicting the mechanical stresses and the fluid transport processes in porous structures (e.g. across the large blood vessels walls). The finite element (FE) formulation of the nonlinear governing equations of motion was the method of solution for a poroelastic (PE) media. This theory and the FE formulations included the anisotropic, nonlinear material; geometric nonlinearity; compressibility and incompressibility conditions; static and dynamic analysis; and the effect of chemical potential difference across the boundaries (known as swelling effect in biological tissues). The theory takes into account the presence and motion of free water within the biological tissue as the structure undergoes finite straining. Since it is well known that biological tissues are capable of undergoing large deformations, the linear theories are unsatisfactory in describing the mechanical response of these tissues. However, some linear analyses are done in this work to help understand the more involved nonlinear behavior. The PE view allows a quantitative prediction of the mechanical response and specifically the pore pressure fluid flow which may be related to the transport of the macromolecules and other solutes in the biological tissues. A special mechanical analysis was performed on a representative arterial walls in order to investigate the effects of nonlinearity on the fluid flow across the walls. Based on a finite strain poroelastic theory developed in this work; axisymmetric, plane strain FE models were developed to study the quasi-static behavior of large arteries. The accuracy of the FE models was verified by comparison with analytical solutions wherever is possible. These numerical models were used to evaluate variables and parameters, that are difficult or may be impossible to measure experimentally. For instance, pore pressure distribution within the tissue, relative fluid flow; deformation of the wall; and stress distribution across the wall were obtained using the poroelastic FE models. The effect of hypertension on the mechanical response of the arterial wall was studied using the nonlinear finite element models. This study demonstrated that the finite element models are powerful tools for the study of the mechanics of complicated structures such as biological tissue. It is also shown that the nonlinear multiphasic theory, developed in this thesis, is valid for describing the mechanical response of biological tissue structures under mechanical loadings.
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Razavi, H. Ali. "Identification and control of grinding processes for intermetalic [sic] compunds [sic]." Diss., Georgia Institute of Technology, 2000. http://hdl.handle.net/1853/18917.

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Amany, Aya Nicole Marie. "Characterization of shear and bending stiffness for optimizing shape and material of lightweight beams." Thesis, McGill University, 2007. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=112553.

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Optimized slender and short-thick beams are used in building, aircraft and machine structures to increase performance at a lower material cost. A previous work proposes an optimum shape, material and size selection model to design lightweight slender beams under pure bending. In short-thick beams, the transverse shear effects are no longer negligible and impact the choice of the optimum shape. This work extends such an optimum selection model to consider both slender and short-thick beams, by formulating the total beam stiffness design requirement as a combination of shear and bending stiffness. Selection charts are developed to show the impact of design variables, such as shape, size, material and slenderness, on the total beam stiffness. The model of total beam stiffness is validated against computational results from finite element analyses of beam models. A case study demonstrates the use of the selection charts to compare the performance of beams at the conceptual design stage.
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Pant, Sudeep Raj. "Mathematical and physical modelling of crack growth near free boundaries in compression." University of Western Australia. School of Civil and Resource Engineering, 2005. http://theses.library.uwa.edu.au/adt-WU2005.0139.

