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Miriam Ryvkin - One of the best experts on this subject based on the ideXlab platform.
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Three dimensional analysis of periodic fiber-reinforced composites with randomly broken and debonded fibers
International Journal of Engineering Science, 2020Co-Authors: Miriam Ryvkin, Jacob AboudiAbstract:Abstract A three-dimensional analysis is presented for the prediction of the behavior of periodic fiber-reinforced composites with numerous broken fibers and debonded fiber-matrix interfaces. The locations of these defects in the composite are randomly determined. The analysis is based on the Representative Cell method and the higher-order theory. In the framework of the Representative Cell method, the problem for the Representative volume element of the damaged composite that includes multiple fibers is reduced, in conjunction with the triple discrete Fourier transform, to the problem for repetitive Cell of undamaged composite including just a single Cell. The solution of this boundary-value problem is obtained by the higher-order theory. The inversion of the transform, in conjunction with an iterative procedure, establishes the elastic field at any point of the damaged composite. The optimal size of the Representative volume element of the damaged composite within which the computations are performed is determined. The present method is capable of predicting the resulting field distributions in the composite as well as the average values of the effective moduli of the randomly damage composite and the resulting stress concentration factors. These average values and the corresponding standard deviations are determined by repeating the analysis several times (scores). A parametric study of the dependence of the effective elastic moduli and stress concentration factors upon the level of damage is performed. In addition, comparisons with a micromechanical theory predictions which are based on the analysis of a repeating unit Cell, established by the assumption of spatial damage periodicity, are given.
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Three-dimensional continuum analysis for a unidirectional composite with a broken fiber
International Journal of Solids and Structures, 2008Co-Authors: Miriam Ryvkin, Jacob AboudiAbstract:AbstractThe three-dimensional problem of a periodic unidirectional composite with a penny-shaped crack traversing one of the fibers is analyzed by the continuum equations of elasticity. The solution of the crack problem is represented by a superposition of weighted unit normal displacement jump solutions, everyone of which forms a Green’s function. The Green’s functions for the unbounded periodic composite are obtained by the combined use of the Representative Cell method and the higher-order theory. The Representative Cell method, based on the triple discrete Fourier transform, allows the reduction of the problem of an infinite domain to a problem of a finite one in the transform space. This problem is solved by the higher-order theory according to which the transformed displacement vector is expressed by a second order expansion in terms of local coordinates, in conjunction with the equilibrium equations and the relevant boundary conditions. The actual elastic field is obtained by a numerical evaluation of the inverse transform. The accuracy of the suggested approach is verified by a comparison with the exact analytical solution for a penny-shaped crack embedded in a homogeneous medium. Results for a unidirectional composite with a broken fiber are given for various fiber volume fractions and fiber-to-matrix stiffness ratios. It is shown that for certain parameter combinations the use of the average stress in the fiber, as it is employed in the framework of the shear lag approach, for the prediction of composite’s strength, leads to an over estimation. To this end, the concept of “point stress concentration factor” is introduced to characterize the strength of the composite with a broken fiber. Several generalizations of the proposed approach are offered
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a continuum approach to the analysis of the stress field in a fiber reinforced composite with a transverse crack
International Journal of Solids and Structures, 2007Co-Authors: Miriam Ryvkin, Jacob AboudiAbstract:Abstract The stress field in a periodically layered composite with an embedded crack oriented in the normal direction to the layering and subjected to a tensile far-field loading is obtained based on the continuum equations of elasticity. This geometry models the 2D problem of fiber reinforced materials with a transverse crack. The analysis is based on the combination of the Representative Cell method and the higher-order theory. The Representative Cell method is employed for the construction of Green’s functions for the displacements jumps along the crack line. The problem of the infinite domain is reduced, in conjunction with the discrete Fourier transform, to a finite domain (Representative Cell) on which the Born–von Karman type boundary conditions are applied. In the framework of the higher-order theory, the transformed elastic field is determined by a second-order expansion of the displacement vector in terms of local coordinates, in conjunction with the equilibrium equations and these boundary conditions. The accuracy of the proposed approach is verified by a comparison with the analytical solution for a crack embedded in a homogeneous plane. Results show the effects of crack lengths, fiber volume fractions, ratios of fiber to matrix Young’s moduli and matrix Poisson’s ratio on the resulting elastic field at various locations of interest. Comparisons with the predictions obtained from the shear lag theory are presented.
