Multi-Scale Finite Element Simulation of Progressive Damage in Composite Structures

A methodology for analyzing progressive damage accumulation on multiple spatial scales (micro- and macro-scale) in composite materials is presented in this paper. Idealization (homogenization) of heterogeneous media and evolution of damage on micro- and macro-scales are considered simultaneously at each incremental analysis step. The classical mathematical homogenization theory is extended to account for damage effects on distinct spatial scales through the introduction of an asymptotic expansion of damage parameter (or damage tensor in general). Local solutions on micro-scale provide the homogenized material properties that a global structure behaves on the macro-scales. The responses in the local fields, i.e. microscopic phases, can be reconstructed through the scale linking relations along with the global responses as input. The application of this multi-scale simulation method to composite patch repair for offshore structures is demonstrated by numerical examples.