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Christian Miehe - One of the best experts on this subject based on the ideXlab platform.
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On evolving deformation microstructures in non-convex partially damaged solids
Journal of the Mechanics and Physics of Solids, 2011Co-Authors: Ercan Gurses, Christian MieheAbstract:Abstract The paper outlines a relaxation method based on a particular isotropic microstructure evolution and applies it to the model problem of rate independent, partially damaged solids. The method uses an incremental variational formulation for standard dissipative materials. In an incremental setting at finite time steps, the formulation defines a quasi-hyperelastic Stress Potential. The existence of this Potential allows a typical incremental boundary value problem of damage mechanics to be expressed in terms of a principle of minimum incremental work. Mathematical existence theorems of minimizers then induce a definition of the material stability in terms of the sequential weak lower semicontinuity of the incremental functional. As a consequence, the incremental material stability of standard dissipative solids may be defined in terms of weak convexity notions of the Stress Potential. Furthermore, the variational setting opens up the possibility to analyze the development of deformation microstructures in the post-critical range of unstable inelastic materials based on energy relaxation methods. In partially damaged solids, accumulated damage may yield non-convex Stress Potentials which indicate instability and formation of fine-scale microstructures. These microstructures can be resolved by use of relaxation techniques associated with the construction of convex hulls. We propose a particular relaxation method for partially damaged solids and investigate it in one- and multi-dimensional settings. To this end, we introduce a new isotropic microstructure which provides a simple approximation of the multi-dimensional rank-one convex hull. The development of those isotropic microstructures is investigated for homogeneous and inhomogeneous numerical simulations.
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On evolving deformation microstructures in non-convex partially damaged solids
Journal of the Mechanics and Physics of Solids, 2011Co-Authors: Ercan Gurses, Christian MieheAbstract:The paper outlines a relaxation method based on a particular isotropic microstructure evolution and applies it to the model problem of rate independent, partially damaged solids. The method uses an incremental variational formulation for standard dissipative materials. In an incremental setting at finite time steps, the formulation defines a quasi-hyperelastic Stress Potential. The existence of this Potential allows a typical incremental boundary value problem of damage mechanics to be expressed in terms of a principle of minimum incremental work. Mathematical existence theorems of minimizers then induce a definition of the material stability in terms of the sequential weak lower semicontinuity of the incremental functional. As a consequence, the incremental material stability of standard dissipative solids may be defined in terms of weak convexity notions of the Stress Potential. Furthermore, the variational setting opens up the possibility to analyze the development of deformation microstructures in the post-critical range of unstable inelastic materials based on energy relaxation methods. In partially damaged solids, accumulated damage may yield non-convex Stress Potentials which indicate instability and formation of fine-scale microstructures. These microstructures can be resolved by use of relaxation techniques associated with the construction of convex hulls. We propose a particular relaxation method for partially damaged solids and investigate it in one- and multi-dimensional settings. To this end, we introduce a new isotropic microstructure which provides a simple approximation of the multi-dimensional rank-one convex hull. The development of those isotropic microstructures is investigated for homogeneous and inhomogeneous numerical simulations. © 2011 Elsevier Ltd. All rights reserved
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Microstructure Development in Standard Dissipative Solids Based on Energy Minimization
GAMM-Mitteilungen, 2006Co-Authors: Christian MieheAbstract:The paper provides an overview about recent developments in the formulation and numerical implementation of incremental minimization principles for inelastic solids and their exploitation with regard to the analysis of deformation microstructures. The point of departure is a general internal variable formulation for standard dissipative materials. Consistent with this type of finite inelasticity we outline a distinct incremental variational formulation of the local constitutive response where an incremental Stress Potential is obtained from a local minimization problem with respect to the internal variables. The existence of the incremental Stress Potential allows the formulation of I BVPs for standard dissipative solids as a sequence of incremental minimization problems. The stability of these incremental problems is controlled by weak convexity properties of the incremental Stress Potential. Micro–structure developments in incrementally non–convex dissipative solids can be resolved by relaxation methods based on convexification analyses. The relaxed problems provide a wel–posed overall response of the instable dissipative solid as close as possible to the original problem. We consider the basic set up of these relaxation analyses for dissipative standard materials in terms of incremental minimization problems for exact and approximated quasi and rankone convexifications and discuss details of their algorithmic implementations. The incremental energy minimization is applied to two conceptual model problems which treat microstructure developments in homogeneous and heterogeneous dissipative solids. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
