Effects of elastic anisotropy on strain localization and flutter instability in plastic solids

The influence of elastic anisotropy on elastic-plastic acceleration wave speeds is analyzed when the elastic anisotropy is described by a second-order fabric tensor. For a particular-and physically sound-structure of the elastic tensor, a correspondence principle is established that reduces the analysis of strain localization to a problem relative to elastic isotropy. Thus analytic solutions available in the framework of elastic-plastic constitutive laws with isotropic elasticity can be used. Applications show the strong effects of elastic anisotropy on all the localization characteristics. For non-associative flow-laws, flutter instability, corresponding to the occurrence of complex conjugate squares of wave speeds, is considered. It is shown that, while this instability is precluded for elastic-plastic solids with elastic isotropy and obeying deviatoric associativity, this exclusion property is not preserved in the presence of anisotropic elasticity. In fact, we exhibit a particular structure of elasticity for which an infinitesimal amount of anisotropy is shown to give rise to flutter. (C) 1999 Elsevier Science Ltd. All rights reserved.