Variational principle for shape memory alloys

TL;DR

This paper reviews the quasistatic behavior of shape memory alloys using a generalized variational principle, providing a mathematical foundation within phenomenological mechanics without microphysical details.

Contribution

It introduces a Reissner-type variational principle for shape memory alloys and justifies it mathematically for 3D bodies, advancing theoretical understanding.

Findings

Provides a variational framework for shape memory alloys

Mathematically justifies the principle for 3D bodies

Focuses on slow temperature variation scenarios

Abstract

The quasistatic problem of shape memory alloys is reviewed within the phenomenological mechanics of solids without microphysics analysis. The assumption is that the temperature variation rate is small. Reissner's type of generalized variational principle is presented, and its mathematical justification is given for three-dimensional bodies made of shape memory materials.