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analysis of material instabilities in inelastic solids by incremental energy minimization and relaxation methods evolving deformation microstructures in finite plasticity
Journal of The Mechanics and Physics of Solids, 2004Co-Authors: Christian Miehe, Marc Lambrecht, Ercan GursesAbstract:Abstract We propose an approach to the definition and analysis of material instabilities in rate-independent standard dissipative solids at finite strains based on finite-step-sized incremental energy minimization principles. The point of departure is a recently developed constitutive minimization principle for standard dissipative materials that optimizes a generalized incremental work function with respect to the internal variables. In an incremental setting at finite time steps this variational problem defines a quasi-hyperelastic Stress Potential. The existence of this Potential allows to be recast a typical incremental boundary-value problem of quasi-static inelasticity into a principle of minimum incremental energy for standard dissipative solids. Mathematical existence theorems for sufficiently regular minimizers then induce a definition of the material stability of the inelastic material response in terms of the sequentially weakly lower semicontinuity of the incremental variational functional. As a consequence, the incremental material stability of standard dissipative solids may be defined in terms of the quasi-convexity or the rank-one convexity of the incremental Stress Potential . This global definition includes the classical local Hadamard condition but is more general. Furthermore, the variational setting opens up the possibility to analyze the post-critical development of deformation microstructures in non-stable inelastic materials based on energy relaxation methods. We outline minimization principles of quasi- and rank-one convexifications of incremental non-convex Stress Potentials for standard dissipative solids . The general concepts are applied to the analysis of evolving deformation microstructures in single-slip plasticity. For this canonical model problem, we outline details of the constitutive variational formulation and develop numerical and semi-analytical solution methods for a first-level rank-one convexification. A set of representative numerical investigations analyze the development of deformation microstructures in the form of rank-one laminates in single slip plasticity for homogeneous macro-deformation modes as well as inhomogeneous macroscopic boundary-value problems. The well-posedness of the relaxed variational formulation is indicated by an independence of typical finite element solutions on the mesh-size.
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analysis of microstructure development in shearbands by energy relaxation of incremental Stress Potentials large strain theory for standard dissipative solids
International Journal for Numerical Methods in Engineering, 2003Co-Authors: Christian Miehe, Marc LambrechtAbstract:We propose a fundamentally new approach to the treatment of shearband localizations in strain softening elastic–plastic solids at finite strains based on energy minimization principles associated with microstructure developments. The point of departure is a general internal variable formulation that determines the finite inelastic response as a standard dissipative medium. Consistent with this type of inelasticity we consider an incremental variational formulation of the local constitutive response where a quasi-hyperelastic Stress Potential is obtained from a local constitutive minimization problem with respect to the internal variables. The existence of this variational formulation allows the definition of the material stability of an inelastic solid based on weak convexity conditions of the incremental Stress Potential in analogy to treatments of finite elasticity. Furthermore, localization phenomena are interpreted as microstructure developments on multiple scales associated with non-convex incremental Stress Potentials in analogy to elastic phase decomposition problems. These microstructures can be resolved by the relaxation of non-convex energy functionals based on a convexification of the Stress Potential. The relaxed problem provides a well-posed formulation for a mesh-objective analysis of localizations as close as possible to the non-convex original problem. Based on an approximated rank-one convexification of the incremental Stress Potential we develop a computational two-scale procedure for a mesh-objective treatment of localization problems at finite strains. It constitutes a local minimization problem for a relaxed incremental Stress Potential with just one scalar variable representing the intensity of the microshearing of a rank-one laminate aligned to the shear band. This problem is sufficiently robust with regard to applications to large-scale inhomogeneous deformation processes of elastic–plastic solids. The performance of the proposed energy relaxation method is demonstrated for a representative set of numerical simulations of straight and curved shear bands which report on the mesh independence of the results. Copyright © 2003 John Wiley & Sons, Ltd.
Marc Lambrecht - One of the best experts on this subject based on the ideXlab platform.