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Analysis of Local Thermomechanical Effects in Fiber-Reinforced Periodic Composites
International Journal of Fracture, 2007Co-Authors: Miriam Ryvkin, Jacob AboudiAbstract:Two approaches are combined to investigate the effect of localized thermomechanical loadings of periodic multiphase materials. The first one, referred to as the Representative Cell method, reduces the infinite domain problem to a problem for the periodicity Cell by means of the discrete Fourier transform. This problem is solved by the discretization of the Cell into several subCells and a second order expansion of the displacements transform vector in terms of local coordinates. Results for boron/epoxy and glass/epoxy composites subjected to localized mechanical and thermal loadings are presented, and they are compared with analytical solutions for homogeneous materials.
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Analysis of local effects in fiber-reinforced periodic composites
2006Co-Authors: Jacob Aboudi, Miriam RyvkinAbstract:Two types of analyses are combined to investigate the effect of localized thermomechanical loadings acting on a region of periodic multiphase materials. In the first analysis, referred to as the Representative Cell method, the infinite domain problem is reduced, in conjunction with the discrete Fourier transform, to a finite domain problem on which Born–von Karman type boundary conditions are applied. In the second analysis, referred to as higher-order theory, the Representative Cell is discretized into several subCells. The transformed elastic field is determined by a second-order expansion of the displacement vector in terms of local coordinates, and by imposing the equilibrium equations, the interfacial traction and displacement conditions, and the Born–von Karman type boundary conditions. The actual non-periodic elastic field at any point is obtained from the Fourier-transformed fields by a numerical inversion. Results are verified by comparison with analytical solutions which can be established in homogeneous materials, and are presented for boron/epoxy and glass/ epoxy composites subjected to various types of localized mechanical and thermal loadings. 2006 Elsevier Ltd. All rights reserved.
Jean-baptiste Leblond - One of the best experts on this subject based on the ideXlab platform.
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a gurson type criterion for porous ductile solids containing arbitrary ellipsoidal voids i limit analysis of some Representative Cell
Journal of The Mechanics and Physics of Solids, 2012Co-Authors: Komlanvi Madou, Jean-baptiste LeblondAbstract:Abstract Gurson (1977) 's famous model of the behavior of porous ductile solids, initially developed for spherical cavities, was extended by Gologanu et al., 1993 , Gologanu et al., 1994 , Gologanu et al., 1997 to spheroidal, both prolate and oblate voids. The aim of this work is to further extend it to general (non-spheroidal) ellipsoidal cavities, through approximate homogenization of some Representative elementary porous Cell. As a first step, we perform in the present Part I a limit-analysis of such a Cell, namely an ellipsoidal volume made of some rigid-ideal-plastic von Mises material and containing a confocal ellipsoidal void, loaded arbitrarily under conditions of homogeneous boundary strain rate. This analysis provides an estimate of the overall plastic dissipation based on a family of trial incompressible velocity fields recently discovered by Leblond and Gologanu (2008) , satisfying conditions of homogeneous strain rate on all ellipsoids confocal with the void and the outer boundary. The asymptotic behavior of the integrand in the expression of the global plastic dissipation is studied both far from and close to the void. The results obtained suggest approximations leading to explicit approximate expressions of the overall dissipation and yield function. These expressions contain parameters the full determination of which will be the object of Part II.
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A Gurson-type criterion for porous ductile solids containing arbitrary ellipsoidal voids—I: Limit-analysis of some Representative Cell
Journal of the Mechanics and Physics of Solids, 2012Co-Authors: Komlanvi Madou, Jean-baptiste LeblondAbstract:Gurson (1977)'s famous model of the behavior of porous ductile solids, initially developed for spherical cavities, was extended by Gologanu et al. (1993, 1994, 1997) to spheroidal, both prolate and oblate voids. The aim of this work is to further extend it to general (non-spheroidal) ellip-soidal cavities, through approximate homogenization of some Representative elementary porous Cell. As a first step, we perform in the present Part I a limit-analysis of such a Cell, namely an ellipsoidal volume made of some rigid-ideal-plastic von Mises material and containing a confo-cal ellipsoidal void, loaded arbitrarily under conditions of homogeneous boundary strain rate. This analysis provides an estimate of the overall plastic dissipation based on a family of trial incompressible velocity fields recently discovered by Leblond and Gologanu (2008), satisfying conditions of homogeneous strain rate on all ellipsoids confocal with the void and the outer boundary. The asymptotic behavior of the integrand in the expression of the global plastic dissipation is studied both far from and close to the void. The results obtained suggest approximations leading to explicit approximate expressions of the overall dissipation and yield function. These expressions contain parameters the full determination of which will be the object of Part II.
