An integral representation of fields with applications to finite element analysis of spatially varying materials. (September 2020) - Kumar, Goldy; Taber, Andrew
Abstract: We propose a representation framework for fields that leverages integral properties to incorporate diverse field models into a single analysis pipeline. This integral representation can be used to embody a variety of spatial data, including vector- and tensor-valued fields, and can be used to generate effective values which match the integral properties of the original field. We apply this representation to the problem of material field modeling, which is otherwise intractable due to the heterogeneous and spatially-varying nature of these fields. We demonstrate the advantages of integral representations by analyzing functionally graded material fields, material properties derived from an additive manufacturing process, and experimental material data. Graphical abstract: Highlights: We developed an integral representation for fields that supports a wide range heterogeneous data. These integral representations can be composed into a single analysis pipeline. We demonstrated our approach by analyzing graded material fields, acquired data (CT Scan), and data from a manufacturing process.