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analysis of material instabilities in inelastic solids by incremental energy minimization and relaxation methods evolving deformation microstructures in finite plasticity
Journal of The Mechanics and Physics of Solids, 2004Co-Authors: Christian Miehe, Marc Lambrecht, Ercan GursesAbstract:Abstract We propose an approach to the definition and analysis of material instabilities in rate-independent standard dissipative solids at finite strains based on finite-step-sized incremental energy minimization principles. The point of departure is a recently developed constitutive minimization principle for standard dissipative materials that optimizes a generalized incremental work function with respect to the internal variables. In an incremental setting at finite time steps this variational problem defines a quasi-hyperelastic Stress Potential. The existence of this Potential allows to be recast a typical incremental boundary-value problem of quasi-static inelasticity into a principle of minimum incremental energy for standard dissipative solids. Mathematical existence theorems for sufficiently regular minimizers then induce a definition of the material stability of the inelastic material response in terms of the sequentially weakly lower semicontinuity of the incremental variational functional. As a consequence, the incremental material stability of standard dissipative solids may be defined in terms of the quasi-convexity or the rank-one convexity of the incremental Stress Potential . This global definition includes the classical local Hadamard condition but is more general. Furthermore, the variational setting opens up the possibility to analyze the post-critical development of deformation microstructures in non-stable inelastic materials based on energy relaxation methods. We outline minimization principles of quasi- and rank-one convexifications of incremental non-convex Stress Potentials for standard dissipative solids . The general concepts are applied to the analysis of evolving deformation microstructures in single-slip plasticity. For this canonical model problem, we outline details of the constitutive variational formulation and develop numerical and semi-analytical solution methods for a first-level rank-one convexification. A set of representative numerical investigations analyze the development of deformation microstructures in the form of rank-one laminates in single slip plasticity for homogeneous macro-deformation modes as well as inhomogeneous macroscopic boundary-value problems. The well-posedness of the relaxed variational formulation is indicated by an independence of typical finite element solutions on the mesh-size.
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analysis of microstructure development in shearbands by energy relaxation of incremental Stress Potentials large strain theory for standard dissipative solids
International Journal for Numerical Methods in Engineering, 2003Co-Authors: Christian Miehe, Marc LambrechtAbstract:We propose a fundamentally new approach to the treatment of shearband localizations in strain softening elastic–plastic solids at finite strains based on energy minimization principles associated with microstructure developments. The point of departure is a general internal variable formulation that determines the finite inelastic response as a standard dissipative medium. Consistent with this type of inelasticity we consider an incremental variational formulation of the local constitutive response where a quasi-hyperelastic Stress Potential is obtained from a local constitutive minimization problem with respect to the internal variables. The existence of this variational formulation allows the definition of the material stability of an inelastic solid based on weak convexity conditions of the incremental Stress Potential in analogy to treatments of finite elasticity. Furthermore, localization phenomena are interpreted as microstructure developments on multiple scales associated with non-convex incremental Stress Potentials in analogy to elastic phase decomposition problems. These microstructures can be resolved by the relaxation of non-convex energy functionals based on a convexification of the Stress Potential. The relaxed problem provides a well-posed formulation for a mesh-objective analysis of localizations as close as possible to the non-convex original problem. Based on an approximated rank-one convexification of the incremental Stress Potential we develop a computational two-scale procedure for a mesh-objective treatment of localization problems at finite strains. It constitutes a local minimization problem for a relaxed incremental Stress Potential with just one scalar variable representing the intensity of the microshearing of a rank-one laminate aligned to the shear band. This problem is sufficiently robust with regard to applications to large-scale inhomogeneous deformation processes of elastic–plastic solids. The performance of the proposed energy relaxation method is demonstrated for a representative set of numerical simulations of straight and curved shear bands which report on the mesh independence of the results. Copyright © 2003 John Wiley & Sons, Ltd.