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[Truncated abstract] The fracture of brittle materials in uniaxial compression is a complex process with the development of cracks generated from initial defects. The fracture mechanism and pattern of crack growth can be altered considerably by the presence of a free surface. In proximity of a free surface, initially stable cracks that require an increase in the load to maintain the crack growth can become unstable such that the crack growth maintains itself without requiring further increase in the load. This leads to a sudden relief of accumulated energy and, in some cases, to catastrophic failures. In the cases of rock and rock mass fracturing, this mechanism manifests itself as skin rockbursts and borehole breakouts or as various non-catastrophic forms of failure, e.g. spalling. Hence, the study of crack-boundary interaction is important in further understanding of such failures especially for the purpose of applications to resource engineering. Two major factors control the effect of the free boundary: the distance from the crack and the boundary shape. Both these factors as well as the effect of the initial defect and the material structure are investigated in this thesis. Three types of boundary shapes - rectilinear, convex and concave - are considered. Two types of initial defects - a circular pore and inclined shear cracks are investigated in homogeneous casting resin, microheterogeneous cement mixes and specially fabricated granulate material. The preexisting defects are artificially introduced in the physical model by the method of inclusion and are found to successfully replicate the feature of pre-existing defects in terms of load-deformation response to the applied external load. It is observed that the possibility of crack growth and the onset of unstable crack growth are affected by the type of initial defect, inclination of the initial crack, the boundary shape and the location of the initial defect with respect to the boundary. The initial defects are located at either the centre or edge of the sample. The stresses required for the wing crack initiation and the onset of unstable crack growth is highest for the initial cracks inclined at 35° to the compression axis, lowest at 45° and subsequently increases towards 60° for all the boundary shapes and crack locations. In the case of convex boundary, the stress of wing crack initiation and the stress of unstable crack growth are lower than for the case of rectilinear and concave boundary for all the crack inclinations and crack locations. The crack growth from a pre-existing crack in a sample with concave boundary is stable, requiring stress increase for each increment of crack growth. The stress of unstable crack growth for the crack situated at the edge of the boundary is lower than the crack located at the centre of the sample for all the crack inclinations and boundary shapes.
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Zheng, Xiao-Qin Materials Science &amp Engineering Faculty of Science UNSW. "Packing of particles during softening and melting process." Awarded by:University of New South Wales. School of Materials Science & Engineering, 2007. http://handle.unsw.edu.au/1959.4/31517.

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Softening deformation of iron ore in the form of sinter, pellet, and lump ore in the cohesive zone of an ironmaking blast furnace is an important phenomenon that has a significant effect on gas permeability and consequently blast furnace production efficiency. The macroscopic softening deformation behavior of the bed and the microscopic deformation behavior of the individual particles in the packed bed are investigated in this study using wax balls to simulate the fused layer behavior of the cohesive zone. The effects of softening temperature, load pressure, and bed composition (mono - single melting particles, including pure or blend particles vs binary ??? two different melting point particles) on softening deformation are examined. The principal findings of this study are: 1. At low softening temperatures, an increase in load pressure increases the deformation rate almost linearly. 2. At higher softening temperatures, an increase in load pressure dramatically increases the deformation rate, and after a certain time there is no more significant change in deformation rate. 3. The bed deformation rate of a mono bed is much greater than that of a binary one. 4. In a binary system, the softening deformation rate increases almost proportionally with the increase in the amount of lower melting point wax balls. 5. In a mono system with blend particles, the content of the lower melting point material has a more significant effect on overall bed deformation than the higher melting point one. 6. The macro softening deformation of the bed behaves the theory of creep deformation. 7. A mathematical model for predicting bed porosity change due to softening deformation based on creep deformation theory has been developed. 8. Increase in load pressure also reduces the peak contact face number of the distribution curves, and this is more prominent with higher porosity values. 9. The contribution of contact face number to bed porosity reduction is more pronounced in a mono system than in a binary system. 10. The porosity reduction in a binary bed is more due to the contact face area increase, presumably of the lower melting point particles. 11. The mono system has a single peak contact face number distribution pattern while the binary system exhibits a bimodal distribution pattern once the higher melting point material starts to deform. 12. In a binary system, an increase in deformation condition severity tends to reduce the contact face number of the higher melting point material without having to increase the contact face number of the lower melting point material accordingly to achieve a given porosity.
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Golden, Christopher Lee. "Analysis of form errors in rings of non-uniform cross section due to workholding and machining loads." Thesis, Atlanta, Ga. : Georgia Institute of Technology, 2008. http://hdl.handle.net/1853/22703.

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Vohra, Sanjay. "A mechanics framework for modeling fiber deformation on draw rollers and freespans." Diss., Available online, Georgia Institute of Technology, 2006, 2006. http://etd.gatech.edu/theses/available/etd-05172006-141347/.

