Numerical methods in engineering

Predicting how and when solid materials crack is one of the central problems in structural engineering, where unexpected fracture can mean catastrophic failure in everything from aircraft fuselages to concrete infrastructure. Classical finite element methods struggle with crack propagation because a growing crack continuously breaks the mesh it relies on, which has pushed researchers toward alternatives such as the Extended Finite Element Method, peridynamics, phase-field models, and meshless approaches using radial basis functions — each offering a different way to represent discontinuities without rebuilding the computational domain at every step. A persistent open question is how to balance physical fidelity with computational cost, particularly for brittle materials where cracks can branch, merge, and change direction unpredictably under complex loading. Active work focuses on coupling these methods together, improving their handling of three-dimensional geometries, and validating simulations against experimental crack paths in real engineering components.

Works

70,335

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1,168,149

Keywords

FractureMeshless MethodsExtended Finite Element MethodPeridynamicsPhase-Field ModelingRadial Basis Functions