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a two scale finite element relaxation analysis of shear bands in non convex inelastic solids small strain theory for standard dissipative materials
Computer Methods in Applied Mechanics and Engineering, 2003Co-Authors: Christian Miehe, Marc LambrechtAbstract:Abstract We propose a fundamentally new approach to the treatment of shear band localizations in strain-softening elastic–plastic solids at small strains based on energy minimization principles associated with micro-structure developments. The point of departure is a general internal variable formulation that determines the inelastic response as a standard dissipative medium. Consistent with this type of inelasticity we consider an incremental variational formulation of the local constitutive response where a quasihyperelastic Stress Potential is obtained from a local constitutive minimization problem with respect to the internal variables. The existence of this variational formulation allows the definition of the material stability of an inelastic solid based on weak convexity conditions of the incremental Stress Potential in analogy to treatments in finite elasticity. Furthermore, localization phenomena are interpreted as micro-structure developments on multiple scales associated with non-convex incremental Stress Potentials in analogy to elastic phase decomposition problems. These micro-structures can be resolved by the relaxation of non-convex energy functionals based on a convexification of the Stress Potential. The relaxed problem provides a well-posed formulation for a mesh-objective analysis of localizations as close as possible to the non-convex original problem. We develop, based on an approximated rank-one convexification of the incremental Stress Potential, a computational two-scale procedure for a mesh-objective treatment of localization problems. It constitutes a local minimization problem for a relaxed incremental Stress Potential with just one scalar variable representing the intensity of the micro-shearing of a rank-one laminate aligned to the shear band. This problem is sufficiently robust with regard to applications to large-scale inhomogeneous deformation processes of elastic–plastic solids. The performance of the proposed energy relaxation method is demonstrated for a representative set of numerical simulations of straight and curved shear bands which illustrate the mesh-independence of the results.
Pradeep R Guduru - One of the best experts on this subject based on the ideXlab platform.
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Measurement of Mechanical Properties and Stress-Potential Coupling in Lithiated Silicon
2011Co-Authors: Vijay A Sethuraman, Michael J. Chon, Pradeep R GuduruAbstract:Silicon is considered to be a promising anode material to increase the specific energy of lithium-ion batteries by as much as 50% 100%. For accurate modeling of battery performance, cycle life and reliability, there is a need to characterize the mechanical properties of lithiated silicon (an amorphous alloy of silicon and lithium). This work presents experimental determination of biaxial modulus and strain rate effects of lithiated silicon as a function of lithium concentration. Further, an analysis of the dependence of electric Potential on the state of Stress of a lithiated-silicon electrode is presented. Based on Larche and Cahn chemical Potential for a solid solution, a thermodynamic argument is made for the existence of the Stress-Potential coupling in lithiated-silicon and, based on the known properties of the material, the magnitude of the coupling is estimated to be ca. 60 mV/GPa in thin-film electrode geometry. An experimental investigation has been carried out in which the Stress was varied incrementally while measuring the electrode Potential simultaneously; the relation between Stress change and electric Potential change is measured to be 100 120 mV/GPa, which is within the same order of magnitude as the prediction. The importance of this coupling will be discussed in the context of interpreting the hysteresis loops observed in Potential vs. state-of-charge plots.
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in situ measurements of Stress Potential coupling in lithiated silicon
Journal of The Electrochemical Society, 2010Co-Authors: Vijay A Sethuraman, Venkat Srinivasan, Allan F Bower, Pradeep R GuduruAbstract:An analysis of the dependence of electric Potential on the state of Stress of a lithiated-silicon electrode is presented. Based on the Larche and Cahn chemical Potential for a solid solution, a thermodynamic argument is made for the existence of the StressPotential coupling in lithiated silicon; based on the known properties of the material, the magnitude of the coupling is estimated to be 60 mV/GPa in thin-film geometry. An experimental investigation is carried out on silicon thin-film electrodes in which the Stress is measured in situ during electrochemical lithiation and delithiation. By progressively varying the Stress through incremental delithiation, the relation between Stress change and electric-Potential change is measured to be 100–120 mV/GPa, which is of the same order of magnitude as the prediction of the analysis. The importance of the coupling is discussed in interpreting the hysteresis observed in the Potential vs state-of-charge plots and the role of Stress in modifying the maximum charge capacity of a silicon electrode under Stress.
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In Situ Measurements of Stress-Potential Coupling in Lithiated Silicon
Journal of The Electrochemical Society, 2010Co-Authors: Vijay A Sethuraman, Venkat Srinivasan, Allan F Bower, Pradeep R GuduruAbstract:An analysis of the dependence of electric Potential on the state of Stress of a lithiated-silicon electrode is presented. Based on the Larch\'e and Cahn chemical Potential for a solid solution, a thermodynamic argument is made for the existence of the Stress-Potential coupling in lithiated-silicon; based on the known properties of the material, the magnitude of the coupling is estimated to be ca. 60 mV/GPa in thin-film geometry. An experimental investigation is carried out on silicon thin-film electrodes in which the Stress is measured in situ during electrochemical lithiation and delithiation. By progressively varying the Stress through incremental delithiation, the relation between Stress change and electric-Potential change is measured to be 100 - 120 mV/GPa, which is of the same order of magnitude as the prediction of the analysis. The importance of the coupling is discussed in interpreting the hysteresis observed in Potential vs. state-of-charge plots, and the role of Stress in modifying the maximum charge capacity of a silicon electrode under Stress.
