3D phenomenological constitutive modeling of shape memory alloys based on microplane theory

摘要

This paper concerns 3D phenomenological modeling of shape memory alloys using microplane theory. In the proposed approach, transformation is assumed to be the only source of inelastic strain in 1D constitutive laws considered for any generic plane passing through a material point. 3D constitutive equations are derived by generalizing the 1D equations using a homogenization technique. In the developed model, inelastic strain is explicitly stated in terms of the martensite volume fraction. To compare this approach with incremental constitutive models, such an available model is applied in its 1D integral form to the microplane formulation, and it is shown that both the approaches produce similar results for different uniaxial loadings. A nonproportional loading is then studied, and the results are compared with those obtained from an available model in which the inelastic strain is divided into two separate portions for transformation and reorientation. A good agreement is seen between the results of the two approaches, indicating the capability of the proposed microplane formulation in predicting reorientation phenomena in shape memory alloys. The results of the model are compared with available experimental results for a nonproportional loading path, and a good agreement is seen between the findings.