A new unsymmetrical decomposition of the damage variable

This work focuses on the dissection of the damage variable within solid materials. The underlying assumption is that damage within a solid primarily stems from the presence of various defects. The conventional approach to breaking down the damage variable into two parts – one attributed to the first defect type and the other to the second defect type – is both explored and expanded in a coherent mathematical manner. Within this context, a novel and asymmetric dissection of the damage variable is formulated. This fresh asymmetrical approach presents an alternative to the traditional symmetric dissection of the damage variable. Initially, the dissection considerations are carried out in a one-dimensional context using scalar values. However, this methodology is subsequently generalized employing tensors. In the end, an illustrative example is demonstrated.