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Optimal Scaling in Solids Undergoing Ductile Fracture by Crazing

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Abstract

We derive optimal scaling laws for the macroscopic fracture energy of polymers failing by crazing. We assume that the effective deformation-theoretical free-energy density is additive in the first and fractional deformation-gradients, with zero growth in the former and linear growth in the latter. The specific problem considered concerns a material sample in the form of an infinite slab of finite thickness subjected to prescribed opening displacements on its two surfaces. For this particular geometry, we derive optimal scaling laws for the dependence of the specific fracture energy on cross-sectional area, micromechanical parameters, opening displacement and intrinsic length of the material. In particular, the upper bound is obtained by means of a construction of the crazing type.

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Authors and Affiliations

  1. Institut für Angewandte Mathematik, Universität Bonn, Endenicher Allee 60, 53115, Bonn, Germany

    Sergio Conti

  2. Division of Engineering and Applied Science, California Institute of Technology, Pasadena, CA, 91125, USA

    Michael Ortiz

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  1. Sergio Conti
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  2. Michael Ortiz
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Correspondence to Michael Ortiz.

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Conti, S., Ortiz, M. Optimal Scaling in Solids Undergoing Ductile Fracture by Crazing. Arch Rational Mech Anal 219, 607–636 (2016). https://doi.org/10.1007/s00205-015-0901-y

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  • DOI: https://doi.org/10.1007/s00205-015-0901-y

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