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Unstructured polygonal meshes with adaptive refinement for the numerical simulation of dynamic cohesive fracture

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Abstract

This paper presents a scheme for adaptive mesh refinement on unstructured polygonal meshes to better capture crack patterns in dynamic cohesive fracture simulations. A randomly seeded polygonal mesh leads to an isotropic discretization of the problem domain, which does not bias crack patterns, but restricts the number of paths that a crack may travel at each node. An adaptive refinement scheme is proposed and investigated through a detailed set of geometric studies. The refinement scheme is selectively chosen to optimize the number of paths that a crack may travel, while still maintaining a conforming domain discretization. The details of the refinement scheme are outlined, along with the criterion used to determine the region of refinement and the method of interpolating nodal attributes. Extrinsic cohesive elements are inserted when and where necessary, and follow the constitutive response of the Park–Paulino–Roesler cohesive model. The influence of bulk and cohesive material heterogeneity is investigated through the use of a statistical distribution of material properties. The adaptive mesh modifications are handled through a compact topological data structure. Numerical examples highlight the features of adaptive refinement in capturing physical fracture patterns while addressing computational cost. Thus, the present approach is a step towards obtaining accurate dynamic fracture patterns and fields with polygonal elements.

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Acknowledgments

Daniel W. Spring, Sofie E. Leon, and Glaucio H. Paulino gratefully acknowledge the support of the Natural Sciences and Engineering Research Council of Canada, the US National Science Foundation (NSF) Graduate Research Fellowship, and the Donald B. and Elizabeth M. Willett endowment at the University of Illinois at Urbana-Champaign, respectively. We also acknowledge support from NSF through Grants #1321661 and #1437535. The authors would also like to extend their appreciation to Dr. Cameron Talischi for his advice and input to this publication.

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  1. Department of Civil and Environmental Engineering, University of Illinois at Urbana-Champaign, 205 North Mathews Ave., Urbana, IL, 61801, USA

    Daniel W. Spring, Sofie E. Leon & Glaucio H. Paulino

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  1. Daniel W. Spring
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  2. Sofie E. Leon
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  3. Glaucio H. Paulino
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Correspondence to Glaucio H. Paulino.

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Spring, D.W., Leon, S.E. & Paulino, G.H. Unstructured polygonal meshes with adaptive refinement for the numerical simulation of dynamic cohesive fracture. Int J Fract 189, 33–57 (2014). https://doi.org/10.1007/s10704-014-9961-5

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