A meshfree peridynamic model for brittle fracture in randomly heterogeneous materials

In this work we aim to develop a unified mathematical framework and reliable computational approach model the brittle fracture in heterogeneous materials with variability material microstructures, provide statistic metrics for quantities of interest, such as toughness. To depict responses naturally describe nucleation growth fractures, consider peridynamics model. particular, stochastic state-based peridynamic is developed, where micromechanical parameters are modeled by finite-dimensional random vector, or combination variables truncating Karhunen-Lo\`{e}ve decomposition principle component analysis (PCA). solve problem, probabilistic collocation method (PCM) employed sample field representing parameters. For each sample, deterministic problem discretized an optimization-based meshfree quadrature rule. We present rigorous proposed scheme demonstrate its convergence number benchmark problems, showing that it sustains asymptotic compatibility spatially achieves algebraic sub-exponential rate space points grows. Finally, validate applicability on real-world crystallization toughening glass-ceramic materials, which at microstructural scale contains both amorphous glass crystalline phases. The solver capture crack initiation glass-ceramics different crystal volume fractions, averaged toughness calculated. numerical estimates show good consistency experimental measurements.