A general framework for mean-field homogenization of multi-layered linear elastic composites subjected to thermal and curing induced strains

Abstract The aim of this work is to derive a general three-scale framework for the homogenization of polymer composites accounting for the degree of cure, besides thermal and mechanical contributions. For this purpose an additive decomposition of the small strain tensor into an elastic, a thermal and a chemical part of the small strain tensor is considered at all three scales. The macroscale of the three-scale framework represents the homogeneous material. The mesoscale is decomposed into a polymer-based material and an inclusion, which is coated or even multi-layered. On this scale, the degree of curing varies between the different constituents and is therefore inhomogeneous. The microscale of the three scale framework represents a step-growth polymerization mechanism. On this scale the degree of cure is homogeneous. Effective thermal, chemical and elastic properties are derived in a general way based on the transformation field analysis and the mean-field homogenization framework. In a comparative study the capability of the proposed framework is shown. In detail, effective properties for a system of multiple growing spheres and for multiple growing ellipsoids are determined versus the degree of cure. Macroscopic effective properties for a fibre reinforced composite are derived versus the degree of cure and versus the matrix volume fraction. Additionally, results for a coated-fibre reinforced composite versus the degree of cure are displayed.