A novel approach to representative orientation distribution functions for modeling and simulation of polycrystalline shape memory alloys

A micromechanical model for polycrystalline shape memory alloys (SMAs) was introduced in a series of papers by Hackl and coauthors. In order to model the polycrystalline aspect, they assumed a specific set of orientation distribution functions that had to be resolved with high numerical effort. Although this model displays interesting aspects, its use to simulate macroscopic specimens is problematic due to the long calculation time.In this paper, we present a new approach to modeling and simulation of polycrystalline SMAs that is based on parameterization of a class of orientation distribution functions by using only a few parameters. A variational concept is applied to derive evolution equations for these parameters. The resultant material model drastically reduces the calculation time and may thus provide an approach to efficient micromechanical simulation of specimens that are of engineering interest.This study presents a variety of different numerical examples, such as pseudoelastic and pseudoplastic material behavior for CuAlNi and NiTi SMAs, to demonstrate the broad applicability of the material model. The numerical benefit of the presented modeling approach is demonstrated by comparative calculations of the new model versus the previous model. Copyright (c) 2014 John Wiley & Sons, Ltd.