A class of thermo-hyperelastic–viscoplastic models for porous materials: theory and numerics

Modelling and numerical issues in conjunction with large strain analysis of thermohyperelastic–viscoplastic models are discussed with emphasis placed on porous materials (metal powders). In order to account for the proper temperature effect on the rate-dependent response of metal powders, the concept of “viscoplastic admissibility” is employed as part of a model framework that includes a dynamic yield surface. A generic class of pressure-sensitive models is considered; a particular model based on quasistatic and dynamic yield surfaces, that are elliptic in the meridian planes in the principal stress space, is used for the subsequent numerical evaluation. The generic model also includes kinematic hardening, thus introducing non-coaxiality between the deformation, the back-stress and the stress tensors (in any given reference configuration). Implicit (backward Euler) integration is used and the corresponding algorithmic tangent stiffness (ATS) tensor is established in a setting that is valid for complete noncoaxiality. For the prototype problem of simple shear (using constant strain approximation), quadratic convergence in the equilibrium iterations is demonstrated. The paper is concluded by an investigation of a Hot-Isostatic-Pressing (HIP) problem, whereby experimental results from the literature are used for calibration of the model parameters.