An efficient explicit–implicit adaptive method for peridynamic modeling of quasi-static fracture formation and evolution

Shiwei Hu, Tianbai Xiao, Mingshuo Han, Zuoxu Li, Erkan Oterkus, Selda Oterkus, Yonghao Zhang*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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.
Original languageEnglish
Article number111046
JournalEngineering Fracture Mechanics
Volume320
Early online date22 Mar 2025
DOIs
Publication statusE-pub ahead of print - 22 Mar 2025

Funding

The authors acknowledge the financial support of the National Science Foundation of China (No. 12302381) and the computing resources provided by Hefei Advanced Computing Center.

Keywords

  • Peridynamics
  • Quasi-static fracture mechanics
  • Computational mechanics
  • Implicit method
  • Explicit ADR

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