A finite element model for shape memory alloys considering thermomechanical couplings at large strains

INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES

卷:46

Article

Christ, Daniel¹  Reese, Stefanie¹ 

[1] Tech Univ Carolo Wilhelmina Braunschweig, Inst Solid Mech, D-38106 Braunschweig, Germany

关键词: Phase transformation;    Thermomechanical processes;    Constitutive behaviour;    Finite strain;    Finite elements;   

DOI  :  10.1016/j.ijsolstr.2009.06.017

来源: Elsevier

【 摘 要 】

In the present work we propose a new thermomechanically coupled material model for shape memory alloys (SMA) which describes two important phenomena typical for the material behaviour of shape memory alloys: pseudoelasticity as well as the shape memory effect. The constitutive equations are derived in the framework of large strains since the martensitic phase transformation involves inelastic deformations up to 8%, or even up to 20% if the plastic deformation after the phase transformation is taken into account. Therefore, we apply a multiplicative split of the deformation gradient into elastic and inelastic parts, the latter concerning the martensitic phase transformation. An extended phase transformation function has been considered to include the tension-compression asymmetry particularly typical for textured SMA samples. In order to apply the concept in the simulation of complex structures, it is implemented into a finite element code. This implementation is based on an innovative integration scheme for the existing evolution equations and a monolithic solution algorithm for the coupled mechanical and thermal fields. The coupling effect is accurately investigated in several numerical examples including pseudoelasticity as well as the free and the suppressed shape memory effect. Finally, the model is used to simulate the shape memory effect in a medical foot staple which interacts with a bone segment. (C) 2009 Elsevier Ltd. All rights reserved.

【 授权许可】

Free