FINITE ELEMENT IMPLEMENTATION OF A SUPER-ELASTIC CONSTITUTIVE MODEL FOR TRANSFORMATION RATCHETTING OF NiTi ALLOY

Abstract

In the previous work, a new constitutive model describing the transformation ratchetting of super-elastic NiTi alloy was proposed. The finite element implementation of the proposed model is discussed in this work, because such implementation is necessary to launch a numerical analysis for the cyclic stress–strain responses of NiTi alloy devices including the transformation ratchetting. During the implementation, a new stress integration algorithm is adopted, and a new expression of the consistent tangent modulus is derived for the forward transformation and the reverse transformation. The finite element implementation is elaborated by the user subroutine of UMAT in ABAQUS based on backward Euler method. The accumulated error during cyclic transformation is controlled by a robust convergence criterion. Finally, the validity of such implementation is verified by several numerical examples.