A new strategy has been introduced by an earlier work where the natural hierarchical character of model descriptions and simulation results are exploited to expedite analysis of problems. Hierarchical techniques are used in the development, organization, and management of finite element models, and for the post-processing of the results from the analyses. In the current work, the hierarchical strategy is used to analyze materials that have a complex microstructure. The hierarchical analysis environment is used to analyze a double cantilever beam (DCB) specimen fabricated with woven composite. Such a configuration contains many microstructural scales such as fiber/matrix, tow architecture, and laminate. The results of a detailed finite element stress analysis on the DCB specimen are presented. The strain energy release rate along the width of the crack front is calculated and is found to be dependent on the local microstructure at the crack front.