Discrete Damage Mechanics

1. Discrete damage mechanics refers to the use of discrete fracture mechanics to predict crack initiation and evolution. We use a shear-lag solution to calculate the loss of laminate stiffness due to a given density of matrix cracks in each lamina, one lamina at a time. The representative volume element (RVE) is shown below. By using a RVE, the characteristic length is a know function of the crack density. Therefore, the finite element implementation does not suffer from "material" mesh-dependency.

RVE used for shear lag analysis

 

2. We calculate the energy release rate G due to a virtual increment of crack density in each lamina, one lamina at a time. Fully developed damage around a hole is shown below, with the model implemented as a user material subroutine in Ansys.

damage around a hole

3. We use failure criterion in terms of energy release rate to predict initiation and evolution of crack density in each lamina, one lamina at a time. Crack initiation is shown in color yellow for a complex shell example. Accurate stress redistribution among laminae allows us to predict damage evolution and ultimate laminate collapse accurately, even when the later is due to a fiber failure mode.

Damage initiation

4. We homogenize the crack density in each lamina by calculating continuum damage values for the lamina that permit us to calculate it's reduced stiffness at any time. In this way, we are able to compute the crack density in multiple-damaging laminae, in a laminate with arbitrary laminate stacking sequence. Fully developed damage is shown below. In this case, the contitutive model is implemented in a shell user-element in Ansys.

fully developed damage

References