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Thesis (Ph. D.)--Polymer, Textile & Fiber Engineering, Georgia Institute of Technology, 2007.
Karl I. Jacob, Committee Chair ; Youjiang Wang, Committee Member ; Mary Lynn Realff, Committee Member ; Arun Gokhale, Committee Member ; Rami Haj-Ali, Committee Member.
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Reddy, Yeruva S. "Numerical simulation of damage and progressive failures in composite laminates using the layerwise plate theory." Diss., Virginia Tech, 1992. http://hdl.handle.net/10919/38534.

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Books on the topic "Deformations (Mechanics) – Mathematical models"

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Army Research Office Workshop on Constitutive Models (1986 Virginia Polytechnic Institute and State University). Constitutive models of deformation. Philadelphia: SIAM, 1987.

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Santaoja, Kari. Mathematical modelling of deformation mechanisms in ice. Espoo, Finland: Valtion teknillinen tutkimuskeskus, 1990.

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Benko, Boris. Numerical modelling of complex slope deformations. Ann Arbor, MI: UMI Dissertation Services, 2001.

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IUTAM Symposium on Theoretical, Computational and Modelling Aspects of Inelastic Media (2008 Cape Town, South Africa). IUTAM Symposium on Theoretical, Computational and Modelling Aspects of Inelastic Media: Proceedings of the IUTAM symposium held at Cape Town, South Africa, January 14-18, 2008. Edited by Reddy B. Dayanand 1953-. New York: Springer, 2008.

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IUTAM Symposium on Theoretical, Computational and Modelling Aspects of Inelastic Media (2008 Cape Town, South Africa). IUTAM Symposium on Theoretical, Computational and Modelling Aspects of Inelastic Media: Proceedings of the IUTAM symposium held at Cape Town, South Africa, January 14-18, 2008. Edited by Reddy B. Dayanand 1953-. New York: Springer, 2008.

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1925-, Avitzur Betzalel, ed. Elementary mechanics of plastic flow in metal forming. Chichester: J. Wiley, 1996.

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Zhuravkov, M. A. Matematicheskoe modelirovanie deformat︠s︡ionnykh prot︠s︡essov v tverdykh deformiruemykh sredakh: Na primere zadach mekhaniki gornykh porod i massivov : kurs lekt︠s︡iĭ. Minsk: BGU, 2002.

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Chislennoe issledovanie prot͡s︡essa deformat͡s︡ii materialov beskoordinatnym metodom. Vladivostok: "Dalʹnauka", 1995.

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1936-, Popova Mariana, ed. Mekhanika na materialite. Sofii︠a︡: Marin Drinov, 2009.

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1936-, Popova Mariana, ed. Mekhanika na materialite. Sofii︠a︡: Marin Drinov, 2009.

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Book chapters on the topic "Deformations (Mechanics) – Mathematical models"

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Sanavia, Lorenzo, Bernhard A. Schrefler, and Paul Steinmann. "A Mathematical and Numerical Model for Finite Elastoplastic Deformations in Fluid Saturated Porous Media." In Modeling and Mechanics of Granular and Porous Materials, 293–340. Boston, MA: Birkhäuser Boston, 2002. http://dx.doi.org/10.1007/978-1-4612-0079-6_10.

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Besseling, J. F., and E. Van Der Giessen. "Elementary models for small deformations." In Mathematical Modelling of Inelastic Deformation, 78–125. Boston, MA: Springer US, 1994. http://dx.doi.org/10.1007/978-1-4899-7186-9_4.

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Gaveau, Bernard, Julian Ławrynowicz, and Leszek Wojtczak. "Statistical Mechanics of a Crystal Surface." In Deformations of Mathematical Structures II, 265–88. Dordrecht: Springer Netherlands, 1994. http://dx.doi.org/10.1007/978-94-011-1896-5_11.

