Parametrically homogenized continuum damage mechanics (PHCDM) models for unidirectional composites with nonuniform microstructural distributions

Abstract This paper develops a parametrically homogenized continuum damage mechanics (PHCDM) model for multiscale analysis of damage and failure in composite structures with nonuniform microstructures. Unidirectional glass fibers are nonuniformly dispersed in the microstructures of these epoxy matrix composites. The PHCDM models are thermodynamically consistent, reduced order constitutive models with coefficients that are explicit functions of microstructural descriptors and evolving material variables. Damage anisotropy is represented through a second order damage tensor that contributes to the evolution of a damage surface in the space of damage work conjugate, which characterizes the initiation and evolution of damage. The nonuniform microstructural morphology descriptors are optimally expressed in terms of representative aggregated microstructural parameters or RAMPs for incorporation in the PHCDM coefficients. Optimal expressions for RAMPs are determined through principal component analysis of the two-point correlation functions. The functional forms of RAMPs in PHCDM coefficients are determined using machine learning tools operating on data generated by micromechanical analysis. It is shown that PHCDM models accounting for the fiber distribution information yield a much higher accuracy than those only accounting for fiber volume fractions. The developed PHCDM model is incorporated in a commercial finite element code and structural analysis of structural composites is executed for understanding concurrent damage and failure at multiple scales. The paper successfully demonstrates the accuracy and significant efficiency of the resulting PHCDM model in analyzing deformation and damage in nonuniform composites across length scales for various loading conditions.