Extension of high-fidelity time-domain spectral element formulation for phase-field modeling of fracture: A static analysis

Abstract

This study presents the first extension of the high-fidelity time-domain spectral element method (TD-SEM) to develop a phase-field model for accurately and efficiently solving fracture problems in solids. TD-SEM combines the flexibility of the finite element method (FEM) with the precision of spectral methods. Compared to the standard finite element method, TD-SEM, which employs high-order shape functions within spectral elements, demonstrates superior accuracy and efficiency in solving continuum mechanics equations. The phase-field formulation captures complex crack behaviors, including initiation, propagation, and branching, without relying on predefined crack paths. Integrating TD-SEM with the phase-field method creates a hybrid technique that leverages the strengths of both frameworks, enabling precise predictions of intricate fracture patterns in solids. This study demonstrates that the phase-field TD-SEM exhibits superior performance compared to phase-field FEM and recently reported accelerated phase-field model in several aspects: it achieves a significantly faster convergence rate, maintains higher accuracy even with coarser meshes in the crack propagation region, and requires less computational effort. The phase-field TD-SEM is integrated into ABAQUS through the utilization of user-element (UEL) and user-material (UMAT) modules, with the weak coupled non-linear system being addressed by the in-built solver. The feasibility and effectiveness of the developed method are validated through several illustrative examples. This extension of high-fidelity TD-SEM for phase-field modeling shows promise for efficiently and accurately simulating crack propagation and phase-field evolution in fracture analysis.