An Efficient Explicit-Implicit Adaptive Method for Peridynamic Modelling of Quasi-Static Fracture Formation and Evolution

TL;DR

This paper develops and compares explicit and implicit peridynamic methods for simulating quasi-static fracture formation, introducing an adaptive scheme that switches between methods for improved efficiency and accuracy.

Contribution

It introduces an implicit bond-based peridynamics method, compares it with explicit ADR, and develops an adaptive explicit-implicit scheme with a switching criterion.

Findings

Implicit methods are more computationally efficient.

Explicit-implicit adaptive method accelerates simulations by 6.4 to 141.7 times.

The adaptive scheme effectively balances accuracy and efficiency.

Abstract

Understanding the quasi-static fracture formation and evolution is essential for assessing the mechanical properties and structural load-bearing capacity of materials. Peridynamics (PD) provides an effective computational method to depict fracture mechanics. The explicit adaptive dynamic relaxation (ADR) method and the implicit methods are two mainstream PD approaches to simulate evolution of quasi-static fractures. However, no comprehensive and quantitative studies have been reported to compare their accuracy and efficiency. In this work, we first develop an implicit method for bond-based peridynamics (BBPD) based on the full nonlinear equilibrium equation and the degenerate form of the bond failure function, where the Jacobian matrices are derived using the Newton-Raphson (NR) scheme. Subsequently, we analyze the solvability of the implicit BBPD scheme. Second, a consistent and comprehensive comparison of accuracy and efficiency of the explicit ADR and implicit methods is conducted, which reveals computational efficiency of the implicit methods and their limitations in accurately describing crack formation. Finally, by utilizing the unique advantage of both methods, we develop an adaptive explicit-implicit method and propose a switching criterion to deploy appropriate scheme accordingly. Four typical quasi-static problems are employed as the numerical experiments, which show the acceleration ratios of the current method range from 6.4 to 141.7 when compared to the explicit ADR. Therefore, the explicit-implicit adaptive method provides a powerful method to simulate quasi-static fracture formation and evolution.