Adaptive discretization of complex planar crack shapes for numerical analysis

Abstract

The study introduced the creation and execution of a resilient discretization technique for the numerical analysis of intricate planar fracture geometries. The programme used adaptive Delaunay triangulation and proposed a technique for producing control points on the border and inside the domain. A hybrid method for mesh creation was used, integrating boundary-fitted discretization with the structured production of interior points. The created programme enabled accurate regulation of mesh density via the h0 parameter and guaranteed a consistent transition between boundary and interior components. The findings revealed the algorithm's capacity to produce high-quality meshes for diverse geometries, with enhanced control over element form and size. Numerical validation affirmed the method's efficacy for element quality, convergence, and adaptability to diverse geometric configurations. The Python implementation enabled integration with other numerical analytic tools and offered a versatile platform for subsequent advancements.