A two-dimensional variational model for the equilibrium configuration of an incompressible, elastic body with a three-well elastic potential (Q2718669)

The paper provides a variational approach to a multiphase elastic body in equilibrium under the action of a given system of forces which includes three different phases, namely an austenitic one and two martensitic phases. It is difficult to develop a full variational theory of the problem. So the authors restrict themselves to a simple case: two-dimensional geometrically linear incompressible elastic body in the absence of thermal effects. The results obtained in the paper are of mathematical interest. Further work is needed to establish a three-dimensional variational model for the discussed problem considering the nonlinearity and thermal effects. To this end, the present reviewer proposed an alternative approach called semi-inverse method [\textit{J.-H. He}, Int. J. Turbo Jet Engines 14, No. 1, 23-28 (1997)].