Progressive homogenization and damage modelling of a fibre reinforced composite with a viscoplastic matrix

The present work proposes a novel approach to perform the progressive computational homogenization and internal damage modelling in a fibre reinforced lamina combined with a separate viscoplastic matrix layer. The proposed formulation is especially useful in the matrix-dominated loading cases, where the viscoplastic strain plays an important role in the computation of homogenized stress field. The layer volume fractions of lamina and pure matrix are first computed, and the macro-scale (homogenized) tangent modulus expression is proposed, incorporating the degradation in lamina and matrix layers, employing Voigt approximation. The applicability of the homogenized tangent modulus is subsequently demonstrated by implementing it in an in-house developed non-linear finite element framework while solving several boundary value problems. It is also demonstrated that, the presented approach can be extended to any layered media having different constitutive responses and inelastic strain.