Efficient phase-field modelling of quasi-brittle fracture with a Taylor series-least square neighboured point method

This study introduces an innovative semi-explicit phase-field model (PFM) designed for the efficient simulation of quasi-brittle fracture in structures, composed of concrete-like materials. The approach establishes direct interactions between points via the Taylor series expansion and least square regression, decoupling the solution from mesh topological constraints. By discretizing damage fields at integration points and approximating the Laplace operator using a neighboured point algorithm, the model mitigates numerical instability and mesh dependency issues inherent in traditional element-based schemes. Ghost points are introduced to enforce Neumann boundary conditions, while the pre-computation of the Laplacian coefficient matrices ensures computational efficiency through vector operations. The semi-explicit framework combines the advantages of explicit time integration for displacement fields with localised Newton iteration for phase-field evolution, eliminating the need for artificial viscosity coefficients and improving numerical stability. Numerical implementations in ABAQUS/Explicit validate the method across typical benchmarks, including mode I and mixed-mode fractures, and meso-scale simulations of concrete with random meso-structures. Results demonstrate negligible mesh sensitivity, accurate crack pattern predictions, and a 70–72% reduction in CPU time compared to fully explicit PFMs, underscoring its suitability for intricate engineering fracture challenges.