General Consistency of Strong Discontinuity Kinematics in Embedded Finite Element Method (E-FEM) Formulations

Area of Science:

• Computational Mechanics
• Materials Science

Background:

• Current Embedded Finite Element Method (E-FEM) formulations for fracture simulations face challenges with kinematic consistency and mesh dependency.
• Existing elemental enhancement functions in E-FEM literature require refinement for accurate local fracture modeling.

Purpose of the Study:

• To investigate the theoretical underpinnings of strong discontinuity methods within E-FEM for fracture simulations.
• To develop novel strong discontinuity enhancement functions addressing kinematic inconsistencies and mesh dependencies.
• To enhance the robustness and accuracy of E-FEM in simulating local fracture phenomena.

Main Methods:

• Review of existing elemental enhancement functions in E-FEM literature.
• Analysis of theoretical pathologies affecting kinematic consistency and mesh dependency in E-FEM fracture models.
• Development of new strong discontinuity enhancement functions for generalized fracture kinematics in 3D.
• Implementation of a robust definition for internal auxiliary functions.
• Conducting element-level simulations to compare various E-FEM approaches, including the novel proposal.

Main Results:

• The proposed strong discontinuity enhancement functions demonstrate improved kinematic coherence between local fracture outputs and element kinematics.
• Simulations confirm that the new E-FEM formulation enhances robustness in fracture simulations.
• The novel approach addresses identified theoretical pathologies in existing E-FEM frameworks.

Conclusions:

• The developed strong discontinuity enhancement functions offer a more robust and kinematically consistent approach to E-FEM fracture simulations.
• This advancement has the potential to significantly improve the applicability and reliability of E-FEM techniques for complex fracture problems.
• The findings suggest a pathway to higher levels of accuracy and reduced mesh dependency in computational fracture mechanics.