Thermo-Elasto-Viscoplastic Modeling Of The Behavior Of Metals Submitted To Finite Strains. A Coupled Thermo-Mechanical Approach.

Abstract

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