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Chapelle, Dominique, and Klaus-Jürgen Bathe. "Shell Mathematical Models." In Computational Fluid and Solid Mechanics, 81–114. Berlin, Heidelberg: Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/978-3-662-05229-7_4.

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Chapelle, Dominique, and Klaus-Jürgen Bathe. "Shell Mathematical Models." In Computational Fluid and Solid Mechanics, 95–134. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-16408-8_4.

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Lévay, Péter. "Adiabatic curvature, chaos and the deformations of Riemann Surfaces." In Mathematical Results in Quantum Mechanics, 307–14. Basel: Birkhäuser Basel, 1999. http://dx.doi.org/10.1007/978-3-0348-8745-8_29.

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Ławrynowicz, Julian, Leszek Wojtczak, Shozo Koshi, and Osamu Suzuki. "Stochastical Mechanics of Particle Systems in Clifford-Analytical Formulation Related to Hurwitz Pairs of Bidimension (8,5)." In Deformations of Mathematical Structures II, 213–62. Dordrecht: Springer Netherlands, 1994. http://dx.doi.org/10.1007/978-94-011-1896-5_10.

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Ashwin, K. P., and Ashitava Ghosal. "Mathematical Model for Pressure–Deformation Relationship of Miniaturized McKibben Actuators." In Lecture Notes in Mechanical Engineering, 267–78. Singapore: Springer Singapore, 2018. http://dx.doi.org/10.1007/978-981-10-8597-0_23.

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Miara, Bernadette. "Mathematical Justifications of Plate Models." In Encyclopedia of Continuum Mechanics, 1514–22. Berlin, Heidelberg: Springer Berlin Heidelberg, 2020. http://dx.doi.org/10.1007/978-3-662-55771-6_138.

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Miara, Bernadette. "Mathematical Justifications of Plate Models." In Encyclopedia of Continuum Mechanics, 1–9. Berlin, Heidelberg: Springer Berlin Heidelberg, 2017. http://dx.doi.org/10.1007/978-3-662-53605-6_138-1.

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Conference papers on the topic "Deformations (Mechanics) – Mathematical models"

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Manzhirov, Alexander V. "Mechanics of Growing Solids: New Track in Mechanical Engineering." In ASME 2014 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/imece2014-36712.

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A vast majority of objects around us arise from some growth processes. Many natural phenomena such as growth of biological tissues, glaciers, blocks of sedimentary and volcanic rocks, and space objects may serve as examples. Similar processes determine specific features of many industrial processes which include crystal growth, laser deposition, melt solidification, electrolytic formation, pyrolytic deposition, polymerization and concreting technologies. Recent researches indicates that growing solids exhibit properties dramatically different from those of conventional solids, and the classical solid mechanics cannot be used to model their behavior. The old approaches should be replaced by new ideas and methods of modern mechanics, mathematics, physics, and engineering sciences. Thus, there is a new track in solid mechanic that deals with the construction of adequate models for solid growth processes. The fundamentals of the mathematical theory of growing solids are under consideration. We focus on the surface growth when deposition of a new material occurs at the boundary of a growing solid. Two approaches are discussed. The first one deals with the direct formulation of the mathematical theory of continuous growth in the case of small deformations. The second one is designed for the solution of nonlinear problems in the case of finite deformations. It is based on the ideas of the theory of inhomogeneous solids and regards continuous growth as the limit case of discrete growth. The constitutive equations and boundary conditions for growing solids are presented. Non-classical boundary value problems are formulated. Methods for solving these problems are proposed.
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Bulgakov, Alexej, and Thomas Bock. "Mathematical Models Construction for Building Robots with Due Account of Elastic Deformations of Mechanisms." In 22nd International Symposium on Automation and Robotics in Construction. International Association for Automation and Robotics in Construction (IAARC), 2005. http://dx.doi.org/10.22260/isarc2005/0012.

