UC Berkeley

In this study we analyze a method for the multiscale modeling of heterogeneous materials with a special emphasis on unidirectional fiber composites. The method relies on defining two problems. The first boundary value problem is defined with homogenized material properties and the second boundary value problem is defined with the exact heterogenous properties. Based on these definitions a modeling error between these two problems is defined and analyzed for both small deformation and finite deformation cases. We introduce a new modeling error that gives insight into the components that contribute to this error. To improve the solution of the homogenized problem without solving the complete heterogeneous problem, we define subdomains that include microstructural information. These smaller subdomains can then be solved and included into the solution space of the homogeneous problem through a simple coupling process. Through defining local error indicators that are related to the global modeling error, we can adaptively select only the subdomains with high local error to be included in the solution space. As a preset to the multiscale process, homogenization techniques are analyzed for random unidirectional fiber composites under small deformations. This allows one to systematically obtain material properties for the homogenized boundary value problem. A thorough analysis is provided to understand the behavior of the error indicator under both small and finite deformations. We also explore the potential reduction in the modeling error when including subdomains in the solution space. The effect the size of the subdomains have on the solution improvement is also investigated.