Mao Xiaoming, Goldbart Paul M, Xing Xiangjun, Zippelius Annette
Department of Physics and Institute for Condensed Matter Theory, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Sep;80(3 Pt 1):031140. doi: 10.1103/PhysRevE.80.031140. Epub 2009 Sep 25.
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.
通过硫化理论研究了软随机固体弹性性质的空间异质性。软随机固体结构中的空间异质性是其合成过程中锁定的涨落的结果，这也导致了它们弹性性质的异质性。硫化理论研究了形成随机固体的系统的半微观模型，并应用副本场理论来处理它们的淬火无序和热涨落。软随机固体的弹性变形被认为是由硫化理论中包含的涨落的戈德斯通部分来描述的，这与一种与液-随机固体转变相关的微妙的自发对称破缺形式有关。这个戈德斯通部分的自由能可以重新解释为来自对具有淬火无序的弹性介质的唯象描述。通过这种比较，我们得出了软随机固体弹性淬火无序的统计，用残余应力和拉梅系数场来表示。特别是，在平衡参考状态下存在很大的残余应力，并且发现涉及残余应力的无序关联函数是长程的，并且由一个通用参数控制，该参数也给出了平均剪切模量。