M Lambrecht - One of the best experts on this subject based on the ideXlab platform.
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energy relaxation of non convex incremental Stress Potentials in a strain softening elastic plastic bar
International Journal of Solids and Structures, 2003Co-Authors: M Lambrecht, Christian Miehe, Joachim DettmarAbstract:Abstract We propose a fundamentally new concept to the treatment of material instabilities and localization phenomena based on energy minimization principles in a strain-softening elastic–plastic bar. The basis is a recently developed incremental variational formulation of the local constitutive response for generalized standard media. It provides a quasi-hyperelastic Stress Potential that is obtained from a local minimization of the incremental energy density with respect to the internal variables. The existence of this variational formulation induces the definition of the material stability of inelastic solids based on convexity properties in analogy to treatments in elasticity. Furthermore, localization phenomena are understood as micro-structure development associated with a non-convex incremental Stress Potential in analogy to phase decomposition problems in elasticity. For the one-dimensional bar considered the two-phase micro-structure can analytically be resolved by the construction of a sequentially weakly lower semicontinuous energy functional that envelops the not well-posed original problem. This relaxation procedure requires the solution of a local energy minimization problem with two variables which define the one-dimensional micro-structure developing: the volume fraction and the intensity of the micro-bifurcation. The relaxation analysis yields a well-posed boundary-value problem for an objective post-critical localization analysis. The performance of the proposed method is demonstrated for different discretizations of the elastic–plastic bar which document on the mesh-independence of the results.
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Energy relaxation of non-convex incremental Stress Potentials in a strain-softening elastic–plastic bar
International Journal of Solids and Structures, 2003Co-Authors: M Lambrecht, Christian Miehe, Joachim DettmarAbstract:Abstract We propose a fundamentally new concept to the treatment of material instabilities and localization phenomena based on energy minimization principles in a strain-softening elastic–plastic bar. The basis is a recently developed incremental variational formulation of the local constitutive response for generalized standard media. It provides a quasi-hyperelastic Stress Potential that is obtained from a local minimization of the incremental energy density with respect to the internal variables. The existence of this variational formulation induces the definition of the material stability of inelastic solids based on convexity properties in analogy to treatments in elasticity. Furthermore, localization phenomena are understood as micro-structure development associated with a non-convex incremental Stress Potential in analogy to phase decomposition problems in elasticity. For the one-dimensional bar considered the two-phase micro-structure can analytically be resolved by the construction of a sequentially weakly lower semicontinuous energy functional that envelops the not well-posed original problem. This relaxation procedure requires the solution of a local energy minimization problem with two variables which define the one-dimensional micro-structure developing: the volume fraction and the intensity of the micro-bifurcation. The relaxation analysis yields a well-posed boundary-value problem for an objective post-critical localization analysis. The performance of the proposed method is demonstrated for different discretizations of the elastic–plastic bar which document on the mesh-independence of the results.
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homogenization of inelastic solid materials at finite strains based on incremental minimization principles application to the texture analysis of polycrystals
Journal of The Mechanics and Physics of Solids, 2002Co-Authors: Christian Miehe, Jan Schotte, M LambrechtAbstract:The paper presents new continuous and discrete variational formulations for the homogenization analysis of inelastic solid materials undergoing finite strains. The point of departure is a general internal variable formulation that determines the inelastic response of the constituents of a typical micro-structure as a generalized standard medium in terms of an energy storage and a dissipation function. Consistent with this type of finite inelasticity we develop a new incremental variational formulation of the local constitutive response, where a quasi-hyperelastic micro-Stress Potential is obtained from a local minimization problem with respect to the internal variables. It is shown that this local minimization problem determines the internal state of the material for finite increments of time. We specify the local variational formulation for a distinct setting of multi-surface inelasticity and develop a numerical solution technique based on a time discretization of the internal variables. The existence of the quasi-hyperelastic Stress Potential allows the extension of homogenization approaches of finite elasticity to the incremental setting of finite inelasticity. Focussing on macro-deformation-driven micro-structures, we develop a new incremental variational formulation of the global homogenization problem for generalized standard materials at finite strains, where a quasi-hyperelastic macro-Stress Potential is obtained from a global minimization problem with respect to the fine-scale displacement fluctuation field. It is shown that this global minimization problem determines the state of the micro-structure for finite increments of time. We consider three different settings of the global variational problem for prescribed displacements, non-trivial periodic displacements and prescribed Stresses on the boundary of the micro-structure and develop numerical solution methods based on a spatial discretization of the fine-scale displacement fluctuation field. Representative applications of the proposed minimization principles are demonstrated for a constitutive model of crystal plasticity and the homogenization problem of texture analysis in polycrystalline aggregates.
