Strain localization in an orthotropic elastoplastic and elasto-viscoplastic material

Abstract

The strain localization phenomena in an orthotropic material are examined for understanding the effect of anisotropy upon the onset of shear localization and the development of shear band. We are concerned with the material instability analysis of an orthotropic elastic-plastic material and the linear stability analysis of an orthotropic thermo elasto-viscoplastic material in order to find the onset of localization. Moreover, finite element simulation for shear strain localization is carried out for both an orthotropic elasto-viscoplastic material and an orthotropic thermo elasto-viscoplastic material under plane strain uniaxial loading. Throughout the analysis, Hill``s orthotropic yield criterion is employed and based upon the representation theorem the plastic spin concept is introduced into the orthotropic elasto-viscoplastic constitutive relation for representing the evolution of orthotropic axes. Under a given plane strain uniaxial loading or plane stress biaxial loading, the procedure of the material instability analysis for the orthotropic rate-independent materials, which emerges as the limit of the rate-dependent solid, is formulated in order to obtain the critical hardening modulus and the corresponding shear band orientation. Moreover, the effect of plastic spin upon the onset of shear band in the orthotropic elastoplastic material is found via this instability analysis. The linear stability analysis procedure of nonlinear governing equations is presented for the thermo - elasto viscoplastic orthotropic material. The energy equation is introduced for the heat transfer analysis in the thermo-mechanical problem. The characteristic equation is obtained for the stability condition of a plane strain block under a homogeneous deformation by introducing an initial perturbation. The effect of initial orthotropic axes as well as wave length of perturbartion upon the shear band orientation is examined. The displacement based finite element method for the quas...