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Mattikalli, Raju, Saba Mahanian, Alan Jones, and Greg Clark. "Modeling Compliant Part Assembly: Mechanics of Deformation and Contact." In ASME 2000 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2000. http://dx.doi.org/10.1115/detc2000/dfm-14036.

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Abstract This paper describes an approach to model the mechanics of assembly by assuming parts are compliant. The approach involves a model of contact between compliant bodies based on variational inequalities. This approach has a number of advantages over current finite element codes, which rely on traditional variational approaches such as penalty force methods and Lagrange multipliers to resolve multiple unknown contact conditions. From a mathematical point of view, contact problems among compliant parts are particularly difficult to handle due to the fact that contact constraints are not permanently active, but depend on deformations. They are inherently non-linear and irreversible in character. To obtain a more mathematically robust way of modeling contact, we present a variational inequalities based approach that produces a quadratic programming (QP) problem. The QP is solved to resolve contact situations and obtain the mechanics of parts during assembly. We apply the method to simulate and design aircraft assembly processes.
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Tan, Zhimin, Michael Case, and Terry Sheldrake. "Higher Order Effects on Bending of Helical Armor Wire Inside an Unbonded Flexible Pipe." In ASME 2005 24th International Conference on Offshore Mechanics and Arctic Engineering. ASMEDC, 2005. http://dx.doi.org/10.1115/omae2005-67106.

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This paper investigates the higher order geometrical effects on the deflections of a helical armour wire when the pipe is subjected to uniform bending and is away from any end effects from its remaining fittings (end fittings), and the effect on the subsequent bending stresses. Due to its complexity in both geometrical shape and loading conditions, the approaches found in the literature are often to assume either a bent helix or geodesic as its deflected configuration with linearized mathematical expressions for simplification. The bending stresses are then calculated based on the geometrical difference between the assumed deflection and the original helical shape. The effect of the wire cross-section characteristics, for example the width and thickness ratio, over its deflection are often ignored. This paper presents an analytical strain energy model to quantify the influence of the wire width and thickness ratio over its final deflection. The higher order geometrical effects are fully considered in determining the wire deflection by using the exact mathematical expressions, and in the subsequent wire deformation and stress calculations. The paper also discusses briefly the structural coupling behavior between the pipe axial and bending deformations raised by using the exact expressions. The analytical results are validated by finite element simulation of an identical structure. The results are shown in good agreement in both deflection and the bi-normal bending stress. The results also show desirable conservatism in the normal and the total bending stresses. The presented analytical approach is demonstrated as an efficient and conservative way for investigating the behaviour of such a helical wire.
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Lortz, Wolfgang, and Radu Pavel. "Advanced Modeling of Drilling – Realistic Process Mechanics Leading to Helical Chip Formation." In ASME 2021 16th International Manufacturing Science and Engineering Conference. American Society of Mechanical Engineers, 2021. http://dx.doi.org/10.1115/msec2021-63790.

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Abstract There is considerable interest in the “Industry 4.0 project”. Industry hopes that a general solution of the metal removal problem will be found through the use of highly automated manufacturing data. Scientists hope that the computer will provide better models based on artificial intelligence and machine learning. Initial attempts leveraging existing models did not result in satisfactory results yet — largely because of mathematical, physical and metallurgical reasons. This paper presents a new mathematical-physical model to describe the total process mechanics from volume conservation, to friction, to metal plasticity with self-hardening or softening effects and dynamic phenomena during metal plastic flow. The softening effects are created by high energy corresponding to high strain-rate resulting in high temperatures. Furthermore, the developed equations for strain-rate discontinuities as well as yield shear stress with body forces have an interdependent relationship and lead to plastic deformation with dynamic behavior in the total chip formation zone. This plastic deformation is the only parameter that will not disappear after completing the process. This leads to the opportunity to check the theoretically developed grid deformation and compare it with practical results of the same area. In this publication this new theory will be used to analyze the complex contact and friction conditions between the chip and tool edge of a twist drill during operation. It will be shown that the existing conditions are leading to high wear at the corner edge and flank wear at the tool cutting edge. In addition, the existing temperatures can be estimated and compared with practical measurements, and all these complex and difficult conditions create a helical spiral chip, which could be developed as it will be presented in this paper.
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Lortz, Wolfgang, and Radu Pavel. "Fundamental Process Mechanics Common to Machining and Grinding Operations." In ASME 2020 15th International Manufacturing Science and Engineering Conference. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/msec2020-8371.

