A large time increment approach for thermo-mechanical problems

We extend a new approach to the non-isothermal case, for the resolution of isothermal viscoplastic problems. The computational method is well suited f or non-linear mechanical behaviour, described by internal variables. This a pproach is in contrast with the classical step-by-step method, as it is an iterative procedure that takes the whole loading process in a single time i nterval into account. The main point is to introduce a formulation of the t hermo-mechanical problem adapted to the strategy that we use; we gather all the non-linearities in the evolution laws in order to obtain the Linear st ate laws by using a change of variables that, also allows us to remove the temperature from the state laws, except from Hooke's elasticity law (in whi ch the effects of temperature are smooth). This formulation, called the nor mal formulation, is of great interest as it is well suited to most of the c lassical computational techniques and is particularly appropriate for the L Arge Time Increment (LATIN) method that we use. Several examples illustrate the possibilities and efficiency of this strategy. A good accuracy is obta ined in a few iterations, even in the case of realistic loading histories, and only a few linear elastic-type global problems have to be solved. (C) 1 999 Elsevier Science Ltd and Civil-Comp Ltd. All rights reserved.