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A Gurson-type criterion for porous ductile solids containing arbitrary ellipsoidal voids—I: Limit-analysis of some Representative Cell
Journal of the Mechanics and Physics of Solids, 2012Co-Authors: Komlanvi Madou, Jean-baptiste LeblondAbstract:Abstract Gurson (1977) 's famous model of the behavior of porous ductile solids, initially developed for spherical cavities, was extended by Gologanu et al., 1993 , Gologanu et al., 1994 , Gologanu et al., 1997 to spheroidal, both prolate and oblate voids. The aim of this work is to further extend it to general (non-spheroidal) ellipsoidal cavities, through approximate homogenization of some Representative elementary porous Cell. As a first step, we perform in the present Part I a limit-analysis of such a Cell, namely an ellipsoidal volume made of some rigid-ideal-plastic von Mises material and containing a confocal ellipsoidal void, loaded arbitrarily under conditions of homogeneous boundary strain rate. This analysis provides an estimate of the overall plastic dissipation based on a family of trial incompressible velocity fields recently discovered by Leblond and Gologanu (2008) , satisfying conditions of homogeneous strain rate on all ellipsoids confocal with the void and the outer boundary. The asymptotic behavior of the integrand in the expression of the global plastic dissipation is studied both far from and close to the void. The results obtained suggest approximations leading to explicit approximate expressions of the overall dissipation and yield function. These expressions contain parameters the full determination of which will be the object of Part II.
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Recent extensions of Gurson's model for porous ductile metals
Continuum Micromechanics, 1997Co-Authors: M. Gologanu, Jean-baptiste Leblond, G. Perrin, J. DevauxAbstract:This paper is devoted to two distinct extensions of Gurson’s (1977) famous model for plastic voided metals. Gurson’s work was based on an approximate limit-analysis of a typical elementary volume in a porous material, namely a hollow sphere subjected to conditions of arbitrary homogeneous boundary strain rate. The first extension envisaged consists in considering a more general geometry, namely a spheroidal volume containing some spheroidal confocal cavity. The aim here is to incorporate void shape effects into Gurson’s model. The second extension again considers a hollow sphere, but now subjected to conditions of inhomogeneous boundary strain rate. The goal is to account for possible strong variations of the macroscopic mechanical fields at the scale of the Representative Cell (i.e. of the void spacing), as encountered near crack tips.
Moshe B. Fuchs - One of the best experts on this subject based on the ideXlab platform.
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Fracture analysis of materials with periodic microstructure by the Representative Cell method
International Journal of Fracture, 2004Co-Authors: Miriam Ryvkin, Moshe B. Fuchs, Fabian Lipperman, Leonid KucherovAbstract:The periodic structure of some natural and especially man-made materials can be manifested not only on an atomic but also on a larger scale. Investigation of mechanical properties of these materials usually hinges on well-developed homogenization methods. On the other hand, these methods are not suitable for fracture analysis where the knowledge of the local stress-strain fields near a flaw (a crack) is required. The result is obtained by the use of the Representative Cell method based on the discrete Fourier transform. This method enables one to determine the exact stress distribution in a periodic structure subjected to arbitrary loading. Direct application of the method is impossible since the crack violates the translational symmetry defined by the material microstructure. This obstacle is overcome by application of the fictitious loading to the uncracked body at the line where the crack is to be located. The amplitude of the loading is adjusted in order to fulfill the boundary conditions imposed on the crack faces. The compatibility equation for deriving this amplitude is obtained by the use of the corresponding Green function, which is found in a closed form. Fracture problems for the two types of materials with a periodic microstructure are considered. The first one is a composite material consisting of dissimilar isotropic elastic layers arranged periodically. The second periodic microstructure is a 2D infinite beam lattice modeling a Cellular material. The analysis of the failure process in the latter case shows that in contrast to the case of homogeneous material, the crack propagation path is not defined by the condition of zero Mode II stress intensity factor.
