Kauçuk benzeri malzemelerde faz alanı yırtılma modellemesi için stokastik uzantı

Rubber-like materials are crucial in engineering applications as they undergo large reversible deformations. Predicting their failure is a complex challenge due to extreme non-linearities and singularities. A leading approach for modeling failure is the phase-field method, which models fracture as a continuous field of damage values that transition diffusely from intact to broken state. While convenient, standard deterministic models assume a homogeneous distribution of the material's critical energy governing fracture resistance. This assumption creates a discrepancy with physical reality. In idealized simulations, lack of internal distribution forces cracks to follow "perfect" paths that coalesce at the geometric center. Real elastomers contain manufacturing defects and heterogeneities, resulting in erratic crack topologies and statistical scatter. We address these limitations by developing a stochastic extension to the phase-field fracture framework. The motivations are to bridge the gap between idealized predictions and the scattered nature of experimental data, while obtaining crack paths similar to experiments. We introduce spatially correlated random fields into the material's critical energy density to mimic natural imperfections and break the artificial symmetry of homogeneous models. The hyperelastic behavior of Nitrile Butadiene Rubber is characterized using the extended eight-chain model, and fracture variability is quantified through uniaxial and Double Edge Notch Tension (DENT) experiments. Gaussian Random Fields (GRF) and gradient-based Perlin noise are implemented to replicate internal heterogeneity. Results demonstrate that introducing structured randomness successfully steers crack propagation, preventing unrealistic fracture paths. The proposed framework accurately reproduces the force-displacement response and the non-symmetric crack topologies observed experimentally.