Milkus Rico, Zaccone Alessio
Statistical Physics Group, Department of Chemical Engineering and Biotechnology, University of Cambridge, New Museums Site, Cambridge CB2 3RA, United Kingdom.
Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB30HE, United Kingdom.
Phys Rev E. 2017 Feb;95(2-1):023001. doi: 10.1103/PhysRevE.95.023001. Epub 2017 Feb 1.
Viscoelasticity has been described since the time of Maxwell as an interpolation of purely viscous and purely elastic response, but its microscopic atomic-level mechanism in solids has remained elusive. We studied three model disordered solids: a random lattice, the bond-depleted fcc lattice, and the fcc lattice with vacancies. Within the harmonic approximation for central-force lattices, we applied sum rules for viscoelastic response derived on the basis of nonaffine atomic motions. The latter motions are a direct result of local structural disorder, and in particular, of the lack of inversion symmetry in disordered lattices. By defining a suitable quantitative and general atomic-level measure of nonaffinity and inversion symmetry, we show that the viscoelastic responses of all three systems collapse onto a master curve upon normalizing by the overall strength of inversion-symmetry breaking in each system. Close to the isostatic point for central-force lattices, power-law creep G(t)∼t^{-1/2} emerges as a consequence of the interplay between soft vibrational modes and nonaffine dynamics, and various analytical scalings, supported by numerical calculations, are predicted by the theory.
自麦克斯韦时代以来，粘弹性就被描述为纯粘性和纯弹性响应的一种插值，但它在固体中的微观原子级机制仍然难以捉摸。我们研究了三种无序固体模型：随机晶格、键耗尽的面心立方晶格和有空位的面心立方晶格。在中心力晶格的简谐近似范围内，我们应用了基于非仿射原子运动推导的粘弹性响应求和规则。后者的运动是局部结构无序的直接结果，特别是无序晶格中缺乏反演对称性的结果。通过定义一个合适的非亲和性和反演对称性的定量且通用的原子级度量，我们表明，在通过每个系统中反演对称性破坏的整体强度进行归一化后，所有三个系统的粘弹性响应都汇聚到一条主曲线上。接近中心力晶格的等静点时，由于软振动模式和非仿射动力学之间的相互作用，出现了幂律蠕变G(t)∼t^(-1/2)，并且该理论预测了由数值计算支持的各种解析标度。
