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A nonlocal fracture criterion and its effect on the mesh dependency of GraFEA

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Abstract

Recently, Khodabakhshi et al. (Meccanica 51(12):3129–3147, 2016. https://doi.org/10.1007/s11012-016-0560-6) presented a new method (by the name GraFEA) capable of studying fracture based on edge breakage within a classical FEA scheme which combines the best features of FEA and bond-breakage methods in a single framework. In this study, an attempt is made to investigate the mesh dependency of GraFEA by a set of numerical examples, and it is shown that using a local fracture criterion for edge failure will yield mesh-dependent results, as is already well known. A physically motivated nonlocal fracture criterion is implemented along with the edge breakage model, and its efficacy in eliminating the mesh sensitivity is investigated. The nonlocal criterion introduces a length scale into the problem. It is shown that by increasing the magnitude of the length scale parameter from zero, the damage pattern moves from localized fracture to diffuse damage pattern, yet with complete material separation (fracture) across a certain plane. It is shown by numerical results that, as expected, the introduction of the nonlocal fracture criterion eliminates the issue of mesh sensitivity, and thus predictions of the approximate crack paths and damage zone can be done within the classical FEA framework without the need for special formulations.

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Notes

  1. Linear triangular elements result in constant strains; therefore, the construction of the stiffness matrix does not require any numerical integration.

  2. The question of whether or not the results are mesh dependent is influenced by what we choose to measure. Following the standard practice in considering mesh dependency of fracture mechanics problems, we mainly check whether the global response is similar. The second thing we check is whether crack paths and damage zones are qualitatively similar. Here, it should be noted that from an experimental point of view even two nominally identical specimens do not show identical crack paths. However, broad features of the fracture zones do show similarities.

  3. The mesh generator used in this study is distmesh which gives approximately equilateral triangular elements. The average side length, \(a_{\text {avg}}\), is calculated over the elements which are located about the central horizontal line (refined area).

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Acknowledgements

The first two authors gratefully acknowledge the support of the present research by the Oscar S. Wyatt Endowed Chair.

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Authors and Affiliations

  1. Oden Institute for Computational Engineering and Sciences, University of Texas at Austin, Austin, TX, USA

    Parisa Khodabakhshi

  2. Department of Mechanical Engineering, Texas A&M University, College Station, TX, 77843-3123, USA

    J. N. Reddy & Arun Srinivasa

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  1. Parisa Khodabakhshi
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  3. Arun Srinivasa
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Correspondence to J. N. Reddy.

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Appendix: Convergence study of nonlocal to local fracture criterion

Appendix: Convergence study of nonlocal to local fracture criterion

In this Appendix, numerical results are provided to prove the convergence of the results from a nonlocal fracture criterion to those of a local fracture criterion with decreasing values of the length scale parameter (\(\ell _\mathrm{c} \rightarrow 0\)). The problem of Sect. 5.1 is reconsidered here with different values for the length scale parameter (\(\ell _\mathrm{c}/r\) starting from 0 and increasing in increments of 1% from 0 to 10%, and increasing in increments of 2% from 10 to 20%). The value of \(\ell _\mathrm{c}=0\%\) corresponds to the local fracture criterion, and \(\ell _\mathrm{c}>0\%\) corresponds to a nonlocal fracture criterion. Figure 18 depicts the damage zone for varying values of the length scale parameter, and one can notice that as \(\ell _\mathrm{c}\) decreases the crack path for the nonlocal fracture criterion approaches that of the local fracture criterion.

Figure 19 demonstrates the force–displacement relationship diagram for different values of \(\ell _\mathrm{c}\) for the problem of the study. Once again the convergence from a nonlocal to a local fracture criterion with decreasing values of the length scale parameter is obvious.

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Khodabakhshi, P., Reddy, J.N. & Srinivasa, A. A nonlocal fracture criterion and its effect on the mesh dependency of GraFEA. Acta Mech 230, 3593–3612 (2019). https://doi.org/10.1007/s00707-019-02479-8

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  • DOI: https://doi.org/10.1007/s00707-019-02479-8

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