On dissipation induced by phase transformations

Summary Motions of hyperelastic materials involving surfaces of strain or stress discontinuities are generally dissipative in the sense that, in any portion of the body that is traversed by a moving singular surface, the rate of work of the external forces differs from the rate of storage of the total energy (the strain energy and the kinetic energy) by the rate of work done in moving the singular surface. Hence, the corresponding continuum theory is capable of modeling dissipative behavior associated with phase transformations which has potential applications in the design ofadaptive structures. The present work indicates that this dissipative behavior is characterized by a material function, called the driving-traction-response function, which is uniquely determined by the strain energy potential of the material. The driving-traction-response function vanishes identically if and only if the Piola-Kirchhoff stress-response function depends upon the deformation gradient linearly.