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Abstract All different production processes have one thing in common: in each case a workpiece with characteristic material behavior, stress, strain, self-hardening and temperature will be produced by a tool with special geometry and individual kinematic conditions, with a wide range of energy in a designed machine tool which is working along programmed lines. For the workpiece material, it is not important from which machine the energy is coming. To be able to predict more accurate values of the production process, it will be necessary to focus more on the complex and difficult process mechanics. The result must have a strong physical base and be in good agreement with practical results To solve these problems, we have to uncover all previous simplification assumptions for the existing models. This leads in a first step to a new fundament in process mechanics, which is only based on mathematics, physics and material behavior with friction conditions, and resulting temperatures during metal plastic flow. The new mathematical equations developed for yield shear stress and strain rate will be presented and discussed in this paper. The plastic deformation is the only parameter that will not disappear after completing the operation. Therefore, this will be the base to compare the developed theoretical deformation with the experimental results for two operations: cutting and grinding. In addition, it could be shown that yield shear stress and corresponding strain rate versus temperatures have an interdependent relationship, which creates the opportunity to determine the temperatures during metal plastic flow.
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Zhao, Huyue, and F. Ehmann Kornel. "Single- and Multi-Stand Chatter Models in Tandem Rolling Mills." In ASME 2008 International Manufacturing Science and Engineering Conference collocated with the 3rd JSME/ASME International Conference on Materials and Processing. ASMEDC, 2008. http://dx.doi.org/10.1115/msec_icmp2008-72530.

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Many different modes of chatter and their possible causes have been identified after years of research, yet no clear and definite theory of their mechanics has been established. One of the most important reasons for this can be attributed to the fact that only oversimplified models with a single input and a single output were historically used to formulate chatter in rolling. Such a situation has hindered a complete analysis of the underlying mechanisms. In this paper, a state-space representation of single- and multi-stand chatter models will be proposed in a rigorous and comprehensive mathematical form for stability analysis of the various chatter mechanisms. First, a dynamic model of the rolling process that utilizes homogeneous deformation theory will be established that includes the material strain-hardening and work roll flattening effects. By coupling this dynamic rolling process model with a structural model for mill stands, a single-stand chatter model in a state-space representation will be proposed. Based on the single-stand chatter model, a multi-stand chatter model will be formulated by incorporating the inter-stand tension variations and the time delay effect of the strip transportation. A simulation program will also be presented for the study of the dynamic rolling process in the time domain and for verifying the results from stability analysis.
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Ebna Hai, Bhuiyan Shameem Mahmood, and Markus Bause. "Adaptive Multigrid Methods for Extended Fluid-Structure Interaction (eXFSI) Problem: Part I — Mathematical Modelling." In ASME 2015 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/imece2015-53265.

