Loss of ellipticity for non-coaxial plastic deformations in additive logarithmic finite strain plasticity

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• 作者：Patrizio Neff^a ; ^{patrizio.neff@uni-due.de" class="auth_mail" title="E-mail the corresponding author} ; Ionel-Dumitrel Ghiba^b ; ^c ; ^{dumitrel.ghiba@uni-due.de" class="auth_mail" title="E-mail the corresponding author} ; ^{dumitrel.ghiba@uaic.ro" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Hencky energy ; Ellipticity domain ; Isotropic formulation ; Additive plasticity
• 刊名：International Journal of Non-Linear Mechanics
• 出版年：2016
• 出版时间：May 2016
• 年：2016
• 卷：81
• 期：Complete
• 页码：122-128
• 全文大小：623 K

文摘

In this paper we consider the additive logarithmic finite strain plasticity formulation from the view point of loss of ellipticity in elastic unloading. We prove that even if an elastic energy $F\mapsto W\left(F\right)=\widehat{W}\left(\log U\right)$ defined in terms of logarithmic strain logU$\log U$, where $U=\sqrt{F^{T}F}$, happens to be everywhere rank-one convex as a function of F  , the new function $F\mapsto \tilde{W}\left(F\right)=\widehat{W}(\log U-\log U_p)$ need not remain rank-one convex at some given plastic stretch U_p (viz. $E_p^{\log }≔\log U_p$). This is in complete contrast to multiplicative plasticity (and infinitesimal plasticity) in which $F\mapsto W\left(F{F}_p^{-1}\right)$ remains rank-one convex at every plastic distortion F_p if F↦W(F)$F\mapsto W\left(F\right)$ is rank-one convex ($\nabla u\mapsto \parallel \mathrm{sym}\nabla u-{\epsilon }_p{\parallel }^2$ remains convex). We show this disturbing feature of the additive logarithmic plasticity model with the help of a recently introduced family of exponentiated Hencky energies.