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Non-Homogenization Approach to the Analysis of Periodic Elastic Systems: Applications to Fracture Mechanics and Topological Optimization
Continuum Models and Discrete Systems, 2004Co-Authors: Miriam Ryvkin, Moshe B. Fuchs, Fabian Lipperman, Eyal MosesAbstract:The Representative Cell method is employed for the analysis of periodic elastic domains. The method is based on the discrete Fourier transform and reduces the analysis of an arbitrarily loaded domain possessing translational symmetry to the analysis of a single repetitive Cell. In the case of topological optimization of periodic structures the problem for the Cell is solved numerically by the use of the finite element method. As an example of a fracture problem the analysis of a 2D regular beam lattice with a flaw is presented. In this case the Cell problem is solved analytically. Crack nucleation and propagation for different layouts with triangular, square and hexagonal Cells is also considered.
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Topological design of modular structures under arbitrary loading
Structural and Multidisciplinary Optimization, 2002Co-Authors: E. Moses, Moshe B. Fuchs, Miriam RyvkinAbstract:A numerical method for the topological design of periodic continuous domains under general loading is presented. Both the analysis and the design are defined over a single Cell. Confining the analysis to the repetitive unit is obtained by the Representative Cell method which by means of the discrete Fourier transform reduces the original problem to a boundary value problem defined over one module, the Representative Cell. The repeating module is then meshed into a dense grid of finite elements and solved by finite element analysis. The technique is combined with topology optimization of infinite spatially periodic structures under arbitrary static loading. Minimum compliance structures under a constant volume of material are obtained by using the densities of material as design variables and by satisfying a classical optimality criterion which is generalized to encompass periodic structures. The method is illustrated with the design of an infinite strip possessing 1D translational symmetry and a cyclic structure under a tangential point force. A parametric study presents the evolution of the solution as a function of the aspect ratio of the Representative Cell.
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A FE methodology for the static analysis of infinite periodic structures under general loading
Computational Mechanics, 2001Co-Authors: E. Moses, Miriam Ryvkin, Moshe B. FuchsAbstract:This paper presents a finite element methodology for the static analysis of infinite periodic structures under arbitrary loads. The technique hinges on the method of Representative Cell which through the discrete Fourier transform reduces the original problem to a boundary value problem defined over one module, the Representative Cell. Starting from the weak form of the transformed problem, or from the FE equations of the infinite structure, the equilibrium equations are written in terms of the complex-valued displacement transforms which are considered as the displacements in the Representative Cell. Having found the displacements in the transformed domain, the real displacements anywhere in the real structure are obtained by numerical integration of the inverse transform. The theory, which is valid for spatial structures with 1D up to 3D translational symmetry, is illustrated with examples of periodic structures having 1D translational symmetry under general static loading.
Jacob Aboudi - One of the best experts on this subject based on the ideXlab platform.
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Three dimensional analysis of periodic fiber-reinforced composites with randomly broken and debonded fibers
International Journal of Engineering Science, 2020Co-Authors: Miriam Ryvkin, Jacob AboudiAbstract:Abstract A three-dimensional analysis is presented for the prediction of the behavior of periodic fiber-reinforced composites with numerous broken fibers and debonded fiber-matrix interfaces. The locations of these defects in the composite are randomly determined. The analysis is based on the Representative Cell method and the higher-order theory. In the framework of the Representative Cell method, the problem for the Representative volume element of the damaged composite that includes multiple fibers is reduced, in conjunction with the triple discrete Fourier transform, to the problem for repetitive Cell of undamaged composite including just a single Cell. The solution of this boundary-value problem is obtained by the higher-order theory. The inversion of the transform, in conjunction with an iterative procedure, establishes the elastic field at any point of the damaged composite. The optimal size of the Representative volume element of the damaged composite within which the computations are performed is determined. The present method is capable of predicting the resulting field distributions in the composite as well as the average values of the effective moduli of the randomly damage composite and the resulting stress concentration factors. These average values and the corresponding standard deviations are determined by repeating the analysis several times (scores). A parametric study of the dependence of the effective elastic moduli and stress concentration factors upon the level of damage is performed. In addition, comparisons with a micromechanical theory predictions which are based on the analysis of a repeating unit Cell, established by the assumption of spatial damage periodicity, are given.
