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

Publication date: 8 October 2014

Abstract: 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 $Fmapsto W(F)=hat{W}(log U)$ defined in terms of logarithmic strain $log U$, where $U=sqrt{F^T, F}$, is everywhere rank-one convex as a function of $F$, the new function $Fmapsto widetilde{W}(F)=hat{W}(log U-log U_p)$ 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 in which $Fmapsto W(F, F_p^{-1})$ remains rank-one convex at every plastic distortion $F_p$ if $Fmapsto W(F)$ is rank-one convex. We show this disturbing feature with the help of a recently considered family of exponentiated Hencky energies.

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