Qualitative analysis of strain localization. Part I: Transversely isotropic elasticity and isotropic plasticity

While the conditions for the onset of strain localization in inelastic materials with isotropic elasticity have been extensively studied in recent years, few attempts have been devoted to investigate the effect of anisotropy and in particular the influence of the anisotropic elastic behavior on the localization phenomenon. In Part I of this paper, the localization analysis will be performed for an elastoplastic von Mises material with transversely isotropic elasticity subjected to uniaxial tension. Numerical and analytical results showing the influence of the deviation from isotropic elasticity on the onset of strain localization are presented. The anisotropic elastic behavior may substantially trigger the shear band initiation and modify the corresponding failure pattern. These observations become critical for highly damaged materials. Further developments concerning both transversely isotropic elasticity and plasticity are given in Part II of the paper.