Scalar Damage Variable D

Use the damage variable to specify damage to the cohesive material.

Damage to the cohesive material is completely specified by a single scalar quantity 0 ≤ D ≤ 1 referred to as the damage variable. D = 0 indicates an undamaged pristine cohesive material with its full original stiffness. D=1 indicates a completely damaged (failed) cohesive material that has zero stiffness and can no longer support any load.

Note: In continuum damage mechanics, the form of the damage variable is most often taken to be a first, second, or fourth order tensor. These higher order tensor forms of the damage variable allow characterization of the damage (broken bond density) in the various coordinate directions. Additionally, we can possibly characterize the effect of each damage orientation on fundamental stiffness modes. But here we assume damage in the cohesive material can be adequately characterized with a single scalar variable. Thus, we are in effect assuming the numerical value of D is indicative of the density of broken molecular bonds and that the orientation of these broken molecular bonds is random.

For all delamination models implemented in Helius PFA, the effect of the scalar damage variable D is always to exert an isotropic reduction in the stiffness of the cohesive material. This is accomplished via the scaling coefficient (1-D), as shown in the following damaged constitutive equations.