Implicit stress integration procedure for large strains of the reformulated Shape Memory Alloys material model

Abstract

© 2019, Springer-Verlag GmbH Germany, part of Springer Nature. Devices made of Shape-Memory Alloys (SMA) often exhibit a superelasticity or a shape memory effect during the exploitation. Both effects include large deformations up to 10% or large rotations, and a large-strain stress integration procedure is necessary for a correct numerical simulation. For this purpose, a reformulation of the existing SMA phenomenological constitutive model is introduced to provide an effective implementation into the Finite Element Method code. All variables are derived in a scalar form, which allows an extension of the small-strain solution to the large-strain problems. The multiplicative decomposition of the deformation gradient is employed to compute the proper strain measure as an input variable for the unified stress integration procedure. An appropriate conjugated stress measure is computed, and the variables necessary for further computation are updated. The verification is presented in several selected examples.