A geometrically characteristic and thermodynamically consistent theory to formulate the plasticity and damage of metallic solids at large deformation

A geometrically characteristic and thermodynamically consistent theory is proposed to describe the full-life mechanics of metallic solids undergoing large deformation. The theory is geometrically characteristic in the sense that the inelastic deformation caused by various crystalline defects is decomposed into a deviatoric part, a volumetric part, and a geometrically insensitive part, and the system thermodynamics is then formulated. The theory reaches its closure by including a finite-strain plastic flow rule originating from the postulate of maximum dissipation, and a set of thermodynamically consistent kinetic equations for the geometrically characteristic field quantities. The present theory is distinguished from existing ductile damage models in the following aspects. Firstly, the proposed geometrically characteristic measure of plasticity is conceptually valid throughout the whole deformation stage, enabling the calibration of the present theory simply against uniaxial loading data. Secondly, the stress calculation here is shown to be unconditionally convergent, and this is in contrast to the use of incremental tangent stiffness matrices whose eigenvalues inevitably turn negative in the softening stage. Thirdly, the anisotropic hardening behaviour can be modelled with low calibration requirements.