Objectivity of the relative power and covariance of the Clausius–Duhem inequality in fracture dynamics

We prove that balance laws at a crack tip, including those of configurational actions, all derive from a requirement of objectivity for the power of actions performed relative to a virtually varying reference configuration. The procedure maintains distinction between balance laws and constitutive structures but avoids postulating balance laws in strong, integral or weak forms. We thus generalize the results to cracks evolving into bodies with active microstructure by exploiting a covariance argument for a version of the Clausius–Duhem inequality. Here, covariance is intended as structure invariance of the inequality under diffeomorphism-based observer changes. The results are independent of specific microstructures.