摘要：Our goal in this paper is to present a complete thermo-viscoplastic formulation at finite strains and its implementation into a finite element code. The formulation is derived from the classical J2-viscoplasticity with a flow criterion expressed in the current configuration in terms of the Cauchy stress tensor and the temperature distribution. A staggered scheme will be used for the resolution of the thermomechanical problem as well as an extension of the radial return algorithm for the integration of the constitutive law. Indeed,as Simo & Miehe showed,1 staggered schemes are very attractive in comparison with monolithic (or simultaneous) schemes mainly because they involve the resolution of two linear symmetric systems in place of one larger nonsymmetric linear system. In the next sections we will briefly formulate the fundamentals of the kinematics for a large deformation approach, and the basic equations governing our model. After this, we will explain, in more details, the foundation of the staggered scheme and of the radial return algorithm introduced before. We will also describe the basis of the methodology used to take into account thermomechanical frictional contact problems. The formulation is inspired by those of Johansson & Klarbring2 and Oancea & Laursen.3 The constitutive equations used to quantify the amount of heat exchange between two bodies in frictional contact being based on the work of Yovanovich.4, 5
