# A three-dimensional constitutive model for the martensitic transformation in polycrystalline shape memory alloys under large deformation

## TL;DR

This paper introduces a 3D constitutive model for polycrystalline shape memory alloys that accurately captures large deformations and rotations using logarithmic strain, improving upon existing models by reducing artificial stress errors.

## Contribution

The paper develops a novel thermodynamics-based model utilizing logarithmic strain and rate, with detailed implementation for simulating large deformation behaviors in SMAs.

## Key findings

- Model accurately predicts cyclic loading behavior of SMA components.
- Implementation in finite element software shows reduced artificial stress errors.
- Numerical experiments validate the model's effectiveness for large deformation analysis.

## Abstract

This work presents a three-dimensional constitutive model for the martensitic transformation in polycrystalline Shape Memory Alloys (SMAs) under large deformation. By utilizing the logarithmic strain and rate, the model is able to account for large strains and rotations that SMA-based components may undertake, but also resolves the artificial stress errors caused by the non-integrable objective rates that are widely used in current commercial finite element software. The model is developed through classical thermodynamic laws combined with the standard Coleman-Noll procedure. The scalar martensitic volume fraction and the second-order transformation strain tensor are chosen as the internal state variables to capture the material response exhibited by polycrystalline SMAs. A detailed implementation procedure of the proposed model is described through a user-defined material subroutine. Numerical experiments considering SMA components including a bar, a beam, a torque tube and a solid flexible structure under stress/thermally-induced phase transformations are investigated via the proposed model, and the results under cyclic loading are compared against the predictions provided by the Abaqus nonlinear solver. The development framework of the proposed model and its implementation procedure can be extended to incorporate other nonlinear phenomena exhibited by SMAs, such as transformation-induced plasticity, viscoplasticity, and damage under large deformation.