Multiple crack detection in 3D using a stable XFEM and global optimization.

Area of Science:

• Computational mechanics
• Structural health monitoring
• Numerical analysis

Background:

• Detecting multiple cracks in three-dimensional (3D) structures is crucial for structural integrity.
• Existing methods face challenges in accurately identifying flaws, especially with sparse data.
• The extended finite element method (XFEM) offers a robust framework for fracture simulation.

Purpose of the Study:

• To propose a novel numerical scheme for the detection of multiple cracks in 3D structures.
• To develop an efficient solution for the inverse problem of flaw identification using boundary measurements.
• To demonstrate the effectiveness of the proposed scheme through numerical simulations.

Main Methods:

• Utilized a variant of the extended finite element method (XFEM) tailored for 3D fracture problems.
• Employed a hybrid optimizer combining heuristic algorithms into a multiscale optimization scheme.
• Addressed the inverse problem by identifying multiple flaws based on sparse boundary measurements.

Main Results:

• The proposed XFEM variant efficiently solved the forward problem of 3D fracture simulation.
• The multiscale optimization scheme effectively tackled the inverse problem of multiple crack detection.
• Numerical case studies demonstrated the scheme's capability across varying complexities.

Conclusions:

• The developed numerical scheme provides an effective approach for detecting multiple cracks in 3D structures.
• The combination of XFEM and a hybrid optimizer offers a powerful tool for structural health monitoring.
• The method shows significant potential for real-world applications in non-destructive testing and structural analysis.