Vijay A Sethuraman - One of the best experts on this subject based on the ideXlab platform.
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Measurement of Mechanical Properties and Stress-Potential Coupling in Lithiated Silicon
2011Co-Authors: Vijay A Sethuraman, Michael J. Chon, Pradeep R GuduruAbstract:Silicon is considered to be a promising anode material to increase the specific energy of lithium-ion batteries by as much as 50% 100%. For accurate modeling of battery performance, cycle life and reliability, there is a need to characterize the mechanical properties of lithiated silicon (an amorphous alloy of silicon and lithium). This work presents experimental determination of biaxial modulus and strain rate effects of lithiated silicon as a function of lithium concentration. Further, an analysis of the dependence of electric Potential on the state of Stress of a lithiated-silicon electrode is presented. Based on Larche and Cahn chemical Potential for a solid solution, a thermodynamic argument is made for the existence of the Stress-Potential coupling in lithiated-silicon and, based on the known properties of the material, the magnitude of the coupling is estimated to be ca. 60 mV/GPa in thin-film electrode geometry. An experimental investigation has been carried out in which the Stress was varied incrementally while measuring the electrode Potential simultaneously; the relation between Stress change and electric Potential change is measured to be 100 120 mV/GPa, which is within the same order of magnitude as the prediction. The importance of this coupling will be discussed in the context of interpreting the hysteresis loops observed in Potential vs. state-of-charge plots.
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in situ measurements of Stress Potential coupling in lithiated silicon
Journal of The Electrochemical Society, 2010Co-Authors: Vijay A Sethuraman, Venkat Srinivasan, Allan F Bower, Pradeep R GuduruAbstract:An analysis of the dependence of electric Potential on the state of Stress of a lithiated-silicon electrode is presented. Based on the Larche and Cahn chemical Potential for a solid solution, a thermodynamic argument is made for the existence of the StressPotential coupling in lithiated silicon; based on the known properties of the material, the magnitude of the coupling is estimated to be 60 mV/GPa in thin-film geometry. An experimental investigation is carried out on silicon thin-film electrodes in which the Stress is measured in situ during electrochemical lithiation and delithiation. By progressively varying the Stress through incremental delithiation, the relation between Stress change and electric-Potential change is measured to be 100–120 mV/GPa, which is of the same order of magnitude as the prediction of the analysis. The importance of the coupling is discussed in interpreting the hysteresis observed in the Potential vs state-of-charge plots and the role of Stress in modifying the maximum charge capacity of a silicon electrode under Stress.
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In Situ Measurements of Stress-Potential Coupling in Lithiated Silicon
Journal of The Electrochemical Society, 2010Co-Authors: Vijay A Sethuraman, Venkat Srinivasan, Allan F Bower, Pradeep R GuduruAbstract:An analysis of the dependence of electric Potential on the state of Stress of a lithiated-silicon electrode is presented. Based on the Larch\'e and Cahn chemical Potential for a solid solution, a thermodynamic argument is made for the existence of the Stress-Potential coupling in lithiated-silicon; based on the known properties of the material, the magnitude of the coupling is estimated to be ca. 60 mV/GPa in thin-film geometry. An experimental investigation is carried out on silicon thin-film electrodes in which the Stress is measured in situ during electrochemical lithiation and delithiation. By progressively varying the Stress through incremental delithiation, the relation between Stress change and electric-Potential change is measured to be 100 - 120 mV/GPa, which is of the same order of magnitude as the prediction of the analysis. The importance of the coupling is discussed in interpreting the hysteresis observed in Potential vs. state-of-charge plots, and the role of Stress in modifying the maximum charge capacity of a silicon electrode under Stress.