Sparse polynomial chaos expansion and adaptive mesh refinement for enhanced fracture prediction using phase-field method

Abstract

Phase-field models (PFMs) have proven to accurately predict complex crack patterns such as crack branching, merging, and crack fragmentation, but they are computationally costly. This study stems from the high computational costs associated with non-adaptive PFMs for brittle fracture analysis, which require dense meshes. This makes training data generation for surrogate models prohibitively expensive. To address these challenges, this paper proposes an adaptive mesh refinement (AMR) informed sparse polynomial chaos expansion (PCE) framework. The AMR algorithm is incorporated into the fracture analysis workflow to maximize the computational efficiency in data generation, eliminating the need for pre-refinement. The AMR informed sparse PCE is calibrated with Bayesian compressive sensing (BCS) to efficiently map domain input parameters to quantities of interest (QoIs), even with limited training data. We employ a multi-output QoI approach to predict load–displacement relationships with high resolution. The novelty of this work lies in the integration of AMR into the PFM workflow and the application of sparse PCE for brittle fracture analysis. Benchmark tests demonstrate the proposed method’s superior accuracy and computational efficiency compared to conventional AMR method, marking a notable improvement in fracture mechanics.