On the thermomechanical coupling in finite strain plasticity theory with non-linear kinematic hardening by means of incremental energy minimization

The thermomechanical coupling in finite strain plasticity theory with non-linear kinematic hardening is analyzed within the present paper. This coupling is of utmost importance in many applications, e.g., in those showing low cycle fatigue (LCF) under large strain amplitudes. Since the by now classical thermomechanical coupling originally proposed by Taylor and Quinney cannot be used directly in case of kinematic hardening, the change in heat as a result of plastic deformation is computed by applying the first law of thermodynamics. Based on this balance law, together with a finite strain plasticity model, a novel variationally consistent method is elaborated. Within this method and following Stainier and Ortiz (2010), all unknown variables are jointly and conveniently computed by minimizing an incrementally defined potential. In sharp contrast to previously published works, the evolution equations are a priori enforced by employing a suitable parameterization of the flow rule and the evolution equations. The advantages of this parameterization are, at least, twofold. First, it leads eventually to an unconstrained stationarity problem which can be directly applied to any yield function being positively homogeneous of degree one, i.e., the approach shows a broad range of application. Secondly, the parameterization provides enough flexibility even for a broad range of non-associative models such as kinematic hardening of Armstrong-Frederick-type. Different to Stainier and Ortiz (2010), the continuous variational problem is approximated by a standard, fully-implicit time integration. The applicability of the resulting numerical implementation is finally demonstrated by analyzing the thermodynamically coupled response for a loading cycle. (C) 2011 Elsevier Ltd. All rights reserved.