Physical interpretation of parameters in synergistic continuum damage mechanics model for laminates

The continuum damage mechanics (CDM) model by Talreja [Talreja R. Damage characterization by internal variables. In: Pipes RB, Talreja R, editors. Comput Mater Series, vol. 9. Dam Mech Comp Mater, Elsevier, Amsterdam; 1994, p. 53–78], which is one of the most efficient for damaged laminate stiffness determination, is analyzed using earlier developed theoretical framework which links the macro-response of a damaged laminate to the opening and sliding displacements of crack surfaces in an exact form. The physical meaning of the material parameters in CDM is revealed. Exact expressions for these parameters are derived and transformation rules with changing layer orientation angle presented. These parameters were previously considered as the most troublesome part of the CDM model with need for additional tests for their determination. The error introduced by the two main assumptions in the CDM model ((a) stiffness change is linear with respect to damage tensor, (b) crack face sliding effect can be neglected) is evaluated and found that the linearization is often justified but sliding cannot be neglected in most of the lay-ups.