Computational modeling and simulation of composite materials based on tomographic images

The goal of this work is to enable automated thermal and mechanical finite element analysis of heterogeneous composite materials based on tomographic images of material specimens. Of particular interest are microvascular materials containing embedded micro-channnels through which a coolant or self-healing agent can be circulated. Such materials have important applications to aircraft, electronics, and many other situations where active management of the thermal environment is desirable. Conventional computational analysis of such materials is complicated by their complex geometry and heterogeneous material properties. In particular, conventional finite element analysis requires highly refined, unstructured meshes that conform to the complex geometry, resulting in high computational cost. We take a different approach based on the Interface Generalized Finite Element Method (IGFEM), in which a structured and relatively coarse finite element mesh is used, with the complex geometry incorporated by means of inter- face surfaces that intersect elements of the mesh. The discretized solution space is then augmented by enrichment functions associated with points of intersection with material interfaces, thereby enabling the accurate capture of discontinuities in the solution gradient along material interfaces. An important feature of our approach is the use of 2D or 3D tomographic images of actual material specimens to determine the complex geometry. Based on such images, we generate a pixel- or voxel-aligned rectangular mesh that is selectively refined to attain the necessary accuracy near material interfaces, as well as satisfying constraints imposed by the finite element methodology. Although quadrilateral or hexahedral elements are obviously most natural in our context, IGFEM has primarily been used only with triangular elements in 2D and tetrahedral elements in 3D because of the much simpler implementation of the intersections of interfaces with mesh elements. The greater complexity of IGFEM using hexahedral meshes becomes more manageable, however, in the context of pixel- or voxel- aligned meshes and pixel- or voxel-defined interfaces. We first consider the 2D case, for which we develop an adaptive mesh generation algorithm as well as an implementation of IGFEM for performing the subsequent analysis. The effectiveness of both is demonstrated by solving a thermal test problem for various geometries inferred from 2D images of heterogenous materials, some artificially generated and others 2D slices of 3D tomographic images of real heterogeneous materials. Results on convergence and complexity are provided, along with comparisons with the conventional finite element method. We then extend the adaptive mesh generation algorithm to the 3D case, addressing the additional constraints and complications that arise in this context. Finally, we show results for a series of complex geometries given by 3D tomographic images, both artificially and experimentally generated