A structured continuum modelling framework for martensitic transformation and reorientation in shape memory materials

Abstract

Models for shape memory material behaviour can be posed in the framework of a structured continuum theory. We study such a framework in which a scalar phase fraction field and a tensor field of martensite reorientation describe the material microstructure, in the context of finite strains. Gradients of the microstructural descriptors naturally enter the formulation and offer the possibility to describe and resolve phase transformation localizations. The constitutive theory is thoroughly described by a single free energy function in conjunction with a path-dependent dissipation function. Balance laws in the form of differential equations are obtained and contain both bulk and surface terms, the latter in terms of microstreses. A natural constraint on the tensor field for martensite reorientation gives rise to reactive fields in these balance laws. Conditions ensuring objectivity as well as the relation of this framework to that provided by currently used models for shape memory alloy behaviour are discussed.

Evolution of multiple Martensite variants in a SMA thick-walled cylinder loaded by internal pressure

“…From them one can see clearly the role played by constitutive and geometrical parameters and thus they allow understanding also more complex problems. Moreover, they provide a reliable evaluation of the residual stresses and strains in the SMA thick-walled cylinder after the isothermal loading process, which can be used also for validating the results of numerical procedures ( Auricchio et al, 2014;Bernardini and Pence, 2016 ).…”