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Nonlocal Continuum Mechanics and Damage Prediction in Solids
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In this study a new computational framework by the name Graph-based Finite Element Approach (GraFEA) is developed for the study of fracture in solids. Conventional finite element method (FEM) is without doubt the most widely-used computational method in the field of solids and structures. However, in its conventional form it is not well-suited for the study of discontinuous displacement fields (e.g. fracture problems). Several remedies have been proposed in the literature, but the amount of complexity of these approaches limits and negatively impacts their integration into the commercial softwares. GraFEA on the other hand builds upon the robustness of conventional FEM, and it can be incorporated into the existing commercial softwares with minor effort. The two distinct features of GraFEA which make it an appealing choice for the study of fracture are: 1. Transformation of the conventional FEM into a nonlocal network: The goal of this transformation is to derive the forces and strains along the edges of the elements of the discretized continuum instead of determining them at the nodes. The network representation resembles the truss network to some extent, with the exception that the force along an edge of interest depends on the collective behavior of the strains along the neighboring edges of the edge of interest, and not only the strain along the edge of interest. Hence, the resulting network is not local as in a simple truss network. 2. Imposition of a nonlocal edge-based fracture criterion: The network representation allows us to study fracture on the discretized body instead of using a continuum approach. This treatment of failure is as simple as that of lattice models without suffering from the limited Poisson’s ratio of 0.25. The nonlocal edge-based fracture criterion is motivated by the idea of weakest link statistics. In this approach, the nonlocal edge-based strain (or force) is compared with a critical value to determine whether the edge is broken or not. The nonlocal edge-based strain is the weighted-averaged value of the strain over a characteristic zone mirrored along the edge of interest. Depending on the relative size of the characteristic zone and the elements, the nonlocal fracture criterion can turn into a local criterion (no averaging required). The network representation of GraFEA is a reformulation of conventional FEM, and it simplifies to FEM for an intact medium. Progression of fracture is studied by incrementally increasing the values of the imposed boundary conditions, and monitoring the breakage of the edges.
Khodabakhshi, Parisa (2018). Nonlocal Continuum Mechanics and Damage Prediction in Solids. Doctoral dissertation, Texas A & M University. Available electronically from