title: 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.
authors.affiliation: Department of Structural and Geotechnical Engineering, University of Rome Sapienza, Via Antonio Gramsci 53, 00197 Rome, Italy davide.bernardini@uniroma1.it.
authors.forename: Davide
authors.initials: D
authors.lastname: Bernardini
authors.affiliation: Department of Mechanical Engineering, Michigan State University, 2452 Engineering Building, East Lansing, MI 48824-1226, USA pence@egr.msu.edu.
authors.forename: Thomas J
authors.identifier: http://orcid.org/0000-0002-5136-3384
authors.initials: TJ
authors.lastname: Pence
keywords: martensite transformation; multi-field theory; reorientation plasticity; shape memory material; thermomechanics