Abstract
This paper performs an in-depth study of the theoretical basis behind the strong discontinuity methods to improve local fracture simulations using the Embedded Finite Element Method (E-FEM). The process starts from a review of the elemental enhancement functions found in current E-FEM literature, providing the reader a solid context of E-FEM fundamentals. A set of theoretical pathologies is then discussed, which prevent current frameworks from attaining full kinematic consistency and introduce unintended mesh dependencies. Based on this analysis, a new proposal of strong discontinuity enhancement functions is presented considering generalised fracture kinematics in a full tridimensional setting and a more robust definition of internal auxiliary functions. Element-level simulations are performed to compare the outputs within a group of selected E-FEM approaches, including the novel proposal. Simulations show that the new element formulation grants a wider level of basic kinematic coherence between the local fracture outputs and element kinematics, demonstrating an increase in robustness that might drive the usefulness of E-FEM techniques for fracture simulations to a higher level.
Highlights
One of the core features of the Embedded Finite Element Method (E-FEM) modelling approach is the ability to simulate local material fractures by the introduction of strong discontinuity enhancement functions to elemental displacement fields
This paper performs an in-depth study of the theoretical basis behind the strong discontinuity methods to improve local fracture simulations using the Embedded Finite Element Method (E-FEM)
Simulations show that the new element formulation grants a wider level of basic kinematic coherence between the local fracture outputs and element kinematics, demonstrating an increase in robustness that might drive the usefulness of E-FEM techniques for fracture simulations to a higher level
Summary
One of the core features of the E-FEM modelling approach is the ability to simulate local material fractures by the introduction of strong discontinuity enhancement functions to elemental displacement fields. The E-FEM approach has been praised for its simple yet powerful capacity for the accurate modelling of local and global fracture processes of quasi-brittle materials over other methods such as X-FEM or the Partition of Unity [3] The latter have a more robust and deeper definition of their kinematics, attacking directly the definition of nodal interpolation functions and their support. The intent of this work is to make an analysis of how the basic definitions of strong discontinuity kinematics have been introduced so far on the E-FEM framework (Sections 2 and 3) to identify the roots of its potential theoretical faults and related numerical issues (Section 4) Some authors provided their valuable insights on these challenges and proposed theoretical enhancements as a workaround [8,11,12,13]. The authors believe it is worth continuing the theoretical works in this line since its physical correctness sets a solid foundation for modelling further complex crack phenomena such as reclosure, local compression and explicit local friction, as well as the possibility to consider other kinds of discontinuities in a simultaneous fashion
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