An analytical–numerical approach for the stability analysis of large strain thermo-elastoplastic material models

The paper deals with the notion of stability for thermo-elastoplastic materials undergoing large strains. The stability analysis is performed by using the perturbation approach applied to a comprehensive material model derived in a thermodynamic format. As the main contribution of this paper a stability condition for a material model incorporating geometrical and material non-linearities under full thermo-mechanical coupling, without typical simplifying assumptions, is derived, and a hybrid analytical-numerical verification of the stability condition at a material point is investigated for the three-dimensional case. Special emphasis is placed on the quasi-static case, for which a specific stability criterion is derived. The theoretical analysis is followed by the numerical verification of the obtained condition. The implementation of the model in the finite element method, using the numerical-symbolic package AceGen, is also presented in the paper. Two representative three-dimensional examples are solved, namely a cube under simple shear and a plate with imperfection, subjected to tension. The obtained results reveal that the type of softening, i.e., thermal or material softening, has a significant influence on the stability at a material point level.