Shape-memory alloys: macromodelling and numerical simulations of the superelastic behavior

Shape-memory alloys show features not present in materials traditionally used in engineering; as a consequence, they are the basis for innovative applications. A review of the available literature shows a dearth of computational tools to support the design process of shape-memory-alloy devices. A major reason is that conventional inelastic models do not provide an adequate framework for representing the unusual macrobehavior of shape-memory materials. The present work focuses on a new family of inelastic models, based on an internal-variable formalism and known as generalized plasticity. Generalized plasticity is adopted herein as framework for the development of one- and three-dimensional constitutive models for shape-memory materials. The proposed constitutive models reproduce some of the basic features of shape-memory alloys, such as superelasticity, different material behavior in tension and compression, and the single-variant-martensite reorientation process. For isothermal conditions the implementation of the model in a finite-element scheme and the form of the algorithmically consistent tangent are discussed in detail. Numerical simulations of typical tests performed on shape-memory materials (e.g. uniaxial loading, four-point bending and three-point bending tests) are presented and compared with available experimental data. Based on the overall developments, it appears that the proposed approach is a viable basis for the development of an effective computational tool to be used in the simulation of shape-memory-alloy devices.