Evolution of fabric tensors in damage mechanics of solids with micro-cracks: Part II – Evolution of length and orientation of micro-cracks with an application to uniaxial tension

In Part II of this work, the equations of thermodynamics are employed in order to derive the exact evolution equations of the fabric tensors defined in Part I (companion paper). In this regard, a thermodynamic force that is associated with the fabric tensor is defined and utilized in the derivation of the evolution equations. A special case of uniaxial tension is solved in order to illustrate the theory.We also derive specific uncoupled equations for the evolution of the length and orientation of micro-cracks. In this regard, some interesting results are obtained. It is concluded that the micro-crack length and orientation cannot evolve simultaneously for the same set of micro-cracks. However, two different sets of micro-cracks may be considered in the same RVE where in one set the micro-crack length evolves, while in the second set the micro-crack orientation evolves.