Size-dependent constitutive model for shape memory alloys based on couple stress elastoplasticity

Abstract

A constitutive model for shape memory alloys considering size effects is developed based on thermodynamic framework. Couple stress elastoplasticity is utilized to simulate size effects. Three material length scale parameters, two for elastic size effect of the austenite and martensite phases and one for crystal structure transformation, are introduced as additional material properties. The developed model is formulated with three-dimensional equations and can be used for the analysis of structures having arbitrary shapes by being adopted into the finite element method. Two benchmark problems (cantilever and bulge test) are solved using the developed model, which shows significant increase in structural stiffness as the size of the structure decreases. The developed size-dependent constitutive model is expected to be utilized for the analysis of micro/nano-scale structures composed of shape memory alloys.