Finite element analysis of adaptative systems

Etienne Patoor 1Bertrand PEULTIER Tarak BEN ZINEB 

1. Laboratoire de Physique et de mécanique des matériaux, UMR CNRS 7554 (LPMM), Ile du Saulcy, Metz 57045, France

Abstract

Shape Memory Alloys are widely used in several fields such as aeronautics or biomedical applications due to their unique behaviors (superelasticity, constrain recovery, shape memory). These behaviors originate from a thermoelastic martensitic transformation responsible for the coupling between mechanical and thermal properties observed in these materials. Optimisation of applications dealing with SMA requires the determination of numerical simulation tools able to capture this coupling. This communication presents the implementation into a commercial FEM code of a SMA constitutive law developed from micromechanical considerations.

This thermomechanical constitutive law is derived from a micromechanical approach in such a way to reach an analytical description adapted to structure analysis by finite element method. In order to preserve a good description of physical phenomena at the origin of SMA behaviours a two internal variables description is introduced. The first variable corresponds to the volume fraction of martensite and the second one is a tensorial one corresponding to the Mean Transformation Strain (MTS) defined over the RVE. This MTS is connected to the phase transformation induced by mechanical and/or thermal loading and also to the reorientation process observed in the martensitic state. This model describes in a unified way superelasticity, constrained recovery and shape memory effect. Simulations obtained are confronted with an experimental data base determined on NiTi alloys.

The implementation of this model in the Abaqus FE code is ensured via the subroutine Umat (User MATerial) where the thermomechanical tangent operators are calculated. This subroutine updates stresses and internal variables. The Newton-Raphson numerical method is adopted for the resolution of this problem. Application of this finite element analysis is presented on SMA structures.

Presentation: oral at E-MRS Fall Meeting 2005, Symposium C, by Etienne Patoor
See On-line Journal of E-MRS Fall Meeting 2005

Submitted: 2005-05-23 07:42
Revised:   2009-06-07 00:44
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