Bond-associated deformation gradients for peridynamic correspondence model

Journal Article · 16 April 2018 · Mechanics Research Communications

DOI: https://doi.org/10.1016/j.mechrescom.2018.04.004 · OSTI ID:1631716

Chen, Hailong  ^[1]

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1. Idaho National Lab. (INL), Idaho Falls, ID (United States)

Non-ordinary state-based peridynamic correspondence material model is known to have issues with material instability, i.e. the existence of zero-energy modes, due to non-unique mapping between deformation states and force states via the conventional peridynamic deformation gradient. In this paper, an alternative approach in which the deformation gradient hence force state are computed specifically for each individual bond is proposed to eliminate the material instability. Bond-associated deformation gradient is calculated based on deformation states of material points within an individual bond’s proximity, termed here as the bond-associated family, rather than a material point’s whole family. This bond-associated deformation gradient can better represent the force state of each individual bond from the deformation states of material points in its proximity, and hence inherently resolves issues of material instability in the conventional correspondence material model. Parametric study on bond-associated horizon size indicates that the optimal size should be no less than the material point’s horizon size but smaller than two times of that value. Comparisons against reference solutions using finite element method establish the validity and accuracy of the proposed formulation.

• Research Organization: Idaho National Laboratory (INL), Idaho Falls, ID (United States)
• Sponsoring Organization: USDOE Office of Energy Efficiency and Renewable Energy (EERE)
• Grant/Contract Number: AC07-05ID14517
• OSTI ID: 1631716
• Report Number(s): INL/JOU--18-45154-Rev000
• Journal Information: Mechanics Research Communications, Journal Name: Mechanics Research Communications Journal Issue: C Vol. 90; ISSN 0093-6413
• Publisher: ElsevierCopyright Statement
• Country of Publication: United States
• Language: English