An Eulerian Model for Pseudoelastic Shape Memory Alloys

Abstract

. BruhnsA thermodynamic model describing pseudoelasticity is proposed. The kinematics are based on a self-consistent Eulerian theory of finite deformations using the logarithmic rate. The thermomechanical state of the material is described by means of the mass fraction of martensite as internal state variable. From the Helmholtz free energy of the two-phase solid, a kinetic law for the evolution of martensite is derived, taking into account the heat generated during phase transition. The material model is implemented into a finite element code in an updated Lagrangian scheme. Its parameters are calibrated to experimental data. The characteristics of the model are illustrated by simulations under different loading conditions.

Thermomechanics of martensitic phase transitions in shape memory alloys, I: Constitutive theories for small and large deformations

“…However, the simulation of certain problems like stents or endoscopic devices requires a geometrically nonlinear theory. Referring to this, only a few geometrically nonlinear concepts have been proposed in the common literature: on the one hand, phenomenological theories were published in Qidwai and Lagoudas 2000;Helm 2001;Müller and Bruhns 2004]. On the other hand, in [Anand and Gurtin 2003;Thamburaja and Anand 2003;Jung et al 2004], the focus has been on micromechanical models at finite deformations.…”

Materialmodelling of shape memory alloys in range of large deformations

“…[5,6]) is preferred. Although a lot of these material models have been implemented into the finite element method, only a few of them are derived in the framework of finite deformations [7,8]. The goal of this work is to propose a three-dimensional material model which is able to reproduce the pseudoelastic behaviour within the large strain regime.…”

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“…However, the simulation of certain problems like stents or endoscopic devices requires a geometrically nonlinear theory. Referring to this, only a few geometrically nonlinear concepts have been proposed in the common literature: on the one hand, phenomenological theories were published in Qidwai and Lagoudas 2000;Helm 2001;Müller and Bruhns 2004]. On the other hand, in [Anand and Gurtin 2003;Thamburaja and Anand 2003;Jung et al 2004], the focus has been on micromechanical models at finite deformations.…”