Discontinuous Bifurcation Analysis of a Coupled Rate-Dependent Damage and Plasticity Model for Impact Responses

Abstract

To identify the transition from continuous to discontinuous modes in the failure evolution of quasibrittle materials under impact, a coupled rate-dependent damage and plasticity model is developed within the thermodynamics framework. Due to the simplicity in model formulation, a continuum tangent stiffness tensor could be obtained for discontinuous bifurcation analysis, and the model parameters could be calibrated from split Hopkins pressure bar experimental data available. The coupled rate-dependent model could describe not only the pressure-dependent hardening/softening response but also the degradation of material stiffness under impact. A geometric criterion with a corresponding solution scheme is presented to explore the rate-dependent transition from continuous to discontinuous failure modes in the Mohr coordinates. The uniaxial compressive loading path is considered to illustrate the loading rate effect on the critical localization orientation and hardening parameters. It appears from the preliminary results that the coupled rate-dependent local continuum model might be combined with a decohesion model via discontinuous bifurcation analysis so that large-scale simulation of failure evolution could be performed without invoking higher-order spatial terms in the stress-strain space.