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Brittle Fracture Modeling Using Ordinary State-Based Peridynamics with Continuous Bond-Breakage Damage

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Abstract

Different damage models are proposed in the literature to predict the behavior of dynamic fracture of brittle materials using the peridynamic formulation. The prototype micro-brittle material proposed by Silling and Askari (Comput. Struct. 83:1526−1535, 2005), PMB, and its modified version proposed by Du et al. (J. Elast. 132:197−218, 2018), DTT, concern bond-breakage damage criteria applied to a bond-based constitutive model. These models consider only the direct interaction between material points and have, therefore, a fixed Poisson’s ratio. Lipton et al. (J. Elast. 133:129−153, 2018) propose a state-based peridynamic model, LSJ, which, in addition to the strain state field, also considers a dilatational term and is coupled with a damage criterion that considers failure not only between bonds but also collectively, among all the bonds connected to a given material point. This criterion has two unrelated damage functions, one associated with the strain state field and the other one with its dilatational part only. In this work, we modify the LSJ model to consider only bond-breakage damage, rather than interaction-breakage damage, and call it the LSJ-T model. We also implement a bond-breakage damage criterion in the two-dimensional ordinary, state-based peridynamic model presented by Le et al. (Int. J. Numer. Methods Eng. 98:547−561, 2014), which we call the LPS-T model. In both cases, when the strain state of a bond reaches a critical value, rather than breaking, it is continuously damaged until bond-breakage occurs. To study the capability of these models in simulating the formation and the propagation of cracks, we have simulated numerically the experiment of a thin glass plate with an initial semi-crack under mode I loading. All the models were able to grasp the main features of crack propagation, such as the crack propagation speed and the crack pattern. Both the DTT and the LSJ-T models have predicted symmetric crack paths and no minor branches, which indicate a stable crack propagation path. We have also considered the experiment of a notched cement-mortar plate with a hole under quasi-static mode I loading. This experiment was simulated numerically using the aforementioned damage models together with a dynamic relaxation method. We have obtained solutions of the associated numerical problems, which yield a convergent sequence of response forces in terms of displacements. In addition, crack patterns predicted by these solutions are in good agreement with crack patterns observed experimentally.

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Notes

  1. See https://github.com/TulioVBP/PDLAB.

  2. See https://www.msi.umn.edu/mangi.

  3. Abaqus SoftwareTM is a product of Dassault Systèmes Simulia Corp.®, Providence, RI, USA.

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Acknowledgements

We thank the reviewers for their insightful comments. Financial support of São Paulo Research Foundation (FAPESP), grants n\(^\circ\) 2019/00428-7 and n\(^\circ\) 2020/04750-8, and of National Council for Scientific and Technological Development (CNPq), grant n\(^\circ\) 420099/2018-2, is gratefully acknowledged. Computational resources provided by the Minnesota Supercomputing Institute (MSI) at the University of Minnesota are also gratefully acknowledged.

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Authors and Affiliations

  1. Department of Structural Engineering, São Carlos School of Engineering, University of São Paulo, Av. Trabalhador Sãocarlense, 400, Cx. P. 359, São Carlos, 13560-590, SP, Brazil

    Adair R. Aguiar

  2. Via San Salvatore, Vercelli, 1, VC, Italy

    Túlio V. B. Patriota

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  1. Adair R. Aguiar
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Correspondence to Adair R. Aguiar.

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Aguiar, A.R., Patriota, T.V.B. Brittle Fracture Modeling Using Ordinary State-Based Peridynamics with Continuous Bond-Breakage Damage. J Peridyn Nonlocal Model 5, 81–120 (2023). https://doi.org/10.1007/s42102-021-00057-y

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  • DOI: https://doi.org/10.1007/s42102-021-00057-y

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