On the Uniqueness of Solution of the Initial Value Problem in Softening Materials

Abstract

The initial value problem in finite “softening” material domains is discussed. An inequality that is true of all materials irrespective of their constitution is first established. It is then shown that the solution to this problem is unique when the attending constitutive equation satisfies another inequality, which is characteristic of material models that we call “positive.” A number of constitutive equations that give rise to realistic softening behavior are shown to lead to a unique solution of the initial value problem.