A micromechanical continuum mixture model is constructed for the stress transfer and residual stiffness in orthogonally cracked laminates. According to this technique, the discrete composite behavior is replaced by that of a higher order continuum. A rational construction of an alternative set of coupled field equations that automatically satisfy all interface conditions leads to simple coupled governing equations for the total composite. This construction procedure is based on some through-thickness approximate distributions for some of the field variables. Once the stress free crack surface boundary conditions are imposed and the stress field components are obtained, we proceed to derive expressions for the residual stiffness of the damaged composite. This is presented in the form of Young's and shear moduli. Treating three-dimensional problems and then identifying the results for the two-dimensional case, it will be shown that much of the earlier results in the literature are obtained as special cases of our work. Confidence in the modeling is further enhanced by showing good agreement with experimental measurements available in the literature.
Abdelrahman, W. G., & Nayfeh, A. H. (1999). Stress transfer and stiffness reduction in orthogonally cracked laminates. Mechanics of Materials, 31(5), 303–316. https://doi.org/10.1016/S0167-6636(99)00002-2