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This contribution is the first part of three papers on Adaptive Multigrid Methods for eXtended Fluid-Structure Interaction (eXFSI) Problem, where we introduce a monolithic variational formulation and solution techniques. In a monolithic nonlinear fluid-structure interaction (FSI), the fluid and structure models are formulated in different coordinate systems. This makes the FSI setup of a common variational description difficult and challenging. This article presents the state-of-the-art of recent developments in the finite element approximation of FSI problem based on monolithic variational formulation in the well-established arbitrary Lagrangian Eulerian (ALE) framework. This research will focus on the newly developed mathematical model of a new FSI problem which is called eXtended Fluid-Structure Interaction (eXFSI) problem in ALE framework. This model is used to design an on-live Structural Health Monitoring (SHM) system in order to determine the wave propagation in moving domains and optimum locations for SHM sensors. eXFSI is strongly coupled problem of typical FSI with a wave propagation problem on the fluid-structure interface, where wave propagation problems automatically adopted the boundary conditions from of the typical FSI problem at each time step. The ALE approach provides a simple, but powerful procedure to couple fluid flows with solid deformations by a monolithic solution algorithm. In such a setting, the fluid equations are transformed to a fixed reference configuration via the ALE mapping. The goal of this work is the development of concepts for the efficient numerical solution of eXFSI problem, the analysis of various fluid-mesh motion techniques and comparison of different second-order time-stepping schemes. This work consists of the investigation of different time stepping scheme formulations for a nonlinear FSI problem coupling the acoustic/elastic wave propagation on the fluid-structure interface. Temporal discretization is based on finite differences and is formulated as an one step-θ scheme; from which we can consider the following particular cases: the implicit Euler, Crank-Nicolson, shifted Crank-Nicolson and the Fractional-Step-θ schemes. The nonlinear problem is solved with Newton’s method whereas the spatial discretization is done with a Galerkin finite element scheme. To control computational costs we apply a simplified version of a posteriori error estimation using the dual weighted residual (DWR) method. This method is used for the mesh adaptation during the computation. The implementation is accomplished via the software library package DOpElib and deal.II for the computation of different eXFSI configurations.
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Lake, Spencer P., Daniel H. Cortes, Jennifer A. Kadlowec, Dawn M. Elliott, and Louis J. Soslowsky. "Comparison of Experimental and Affine-Predicted Fiber Kinematics in Human Supraspinatus Tendon." In ASME 2010 Summer Bioengineering Conference. American Society of Mechanical Engineers, 2010. http://dx.doi.org/10.1115/sbc2010-19234.

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Mathematical modeling approaches are frequently used to characterize and predict the mechanics of biological soft tissues. Structurally-based continuum models, which describe the relationship of the constituents’ properties (i.e., collagen fibers, matrix) to overall tissue properties, require knowledge of the relationship between microscopic (fiber) and macroscopic (tissue) deformation. The most common and straightforward approach is the use of an affine model, which assumes that local fiber kinematics follow the global tissue deformation. Although the affine assumption is often used in constitutive modeling, several studies have reported non-affine fiber behavior in soft tissue testing [1–2]. Our recent work has quantified the anisotropic and inhomogeneous mechanical and organizational properties of human supraspinatus tendon (SST) [3–4]. We have also utilized a fiber dispersion model to examine SST [5]; however the relationship between macroscopic and microscopic deformation in this tendon remains unknown. Therefore, the purpose of this study was to examine the affine assumption in human SST fiber kinematics by comparing experimentally-measured fiber alignment to the affine model prediction.
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Green, Christopher K., Jeffrey L. Streator, Comas Haynes, and Edgar Lara-Curzio. "Leakage Studies With Seals for Solid-Oxide Fuel Cells." In ASME/STLE 2007 International Joint Tribology Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/ijtc2007-44243.

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This research seeks to characterize the gas leakage of a mica-based compressive seal assembly in planar solid-oxide fuel cells through modeling and experiment. In particular, it is of interest to assess how certain physical parameters (i.e., seal material composition, compressive applied stress, and surface finish) affect leakage rates. Finite element analysis is used to determine the macroscopic stresses and deformations in the sealing interface, while a microscale contact mechanics analysis is employed to model the role of surface roughness on the mean interfacial gap at the interface. An averaged Reynolds equation from mixed lubrication theory is applied to model the leakage flow across the sealed interface, which is of nanometer to micrometer dimensions in the vertical direction. In conjunction with the mathematical modeling, leakage results are reported. For these tests, an annular Inconel tube was pressed against a stainless steel substrate, creating an annular sealing zone. The inside of the tube is pressurized with a test gas, the mass of which is monitored during the leakage experiment. Test results are compared to model predictions.
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