Soft random solids and their heterogeneous elasticity

Xiaoming Mao, Paul M. Goldbart, Xiangjun Xing, and Annette Zippelius
Phys. Rev. E 80, 031140 – Published 25 September 2009

Abstract

Spatial heterogeneity in the elastic properties of soft random solids is examined via vulcanization theory. The spatial heterogeneity in the structure of soft random solids is a result of the fluctuations locked-in at their synthesis, which also brings heterogeneity in their elastic properties. Vulcanization theory studies semimicroscopic models of random-solid-forming systems and applies replica field theory to deal with their quenched disorder and thermal fluctuations. The elastic deformations of soft random solids are argued to be described by the Goldstone sector of fluctuations contained in vulcanization theory, associated with a subtle form of spontaneous symmetry breaking that is associated with the liquid-to-random-solid transition. The resulting free energy of this Goldstone sector can be reinterpreted as arising from a phenomenological description of an elastic medium with quenched disorder. Through this comparison, we arrive at the statistics of the quenched disorder of the elasticity of soft random solids in terms of residual stress and Lamé-coefficient fields. In particular, there are large residual stresses in the equilibrium reference state, and the disorder correlators involving the residual stress are found to be long ranged and governed by a universal parameter that also gives the mean shear modulus.

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  • Received 19 December 2008

DOI:https://doi.org/10.1103/PhysRevE.80.031140

©2009 American Physical Society

Authors & Affiliations

Xiaoming Mao1,2, Paul M. Goldbart1, Xiangjun Xing3, and Annette Zippelius4,5

  • 1Department of Physics and Institute for Condensed Matter Theory, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, Illinois 61801, USA
  • 2Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
  • 3Department of Physics, Syracuse University, Syracuse, New York 13244, USA
  • 4Institut für Theoretische Physik, Georg-August-Universität Göttingen, 37077 Göttingen, Germany
  • 5Max Planck Institute for Dynamics and Self Organization, Bunsenstrasse 10, 37073 Göttingen, Germany

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Vol. 80, Iss. 3 — September 2009

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