1. Introduction#

Here we present a law of thermoelastoplastic behavior written in large deformations proposed by SIMO J.C. and MIEHE C. [bib1] which tends in small deformations to the model of elastoplastic behavior with isotropic work hardening and Von Mises criterion, described in [R5.03.02]. The kinematic choices make it possible, as with the simple update available via the keyword PETIT_REAC, to treat large displacements and large deformations but also large rotations in an exact manner.

The specific features of this model are as follows:

  • just as in small deformations, it is assumed the existence of a relaxed configuration, that is to say locally free of stress, which makes it possible to decompose the total deformation into a thermoelastic part and a plastic part,

  • the decomposition of this deformation into thermoelastic and plastic parts is no longer additive as in small deformations (or for large deformation models written in deformation rate with for example a Jaumann derivative) but multiplicative,

  • the elastic deformations are measured in the current configuration (deformed) while the plastic deformations are measured in the initial configuration,

  • as in small deformations, the stresses depend only on thermo-elastic deformations,

  • plastic deformations occur at a constant volume. The volume variation is then only due to thermoelastic deformations,

  • During its numerical integration, this model leads to an incrementally objective model (cf. [§3.3]), which makes it possible to obtain the exact solution in the presence of large rotations.

A viscous version of this model is also available (hyperbolic sine law as in the case of the Rousselier model ROUSS_VISC, cf. [R5.03.07]).

Subsequently, we briefly recall some concepts of mechanics in large deformations, then we present the behavioral relationships of the model and its numerical integration to treat the equilibrium equations.

An Eulerian variational formulation is proposed, with an update of the geometry. As such, we express the work of internal forces and its variation (in order to be solved by the Newton method) for the continuous problem, which provide respectively after discretization by finite elements the vector of internal forces and the tangent matrix.

Note Bene:

An in-depth presentation on major deformations can be found in [bib2] or [bib3].

This document is taken from [bib4] where we give a more detailed presentation of the elastoplastic model, its numerical integration and where we give some examples of validation.