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Published October 2019 | public
Journal Article

Anisotropy of the effective toughness of layered media


This continues the study of the effective toughness of layered materials started in Hossain et al. (2014) and Hsueh et al. (2018), with a focus on anisotropy. We use the phase-field model and the surfing boundary condition to propagate a crack macroscopically at various angles to the layers. We study two idealized situations, the first where the elastic modulus is uniform while the toughness alternates and a second where the toughness is uniform and the elastic modulus alternates. We find that in the first case of toughness heterogeneity the effective toughness displays 'anomalous isotropy' in that it is independent of the propagation direction and equal to that of the tougher material except when the crack propagation is parallel to the layers. In the second case of elastic heterogeneity, we find the behavior more anisotropic and consistent with the toughening effects of stress fluctuation and need for crack renucleation at the compliant-to-stiff interface. In both cases, the effective toughness is not convex in the sense of interfacial energy or Wulff shape reflecting the fact that crack propagation follows a critical path. Further, in both cases the crack path is not straight and consistent with a maximal dissipation principle. Finally, the effective toughness depends on the contrast and pinning, rather than on the extent of crack fluctuation.

Additional Information

© 2019 Elsevier Ltd. Received 16 April 2019, Revised 25 June 2019, Accepted 28 June 2019, Available online 29 June 2019. We gratefully acknowledge the support of the US National Science Foundation through Award no. DMS-1535083 and DMS-1535076 under the Designing Materials to Revolutionize and Engineer our Future (DMREF) Program. Some numerical simulations were performed using the Extreme Science and Engineering Discovery Environment (XSEDE) stampede2 at the Texas Advanced Computing Center (TACC) through the allocation TG-DMS060014, supported by National Science Foundation grant number ACI-1548562. The rest of simulations were performed at the Caltech high performance cluster supported in part by the Moore Foundation, USA.

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August 22, 2023
October 20, 2023