Abstract
Abstract This research introduces the Stochastic Extended Isogeometric Analysis (XIGA) method to investigate fracture behavior of isotropic and orthotropic materials under mechanical, thermal, and thermomechanical loads. Employing knot spans from Isogeometric Analysis (IGA) for domain discretization, the study utilizes identical basis functions for geometry construction and solution discretization. Utilizing Extended Finite Element Method (XFEM) enrichment functions, accurate crack face displacement discontinuity and tip singularity within the stress field are characterized. Additionally, employing a second-order perturbation technique within XIGA framework, the research derives mean and coefficient of variance values for mixed-mode Stress Intensity Factors (SIF). Stochastic variations in material elastic properties, crack length, and crack angle are considered in this computation. Credibility and robustness of the study are confirmed through comparative analyses against available literatures and Monte Carlo Simulations (MCS). The observed exceptional agreement validates the precision and reliability of the proposed stochastic XIGA method for fracture analysis in orthotropic material systems under thermomechanical loading conditions.
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