Revisiting the composite laminate problem with an adaptive multi-level computational model

The series of free-edge boundary-value problems treated by Pagano and Rybicki (Pagano NJ, Rybicki EF. On the significance of effective modulus solutions for fibrous composite. J Comp Mat 1974;8: 214–28; Rybicki EF, Pagano NJ. A study of the influence of microstructure on the modified effective modulus approach for composite laminates. Proceedings of the 1975 Int. Conf. Compos. Mater 1976;2:198–207) demonstrates the breakdown of homogenization in the region of macroscopic gradients. Their study shows the need for an appropriate level of resolution in determining reasonably accurate stresses in the region of macro gradients. Problems of this type can be readily handled by using an adaptive multi-level computational model with varying resolutions for critical and non-critical regions. The model introduces three levels, a pure macroscopic problem with homogenized coefficients modeled through a conventional displacement based FE code, macro-micro coupling through asymptotic homogenization where periodicity of microstructure is assumed, and microscopic analysis using a Voronoi cell finite-element model. The effect of increasing number of rows on the results is studied by the multiscale model and the homogenized model. Fiber/matrix interfacial stresses are also provided as these are expected to initiate the failure process in these fiber-reinforced composite laminates.