ABSTRACT
Computational models for micromechanical analysis of discontinuously heterogeneous microstructures, such as composites, require robust mesh generators that can adequately account for the morphology of domain discontinuities. Conventional mesh generators [96, 13] that use coordinate transformation methods [100], discrete transfinite mapping methods [175, 176], drag mesh methods [340], quadtree/octree approaches [363, 362, 372], etc. can require many special operations to provide adequate means for automatic discretization of such domains. Limitations of conventional mesh generators predominantly arise out of morphological incompatibility of the generated mesh with physical discontinuities in the domain. For example, when second-phase heterogeneities (e.g., inclusions or holes of varying shapes and sizes) are nonuniformly dispersed in the matrix material, a high probability exists that they will be dissected into multiple segments by element boundaries of the mesh. This can lead to significant computational and bookkeeping difficulties due to element sharing by the heterogeneities. Alternatively, an element could potentially contain multiple material phases, depending on the local distribution density. Computational algorithms must adequately account for these non-uniformities prior to analysis. The demands on mesh generators are further compounded when simulations require re-meshing to overcome element distortion and improper boundary representation. Limitations in generating
a robust mesh, as well as limitations of conventional computational methods such as the finite element method for analyzing this class of problems, have led to the development of alternative methods of domain discretization and analysis.
