Polymer matrix composites (PMCs) and ceramic matrix composites (CMCs) are increasingly used in a wide range of applications. With the demand for lighter and more versatile structural components, the need to understand interactive and complex failure mechanisms in these materials has grown and has become the focus of many research projects. The deformation response, subsequent damage development, and failure of these multi-constituent materials are dependent on microstructural details such as variations in fiber packing arrangement, properties at fiber-matrix interfaces, and interactions between neighboring fibers. This dependency of failure modes on the microstructure is well known for composite materials which led to the development of numerous homogenized theories. Kanoute et al. [
1] reviewed various multi-scale methods for mechanical and thermomechanical responses of composites. Heinrich and Waas [
2] utilized the smeared crack approach to describe the post-peak softening in laminated materials. They predicted the cracking behavior of an open-hole tensile specimen and recorded crack directions for various fiber angles. Accurate numerical predictions for layered, fibrous materials are inherently difficult due to the intricate mechanisms that tie global component failure to microstructural degradation. Modeling strategies based on homogenized material properties neglect the importance of the physical behavior at the microstructural level, and thus, homogenized models fail to predict experimentally observed critical parameters accurately. Those include, e.g., maximum load, strain to failure, crack spacing, and other salient features. Oftentimes, the material orientation is used as a guide for directing failure. This might lead to erroneous crack paths for materials with similar fiber and matrix properties such as CMCs. Hence, multi-scale methods have become the focus of many research papers in recent years. These models dehomogenize the strain and stress state for each constituent. Typically, a representative volume element (RVE) that preserves the microstructural dimensions is identified. Yuan and Fish [
3] developed a computational homogenization approach for linear and nonlinear solid mechanics problems. In this work, two commercial solvers were bridged by a python code. The authors showed that linear problems could be accurately modeled. Ghosh et al. [
4] introduced a multi-scale methodology based on the Voronoi cell finite element method (VCFEM). Material coefficients are generated by VCFEM and used in a global finite element model. Nonlinearities can be included in the finite element formulation of the Voronoi cells. Key et al. [
5] used multi-continuum technology in a multi-scale simulation to analyze the separation of rib to skin interfaces. Multi-continuum theory decomposes the stress and strain field for each constituent using volume averages. This method is numerically fast with the cost of inaccuracy particularly for components that experience high shear. Bacarreza et al. [
6] developed a semi-analytical homogenization method to model damage in woven composite materials. Effective material properties are derived and used in a progressive damage analysis. Nonlocal or gradient failure theories assume that the post-peak stress-strain behavior of an element is influenced by the field gradients within a characteristic radius around the element. Jirásek [
7] analyzed analytical and numerical solutions of simple one-dimensional localization problems. Aboudi et al. [
8] introduced the generalized method of cells (GMC), a semi-analytical method, which discretized the microstructure with rectangular subcells. Pineda et al. [
9] achieved mesh objectivity with a thermodynamics-based approach within GMC as well as high-fidelity generalized method of cells (HFGM). Multi-scaling methods often suffer from lower computational efficiency compared to homogenized models. This disadvantage can usually be overcome by using the multi-scale method in areas where microstructural failure is to be expected, e.g., at stress concentrators (notches, etc.). Homogenized element stress-strain relation can be utilized in regions of low failure probability. In recent years, significant improvements have been made in terms of fidelity and computational efficiency [
10-
13].
In the present paper, the commercial finite element software suite Abaqus is used to generate lamina-level structural model of a ceramic matrix composite (CMC). A second sub-scale microstructural model has been developed and fully integrated with the main Abaqus solver through a user material subroutine (UMAT). Integrated finite element method (IFEM) calculates the reaction of a microstructural model to an imposed displacement field. The microstructural model consists of a RVE which includes all constituents of the real material, e.g., fiber, matrix, and fiber/matrix interfaces, details of packing, and nonuniformities in properties. The energy-based crack band theory (CBT), first introduced by Baz̆ant [
14], is implemented within IFEM constitutive laws to predict micro-cracking in all constituents that are included in the micromechanics model. The communication between the micro- and macro-scale is achieved through the exchange of strain, stress, and stiffness tensors. Important failure parameters, e.g., crack path and proportional limit, are part of the solution and predicted with a high level of accuracy. Numerical predictions are validated against experimental results.