Abstract
A new enriched finite element technique, named the Discontinuity-Enriched Finite Element Method (DE-FEM), was introduced recently for solving problems with both weak and strong discontinuities in 2-D. In this mesh-independent procedure, enriched degrees of freedom are added to new nodes collocated at the intersections between discontinuities and the sides of finite elements of the background mesh. In this work we extend DE-FEM to 3-D and describe in detail the implementation of a geometric engine capable of handling interactions between discontinuities and the background mesh. Several numerical examples in linear elastic fracture mechanics demonstrate the capability and performance of DE-FEM in handling discontinuities in a fully mesh-independent manner. We compare convergence properties and the ability to extract stress intensity factors with standard FEM. Most importantly, we show DE-FEM provides a stable formulation with regard to the condition number of the resulting system stiffness matrix.
Highlights
Enriched finite element methods have fundamentally changed the modeling of problems containing discontinuities
We show Discontinuity-Enriched Finite Element Method (DE-FEM) provides a stable formulation with regard to the condition number of the resulting system stiffness matrix. ⃝c 2019 The Authors
In this paper we extend DE-FEM to 3-D, and we discuss in detail its computer implementation in a displacement-based finite element code
Summary
Enriched finite element methods have fundamentally changed the modeling of problems containing discontinuities. S.J. van den Boom, F. van Keulen et al / Computer Methods in Applied Mechanics and Engineering 355 (2019) 1097–1123 a single formulation to model problems containing both weak and strong discontinuities (C−1-continuous field) by placing enriched degrees of freedom (DOFs) only to nodes created along discontinuities. Creating matching meshes in general can be quite challenging depending on the morphology of the problem, because of the strict conditions on mesh quality that are required—elements with bad aspect ratios could reduce the approximation accuracy [4]; robustness is still questionable, especially for 3-D FE meshes, as issues remain in generating meshes that correctly match boundaries [5] Numerical techniques such as Universal Meshes [6] and the Conforming to Interface Structured Adaptive Mesh Refinement (CISAMR) [7] have been proposed to modify meshes locally to discontinuities. We showcase DE-FEM in the challenging problem of intersecting weak and strong discontinuities, which is handled effortlessly by means of the hierarchical implementation ala HIFEM
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