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Micromorphic approach for gradient elasticity, viscoplasticity, and damage / Samuel Forest in Journal of engineering mechanics, Vol. 135 N°3 (Mars 2009) 

Public ISBD [article]  in Journal of engineering mechanics > Vol. 135 N°3 (Mars 2009) . - pp. 117-131 Titre : Micromorphic approach for gradient elasticity, viscoplasticity, and damage Type de document : texte imprimé Auteurs : Samuel Forest, Auteur Article en page(s) : pp. 117-131 Note générale : Mécanique appliquée Langues : Anglais (eng) Mots-clés : Elasticity  Damage  Viscoplasticity. Résumé : A unifying thermomechanical framework is presented that reconciles several classes of gradient elastoviscoplasticity and damage models proposed in the literature during the last 40 years. It is based on the introduction of the micromorphic counterpart chiphi of a selected state or internal variable phi in a standard constitutive model. In addition to the classical balance of momentum equation, a balance of micromorphic momentum is derived that involves generalized stress tensors. The corresponding additional boundary conditions are also deduced from the procedure. The power of generalized forces is assumed to contribute to the energy balance equation. The free energy density function is then chosen to depend on a relative generalized strain, typically phi-chiphi, and the microstrain gradient [del]chiphi. When applied to the deformation gradient itself, phi[equivalent][bold F][underaccent undertilde [below] , the method yields the micromorphic theory of Eringen and Mindlin together with its extension to finite deformation elastoviscoplasticity by Forest and Sievert. If the selected variable is the cumulative plastic strain, the theory reduces to the so-called “nonlocal implicit gradient-enhanced elastoplasticity model” by Engelen, Geers, and Peerlings, provided that simplified linear relationships are adopted between generalized stresses and strains. The same holds if the micromorphic variable coincides with a microdamage variable. If the internal constraint is introduced that the micromorphic variable chiphi remains as close as possible to the macroscopic variable phi, the micromorphic model reduces to the second gradient or gradient of internal variable approach as defined by Maugin. If the selected variable is the cumulative plastic strain or the full plastic strain tensor, the constrained micromorphic theory delivers Aifantis-like strain gradient plasticity models. The advantage of the micromorphic approach is that it provides the generalized balance equation under nonisothermal conditions and offers the setting for anisotropic nonlinear constitutive relations between generalized stress and strains in contrast to most existing models. In rate-independent plasticity, it is shown that there is generally no need for a variational formulation of the yield condition. DEWEY : 620.1 ISSN : 0733-9399 En ligne : http://ascelibrary.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=JENMDT000 [...] [article] Micromorphic approach for gradient elasticity, viscoplasticity, and damage [texte imprimé] / Samuel Forest, Auteur . - pp. 117-131. Mécanique appliquée Langues : Anglais (eng) in Journal of engineering mechanics > Vol. 135 N°3 (Mars 2009) . - pp. 117-131 Mots-clés : Elasticity  Damage  Viscoplasticity. Résumé : A unifying thermomechanical framework is presented that reconciles several classes of gradient elastoviscoplasticity and damage models proposed in the literature during the last 40 years. It is based on the introduction of the micromorphic counterpart chiphi of a selected state or internal variable phi in a standard constitutive model. In addition to the classical balance of momentum equation, a balance of micromorphic momentum is derived that involves generalized stress tensors. The corresponding additional boundary conditions are also deduced from the procedure. The power of generalized forces is assumed to contribute to the energy balance equation. The free energy density function is then chosen to depend on a relative generalized strain, typically phi-chiphi, and the microstrain gradient [del]chiphi. When applied to the deformation gradient itself, phi[equivalent][bold F][underaccent undertilde [below] , the method yields the micromorphic theory of Eringen and Mindlin together with its extension to finite deformation elastoviscoplasticity by Forest and Sievert. If the selected variable is the cumulative plastic strain, the theory reduces to the so-called “nonlocal implicit gradient-enhanced elastoplasticity model” by Engelen, Geers, and Peerlings, provided that simplified linear relationships are adopted between generalized stresses and strains. The same holds if the micromorphic variable coincides with a microdamage variable. If the internal constraint is introduced that the micromorphic variable chiphi remains as close as possible to the macroscopic variable phi, the micromorphic model reduces to the second gradient or gradient of internal variable approach as defined by Maugin. If the selected variable is the cumulative plastic strain or the full plastic strain tensor, the constrained micromorphic theory delivers Aifantis-like strain gradient plasticity models. The advantage of the micromorphic approach is that it provides the generalized balance equation under nonisothermal conditions and offers the setting for anisotropic nonlinear constitutive relations between generalized stress and strains in contrast to most existing models. In rate-independent plasticity, it is shown that there is generally no need for a variational formulation of the yield condition. DEWEY : 620.1 ISSN : 0733-9399 En ligne : http://ascelibrary.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=JENMDT000 [...]

