Fracture Mechanics · XFEM · Inverse Problem

Fracture Mechanics FEM & XFEM-Based Crack Identification

A finite element analysis project focused on crack and flaw identification in heterogeneous materials using inverse problem formulation, genetic algorithm optimization, and XFEM-based crack modeling.

Tools

FEM, XFEM, MATLAB

Methods

Inverse Analysis, Genetic Algorithm, Crack Modeling

Institution

Columbia University

Identified flaw region using multiscale crack detection workflow — Identified flaw region from the multiscale detection workflow.

Convergence history for one-parameter crack estimation.

Project Overview

This project studied crack and flaw identification in finite element models of heterogeneous materials. The work combined forward elasticity analysis, inverse problem formulation, genetic algorithm optimization, and XFEM-based crack modeling to estimate crack or hole parameters from structural response data.

The project considered voided microstructures, isotropic damage modeling, crack-mesh intersection representation, XFEM enrichment, and numerical examples for crack detection. The goal was to connect fracture mechanics theory with computational implementation and optimization-based flaw identification.

Material Model Damage FEM

Used an isotropic damage model for voided heterogeneous microstructures.

Optimization GA

Applied genetic algorithm search for inverse crack or flaw identification.

Crack Modeling XFEM

Used enrichment functions to model cracks without conforming the mesh to the crack.

Application NDT

Framed crack identification as a non-destructive detection problem.

My Role

Reviewed fracture mechanics and computational homogenization concepts.
Formulated forward and inverse elasticity problems for crack and hole identification.
Studied genetic algorithm optimization for global search of flaw parameters.
Built the conceptual XFEM workflow for crack-mesh intersection and enrichment.
Analyzed numerical examples involving cracked domains and convergence behavior.
Prepared visual explanations of microstructures, crack databases, and XFEM-GA workflows.

Microstructure & Damage Modeling

The project began with voided microstructures representing heterogeneous material behavior. A simple isotropic damage model was used to describe material degradation, with damage governed by an exponential evolution law.

Voided microstructures with different dimensions — Voided microstructures used to represent heterogeneous material behavior.

Forward elasticity problem domain with crack and hole boundaries — Forward elasticity problem with displacement, traction, crack, and hole boundaries.

GA-Based Inverse Identification

The inverse problem was formulated as an optimization problem, where candidate crack or hole parameters were updated to minimize the difference between measured and simulated response data. A genetic algorithm was used because it is suitable for global search and does not require an explicitly differentiable objective function.

Genetic algorithm flow chart — Genetic algorithm workflow for population update, selection, crossover, and mutation.

Objective function convergence with grid size — Objective function values used to evaluate convergence behavior.

XFEM Crack Modeling

The XFEM-based scheme was used to represent cracks without forcing the finite element mesh to conform to the crack geometry. Crack information was represented through crack tips, crack-mesh intersections, and a linked-list structure used during the enrichment process.

Crack database and linked list representation — Crack database containing crack tips and crack-mesh intersection points.

XFEM-GA algorithm flow chart — XFEM-GA algorithm flow connecting XFEM simulation and GA-based fitness evaluation.

Project Gallery

Microstructure models, XFEM workflows, crack detection, and convergence results.

Scattered plate sensing model — Scattered plate sensing setup for crack identification.

XFEM enrichment visualization — Visualization of enrichment around the crack region.

Mesh comparison for cracked square membrane — Mesh comparison for the cracked square membrane problem.

FEM mesh with double nodes along crack — FEM mesh with double nodes along the crack path.