Decomposition of fabric tensors in materials science and damage mechanics

Abstract This work deals with damage mechanics of materials and is not concerned with fracture mechanics. The reduction in stiffness of the material and other material properties characterize this. This is also linked to the microstructure using fabric tensors. A new decomposition of fabric tensors is derived. The decomposition is implicit and is based on the decomposition of the damage tensor that was derived previously by the authors. The general fabric tensor G is decomposed into individual fabric tensors G A and G B for different individual damage processes. The superscripts A and B may, for example, represent cracks and voids, etc. or any other damage processes. Furthermore, another decomposition is formulated that is exponential in nature. In addition, the decomposition is generalized to three different damage processes, including a third unidentified defect. Finally, an unsymmetrical decomposition of fabric tensors is also derived.