Damage as a Material Phase Transition

We propose paradigmatic examples to show how material damage effects can be described as a solid-solid phase transition. Start- ing from the pioneering work of J.L. Ericksen [8] and the extensions of R.L. Fosdick to three-dimensional non linear elasticity, we describe the insurgence of damage as a transition between two material states (dam- age and undamaged) characterized by two different energy wells. We consider the two separate constitutive assumptions of a simple damage- able Neo-Hookean material and a more complex microstructure inspired Gent material with variable limit threshold of the first invariant. In both cases we study two different deformation shear classes, one homogeneous and the other one inhomogeneous and obtain fully analytic description of the system damage response under cyclic loading. While the assumption of two only (damaged and undamaged) configurations is simplistic, the model can be extended to systems with more energy wells with varaible degrees of damage.