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

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.

References in corpus (3)

• A Finite Strain Constitutive Model for Martensitic Transformation in Shape Memory Alloys Based on Logarithmic Strain
• A Finite Strain Constitutive Model Considering Transformation Induced Plasticity for Shape Memory Alloys under Cyclic Loading
• A Three-dimensional Constitutive Model for Polycrystalline Shape Memory Alloys Under Large Strains Combined With Large Rotations

Cited by in corpus (4)

• Parallel Projection---An Improved Return Mapping Algorithm for Finite Element Modeling of Shape Memory Alloys
• Phase Transformation Characteristics of High-Temperature Shape Memory Alloy under Tension, Compression, and Bending Actuation Cycling
• Finite strain constitutive modeling for shape memory alloys considering transformation-induced plasticity and two-way shape memory effect
• Finite-strain constitutive model for shape memory alloys formulated in the logarithmic strain space