Damage as a Material Phase Transition

Abstract We propose paradigmatic examples to show how material damage phenomena can be efficiently described as a solid-solid phase transition. Starting from the pioneering work of J.L. Ericksen (J. Elast. 5(3):191–201, 1975) and extensions R.L. Fosdick other authors three-dimensional non linear elasticity, we describe insurgence hard → soft transition between two states (damage undamaged) characterized by different energy wells. consider separate constitutive assumptions simple Neo-Hookean type damageable more complex microstructure inspired Gent with variable limit threshold first invariant. In both cases study deformation shear classes, one homogeneous inhomogeneous obtain fully analytic description system response under cyclic loading. The considered classes are aimed at attaining descriptions. On hand, remark that proposed, Griffith type, variational approach damage, based on density functions for damaged undamaged phases, resulting (rank-one) convex energy, extended systems functions, possibly larger number wells representing an increasing degree damage.