Homogenization based damage models for monotonic and cyclic loading in three-dimensional composite materials

This dissertation develops a three dimensional homogenization based continuum damage mechanics (HCDM) model for fiber reinforced composites undergoing micromechanical damage under monotonic and cyclic loading. Micromechanical damage in a representative volume element (RVE) of the material occurs by fiber-matrix interfacial debonding, which is simulated using a hysteretic bilinear cohesive zone model. The proposed HCDM model expresses a damage evolution surface in the strain space in the principal damage coordinate system (PDCS). PDCS enables the model to account for the effect of non-proportional load history. The material constitutive law involves a fourth order orthotropic tensor with stiffness characterized as a macroscopic internal variable. Three dimensional damage in composites is accounted for through functional forms of the fourth order damage tensor in terms of components of macroscopic strain and elastic stiffness tensor. The HCDM model parameters are calibrated from homogenized micromechanical solutions of the RVE for a few representative strain histories. The proposed model is validated by comparing the CDM results with homogenized micromechanical response of single and multiple fiber RVEs subjected to arbitrary loading history. Finally the HCDM model is incorporated in a macroscopic finite element code to conduct damage analysis in structures. The effect of different microstructures on the macroscopic damage progression is examined through this study.;To efficiently simulate the dynamic response of heterogeneous microstructures, an assumed stress hybrid Voronoi Cell Finite Element Method (VCFEM) for stress wave propagation is developed. In the proposed formulation, stresses in the domain and compatible displacements at the element boundary are approximated independently. The inertia field is approximated in terms of stresses so as to satisfy the equilibrium a-priori. The weak forms of kinematics and traction reciprocity are obtained by minimization of the complementary variational principle. As stress wave is a local disturbance, localization and multi-resolution properties of the wavelet functions are exploited to adaptively enrich the stress functions locally near the wave front. At the outset, a stable, accurate, and computationally efficient adaptive computational framework is developed for micromechanical response of composites under impact loading. The effectiveness of the proposed method is demonstrated through comparison with conventional FEM packages.