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Field distributions in piezoelectric composites with semi-infinite cracks
Journal of Intelligent Material Systems and Structures, 2016Co-Authors: Jacob AboudiAbstract:A method is offered for the prediction of the electromechanical field in periodic piezoelectric composites with embedded semi-infinite cracks. It is based on the knowledge of the K-field in piezoelectric materials in which the material constants are replaced by the effective moduli of the piezoelectric composite. In addition to the existing semi-infinite crack, the proposed method can analyze localized inhomogeneities near the crack tip. The established effective K-field is applied at the boundaries of a rectangular domain that should be sufficiently far away from the crack tip and the other inhomogeneities. The proposed approach is based on the combined utilization of a micromechanical analysis, the Representative Cell method and the higher-order theory. The micromechanical analysis establishes the effective electromechanical constants of the piezoelectric composite, and the Representative Cell method reduces the periodic composite that is discretized into numerous identical Cells to a single Cell proble...
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Three-dimensional continuum analysis for a unidirectional composite with a broken fiber
International Journal of Solids and Structures, 2008Co-Authors: Miriam Ryvkin, Jacob AboudiAbstract:AbstractThe three-dimensional problem of a periodic unidirectional composite with a penny-shaped crack traversing one of the fibers is analyzed by the continuum equations of elasticity. The solution of the crack problem is represented by a superposition of weighted unit normal displacement jump solutions, everyone of which forms a Green’s function. The Green’s functions for the unbounded periodic composite are obtained by the combined use of the Representative Cell method and the higher-order theory. The Representative Cell method, based on the triple discrete Fourier transform, allows the reduction of the problem of an infinite domain to a problem of a finite one in the transform space. This problem is solved by the higher-order theory according to which the transformed displacement vector is expressed by a second order expansion in terms of local coordinates, in conjunction with the equilibrium equations and the relevant boundary conditions. The actual elastic field is obtained by a numerical evaluation of the inverse transform. The accuracy of the suggested approach is verified by a comparison with the exact analytical solution for a penny-shaped crack embedded in a homogeneous medium. Results for a unidirectional composite with a broken fiber are given for various fiber volume fractions and fiber-to-matrix stiffness ratios. It is shown that for certain parameter combinations the use of the average stress in the fiber, as it is employed in the framework of the shear lag approach, for the prediction of composite’s strength, leads to an over estimation. To this end, the concept of “point stress concentration factor” is introduced to characterize the strength of the composite with a broken fiber. Several generalizations of the proposed approach are offered
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a continuum approach to the analysis of the stress field in a fiber reinforced composite with a transverse crack
International Journal of Solids and Structures, 2007Co-Authors: Miriam Ryvkin, Jacob AboudiAbstract:Abstract The stress field in a periodically layered composite with an embedded crack oriented in the normal direction to the layering and subjected to a tensile far-field loading is obtained based on the continuum equations of elasticity. This geometry models the 2D problem of fiber reinforced materials with a transverse crack. The analysis is based on the combination of the Representative Cell method and the higher-order theory. The Representative Cell method is employed for the construction of Green’s functions for the displacements jumps along the crack line. The problem of the infinite domain is reduced, in conjunction with the discrete Fourier transform, to a finite domain (Representative Cell) on which the Born–von Karman type boundary conditions are applied. In the framework of the higher-order theory, the transformed elastic field is determined by a second-order expansion of the displacement vector in terms of local coordinates, in conjunction with the equilibrium equations and these boundary conditions. The accuracy of the proposed approach is verified by a comparison with the analytical solution for a crack embedded in a homogeneous plane. Results show the effects of crack lengths, fiber volume fractions, ratios of fiber to matrix Young’s moduli and matrix Poisson’s ratio on the resulting elastic field at various locations of interest. Comparisons with the predictions obtained from the shear lag theory are presented.
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Analysis of Local Thermomechanical Effects in Fiber-Reinforced Periodic Composites
International Journal of Fracture, 2007Co-Authors: Miriam Ryvkin, Jacob AboudiAbstract:Two approaches are combined to investigate the effect of localized thermomechanical loadings of periodic multiphase materials. The first one, referred to as the Representative Cell method, reduces the infinite domain problem to a problem for the periodicity Cell by means of the discrete Fourier transform. This problem is solved by the discretization of the Cell into several subCells and a second order expansion of the displacements transform vector in terms of local coordinates. Results for boron/epoxy and glass/epoxy composites subjected to localized mechanical and thermal loadings are presented, and they are compared with analytical solutions for homogeneous materials.
