Dual‐horizon peridynamics

By Huilong Ren, Xiaoying Zhuang, Yongchang Cai, Timon Rabczuk. 2015

730 citations recorded by the source corpus.

In this paper, we develop a dual‐horizon peridynamics (DH‐PD) formulation that naturally includes varying horizon sizes and completely solves the ‘ghost force’ issue. Therefore, the concept of dual horizon is introduced to consider the unbalanced interactions between the particles with different horizon sizes. The present formulation fulfills both the balances of linear momentum and angular momentum exactly. Neither the ‘partial stress tensor’ nor the ‘slice’ technique is needed to ameliorate the ghost force issue. We will show that the traditional peridynamics can be derived as a special case of the present DH‐PD. All three peridynamic formulations, namely, bond‐based, ordinary state‐based, and non‐ordinary state‐based peridynamics, can be implemented within the DH‐PD framework. Our DH‐PD formulation allows for h‐adaptivity and can be implemented in any existing peridynamics code with minimal changes. A simple adaptive refinement procedure is proposed, reducing the computational cost. Both two‐dimensional and three‐dimensional examples including the Kalthoff–Winkler experiment and plate with branching cracks are tested to demonstrate the capability of the method. Copyright © 2016 John Wiley & Sons, Ltd.

Subfields: Civil and Structural Engineering, Electrical and Electronic Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/fe34c4895a076692e8ca3ba2b1bdcdba5da77a93

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In Civil and Structural Engineering

In Electrical and Electronic Engineering

In Mechanics of Materials

Citations in the corpus

A phase-field modeling approach of fracture propagation in poroelastic media (2018, methodology): “The cracking particle method [9], peridynamics [10] and dualhorizon peridynamics [11] are discrete crack approaches which do not exhibit such drawbacks and are therefore well suited for dynamic fracture including complex crack interactions.”
A coupled thermo-mechanical bond-based peridynamics for simulating thermal cracking in rocks (2018, background): “Ren et al. (2016, 2017) proposed the dual-horizon peridynamicmethod to study dynamic fracture behaviors in brittle solids.”
Phase field modeling of quasi-static and dynamic crack propagation: COMSOL implementation and case studies (2018, methodology): “6 2D dynamic shear loading of Kalthoff experiment We next test our method for dynamic fracture by taking advantage of the Kalthoff-Winkler experiments [52] which has been studied by several other researchers [14, 53–59].”
Dual-horizon peridynamics: A stable solution to varying horizons (2017, methodology): “We showed in [26] that DH-PD fulfills these basic principles.”