Multilevel Embedded Finite Element Method

Project Overview

The multilevel embedded finite element method is based on the principles of strong discontinuity approach and extends its capabilities to model and simulate complex branching mechanisms using physically motivated thresholds in brittle engineering materials.

Key Features

• Implementation of strong discontinuity approach (embedded finite element method) to model crack propagation without remeshing, allowing for more efficient computational analysis of complex fracture patterns.
• Integration of traction separation laws to accurately represent the nonlinear behavior in the process zone ahead of the crack tip, capturing the progressive material degradation.
• Development of sub-domain boundary value problems that automatically increase mesh density at high-stress gradient regions near crack tips while maintaining coarser meshes elsewhere.
• Incorporation of crack tracking algorithms to visualize complex fracture phenomena such as branching.

Technical Implementation

• The system utilizes finite element analysis program (FEAP) from Berkeley.
• Development of custom finite element code in Fortran with parallel processing capabilities using MPI for distributed computing across multiple nodes.
• Implementation of robust numerical integration schemes for elements with strong discontinuity using linear and constant separation modes.
• Geometry and loads for varied initial boundary value problems from literature are created to validate the implementation.
• Method of domain decomposition is used to link sub-boundary value problems to global boundary value problems.

Challenges and Solutions

• Addressing numerical stability issues arising from ill-conditioning of the stiffness matrix when strong discontinuities pass very close to element nodes.
• Managing computational costs associated with tracking multiple crack fronts within a sub-boundary value problem.
• Developing physically robust criteria for crack initiation and propagation that remain stable under various loading conditions and material properties.
• Handling convergence difficulties in nonlinear iterations when multiple cracks interact or when using elastoplastic material constitutive models.

Results and Impact

• Successful validation of the implemention against experimental data for brittle and quasi-brittle materials, showing excellent agreement in crack path predictions.
• Demonstration of significant computational efficiency improvements compared to traditional remeshing approaches, with up to 70% reduction in simulation time.
• Accurate prediction of complex fracture patterns like micro-branching and bifurcation under dynamic loading conditions.
• Publication of findings in high-impact journals and presentation at international conferences, leading to collaboration opportunities with industry partners.