Microplane Modeling for Inelastic Responses of Shape Memory Alloys

Shape memory alloys (SMAs) are a class of smart materials. In these alloys, an inelastically deformed configuration can recover to their original shape upon heating to a specific temperature. One of the main challenges in modeling these materials under multiaxial loadings is that the so-called normality rule does not necessarily hold true as the direction of inelastic strain rate vector does not coincide with the deviatoric stress vector for nonproportional loadings. Therefore, any generalization of 1-D constitutive equations to 3-D cases based on J2 or J2-J3 plasticity is valid only for proportional loadings. Microplane modeling approach is a promising candidate for overcoming this challenge since 1-D constitutive models in this method are generalized to 3-D through a particular homogenization technique. All the material parameters can be obtained using uniaxial tension–compression tests. These features make microplane theory an efficient approach in constitutive modeling of shape memory alloys. In this chapter, first, the basic concepts of microplane theory are reviewed. Then, a microplane model for SMAs along with an efficient technique in numerical implementation of the constitutive equations is presented. Introduction of tension–compression asymmetry is further discussed and verified. Finally, modeling of plastic and cyclic response is explained, and the theoretical results are validated against experimental findings.