Multi-Scale Model of Failure in a Composite Material

This work develops an adaptive concurrent multi-level computational model for multi-scale analysis of composite structures undergoing damage initiation and growth due to microstructural damage induced by debonding at the fiber-matrix interface. The model combines macroscopic computations using a continuum damage model with explicit micromechanical computations, including explicit debonding at the fiber-matrix interface. Macroscopic computations are done by conventional FEM models while the Voronoi cell FEM is used for micromechanical analysis. Three hierarchical levels of different resolution adaptively evolve to improve the accuracy of solutions.

For micromechanical analysis, an eXtended Voronoi cell finite element model (X-VCFEM) is developed for modeling multiple cohesive crack propagation in brittle materials. The incremental crack directions and growth lengths are determined in terms of the cohesive energy near the crack tip. In addition to polynomial terms, stress functions include branch functions in conjunction with level set methods and multi-resolution wavelet functions. Next the X-VCFEM is used to model interfacial debonding with arbitrary matrix cohesive cracking in fiber-reinforced composites. Initiation and propagation of debonding depends not only on the total cohesive energy, but also on the traction-displacement curve. Finally, a VCFEM is also developed for transient elastodynamic analysis in time domain is developed.