Plasticité cristalline et transition d’échelle / Marc Fivel

Public ISBD in Techniques de l'ingénieur : étude et propriétés des métaux Ti551. Etude des métaux et des alliages / Bréchet, Yves  Titre : Plasticité cristalline et transition d’échelle : cas du monocristal : réf. internet M4016 Type de document : texte imprimé Auteurs : Marc Fivel, Auteur ; Samuel Forest, Auteur Année de publication : 2004 Importance : p. 207 - 230 Note générale : Bibliogr. p. 227 - 229 Langues : Français (fre) Mots-clés : Plasticité  cristalline Monocristal  --  Simulations Echelle  atomique  --  Simulations Note de contenu : Sommaire : 1. Simulations à l’échelle atomique 2. Simulations de dynamique des dislocations. Cas des CFC 3. Simulation du monocristal : lois de comportement à variables internes in Techniques de l'ingénieur : étude et propriétés des métaux Ti551. Etude des métaux et des alliages / Bréchet, Yves  Plasticité cristalline et transition d’échelle : cas du monocristal : réf. internet M4016 [texte imprimé] / Marc Fivel, Auteur ; Samuel Forest, Auteur . - 2004 . - p. 207 - 230. Bibliogr. p. 227 - 229 Langues : Français (fre) Mots-clés : Plasticité  cristalline Monocristal  --  Simulations Echelle  atomique  --  Simulations Note de contenu : Sommaire : 1. Simulations à l’échelle atomique 2. Simulations de dynamique des dislocations. Cas des CFC 3. Simulation du monocristal : lois de comportement à variables internes

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Plasticité cristalline et transition d’échelle : cas du polycristal / Marc Fivel

Public ISBD in Techniques de l'ingénieur : étude et propriétés des métaux Ti551. Etude des métaux et des alliages / Bréchet, Yves  Titre : Plasticité cristalline et transition d’échelle : cas du polycristal : réf. internet M4017 Type de document : texte imprimé Auteurs : Marc Fivel, Auteur ; Samuel Forest, Auteur Année de publication : 2004 Importance : p. 231 - 242 Langues : Français (fre) Mots-clés : Polycristal  --  Comportement Effets  échelle  --  Modélisation,  Simulation Note de contenu : Sommaire : 1. Comportement du polycristal 2. Modélisation et simulation des effets d’échelle in Techniques de l'ingénieur : étude et propriétés des métaux Ti551. Etude des métaux et des alliages / Bréchet, Yves  Plasticité cristalline et transition d’échelle : cas du polycristal : réf. internet M4017 [texte imprimé] / Marc Fivel, Auteur ; Samuel Forest, Auteur . - 2004 . - p. 231 - 242. Langues : Français (fre) Mots-clés : Polycristal  --  Comportement Effets  échelle  --  Modélisation,  Simulation Note de contenu : Sommaire : 1. Comportement du polycristal 2. Modélisation et simulation des effets d’échelle

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