Komlanvi Madou - One of the best experts on this subject based on the ideXlab platform.
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a gurson type criterion for porous ductile solids containing arbitrary ellipsoidal voids i limit analysis of some Representative Cell
Journal of The Mechanics and Physics of Solids, 2012Co-Authors: Komlanvi Madou, Jean-baptiste LeblondAbstract:Abstract Gurson (1977) 's famous model of the behavior of porous ductile solids, initially developed for spherical cavities, was extended by Gologanu et al., 1993 , Gologanu et al., 1994 , Gologanu et al., 1997 to spheroidal, both prolate and oblate voids. The aim of this work is to further extend it to general (non-spheroidal) ellipsoidal cavities, through approximate homogenization of some Representative elementary porous Cell. As a first step, we perform in the present Part I a limit-analysis of such a Cell, namely an ellipsoidal volume made of some rigid-ideal-plastic von Mises material and containing a confocal ellipsoidal void, loaded arbitrarily under conditions of homogeneous boundary strain rate. This analysis provides an estimate of the overall plastic dissipation based on a family of trial incompressible velocity fields recently discovered by Leblond and Gologanu (2008) , satisfying conditions of homogeneous strain rate on all ellipsoids confocal with the void and the outer boundary. The asymptotic behavior of the integrand in the expression of the global plastic dissipation is studied both far from and close to the void. The results obtained suggest approximations leading to explicit approximate expressions of the overall dissipation and yield function. These expressions contain parameters the full determination of which will be the object of Part II.
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A Gurson-type criterion for porous ductile solids containing arbitrary ellipsoidal voids—I: Limit-analysis of some Representative Cell
Journal of the Mechanics and Physics of Solids, 2012Co-Authors: Komlanvi Madou, Jean-baptiste LeblondAbstract:Gurson (1977)'s famous model of the behavior of porous ductile solids, initially developed for spherical cavities, was extended by Gologanu et al. (1993, 1994, 1997) to spheroidal, both prolate and oblate voids. The aim of this work is to further extend it to general (non-spheroidal) ellip-soidal cavities, through approximate homogenization of some Representative elementary porous Cell. As a first step, we perform in the present Part I a limit-analysis of such a Cell, namely an ellipsoidal volume made of some rigid-ideal-plastic von Mises material and containing a confo-cal ellipsoidal void, loaded arbitrarily under conditions of homogeneous boundary strain rate. This analysis provides an estimate of the overall plastic dissipation based on a family of trial incompressible velocity fields recently discovered by Leblond and Gologanu (2008), satisfying conditions of homogeneous strain rate on all ellipsoids confocal with the void and the outer boundary. The asymptotic behavior of the integrand in the expression of the global plastic dissipation is studied both far from and close to the void. The results obtained suggest approximations leading to explicit approximate expressions of the overall dissipation and yield function. These expressions contain parameters the full determination of which will be the object of Part II.
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A Gurson-type criterion for porous ductile solids containing arbitrary ellipsoidal voids—I: Limit-analysis of some Representative Cell
Journal of the Mechanics and Physics of Solids, 2012Co-Authors: Komlanvi Madou, Jean-baptiste LeblondAbstract:Abstract Gurson (1977) 's famous model of the behavior of porous ductile solids, initially developed for spherical cavities, was extended by Gologanu et al., 1993 , Gologanu et al., 1994 , Gologanu et al., 1997 to spheroidal, both prolate and oblate voids. The aim of this work is to further extend it to general (non-spheroidal) ellipsoidal cavities, through approximate homogenization of some Representative elementary porous Cell. As a first step, we perform in the present Part I a limit-analysis of such a Cell, namely an ellipsoidal volume made of some rigid-ideal-plastic von Mises material and containing a confocal ellipsoidal void, loaded arbitrarily under conditions of homogeneous boundary strain rate. This analysis provides an estimate of the overall plastic dissipation based on a family of trial incompressible velocity fields recently discovered by Leblond and Gologanu (2008) , satisfying conditions of homogeneous strain rate on all ellipsoids confocal with the void and the outer boundary. The asymptotic behavior of the integrand in the expression of the global plastic dissipation is studied both far from and close to the void. The results obtained suggest approximations leading to explicit approximate expressions of the overall dissipation and yield function. These expressions contain parameters the full determination of which will be the object of Part II.