Material forces and phase transitions in elasticity

Abstract

A computational scheme for the determination of the interface in a strain-induced phase-transition problem for an elastic bar is proposed. The algorithm is based on the material force notion and more specifically on the simultaneous solution of equilibrium equations for the physical and material forces. The weak form of both equations is derived with the aid of a variational principle that accounts for the variations of the dependent and the independent variables. The whole scheme concludes in a nonlinear algebraic system which is numerically solved by the Newton method. The numerical results thus derived seem to be quite encouraging for further application of the concept of material forces in computations related to phase transition problems. The austenite-martensite transformation could be a possible application of the proposed model.

The concept of material forces in phase transition problems within the level-set framework

“…In contrast to the phase field theory, the sharp interface theory treats phase boundaries as discontinuity surfaces of zero thickness [2][3][4][5][6]. Far away from the interface, the basic equations of continuum mechanics are satisfied.…”