Imposition of local boundary conditions in peridynamics without a fictitious layer and unphysical stress concentrations

Behera, Deepak; Roy, Pranesh; Anicode, Sundaram Vinod K.; Madenci, Erdogan; Spencer, Benjamin

doi:10.1016/j.cma.2022.114734

Title: Imposition of local boundary conditions in peridynamics without a fictitious layer and unphysical stress concentrations

Journal Article · 31 March 2022 · Computer Methods in Applied Mechanics and Engineering

DOI: https://doi.org/10.1016/j.cma.2022.114734 · OSTI ID:1862687

Behera, Deepak ^[1]; Roy, Pranesh ^[2]; Anicode, Sundaram Vinod K. ^[1];

^[1];

^[3]

Univ. of Arizona, Tucson, AZ (United States)
Univ. of Arizona, Tucson, AZ (United States); Indian Institute of Technology, Dhanbad (India)
Idaho National Lab. (INL), Idaho Falls, ID (United States)

Here, this study introduces a general approach for the imposition of local boundary conditions in non- ordinary state-based peridynamics (NOSB PD) to eliminate the displacement kinks near the boundary without a fictitious layer under quasi-static loading conditions. It identifies the underlying reason for the unphysical displacement kinks. Under an imposed linear displacement field, the NOSB PD equilibrium equation is not satisfied near the boundary due to the unsymmetric horizon of material points. However, the equilibrium equation derived by using the PD differential operator is satisfied at such material points. Therefore, the material body is divided into three regions to satisfy the equilibrium equations and to impose displacement and tractions boundary conditions. This approach does not deviate from the original NOSB PD; however, it provides a simple solution to eliminate the displacement kink near the boundary, which leads to unphysical stress concentrations. Its efficacy is demonstrated by considering elastic rectangular and square plates subjected to various types of boundary conditions leading to homogeneous as well as nonhomogeneous deformations. The creep response of a rectangular plate further proves the robustness of the present approach. Also, a quasi-static crack propagation from a pre-existing crack in a square plate under mode-I, mode-II and mixed-mode loading conditions demonstrates its capability for failure prediction based on the critical stretch criteria. Finally, its applicability for 3D analysis is demonstrated by considering a rectangular prism under applied stretch and normal stress.

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Research Organization:: Idaho National Laboratory (INL), Idaho Falls, ID (United States)

Sponsoring Organization:: USDOE Office of Nuclear Energy (NE), Nuclear Energy University Program (NEUP); Air Force Office of Scientific Research (AFOSR)

Grant/Contract Number:: AC07-05ID14517; NE0008537

OSTI ID:: 1862687

Report Number(s):: INL/JOU-21-63107

Journal Information:: Computer Methods in Applied Mechanics and Engineering, Journal Name: Computer Methods in Applied Mechanics and Engineering Journal Issue: N/A Vol. 393; ISSN 0045-7825

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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97 MATHEMATICS AND COMPUTING
42 ENGINEERING
peridynamics
nonlocal
boundary conditions
displacement
traction

Title: Imposition of local boundary conditions in peridynamics without a fictitious layer and unphysical stress concentrations

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