Brezmrežna numerična rešitev modela faznega polja za nastanek in razširjanje razpok pri termomehanskem procesiranju jekel

Accurately predicting crack initiation and propagation in brittle materials under complex mechanical and thermo-mechanical loads presents a significant challenge in computational mechanics. This study introduces a robust meshless framework that employs the Local Radial Basis Function Collocation Method (LRBFCM) for the first time to address challenges associated with modelling Phase Field (PF) fracture problems. A preliminary investigation evaluates polyharmonic splines (PHS) and multiquadrics (MQ) as radial basis functions for diffusion problems, emphasising PHS's enhanced stability and accuracy. Consequently, the PHS is utilised exclusively as an interpolation function in the fourth-order PF modelling of crack propagation, integrated with mechanical and thermal fields in a staggered approach. The isotropic PF is employed for mode I crack propagation, which is extended to the hybrid PF method. The hybrid PF method has been validated for crack propagation against benchmark problems subjected to tensile, shear, compressive, and coupled thermo-mechanical loads. The results indicate high accuracy and strong convergence for both regular and scattered node arrangements. Substantial reductions in computational costs are achieved through node pre-refinement and adaptive loading size. This study represents the first application of LRBFCM in PF fracture modelling, establishing a robust platform for simulating intricate fracture phenomena during the thermo-mechanical processing of steel.