Snoeijer J H, Pandey A, Herrada M A, Eggers J
Physics of Fluids Group, Faculty of Science and Technology, Mesa+ Institute, University of Twente, 7500 AE Enschede, The Netherlands.
Depto. de Mecánica de Fluidos e Ingeniería Aeroespacial, Universidad de Sevilla, 41092 Sevilla, Spain.
Proc Math Phys Eng Sci. 2020 Nov;476(2243):20200419. doi: 10.1098/rspa.2020.0419. Epub 2020 Nov 18.
Soft materials that are subjected to large deformations exhibit an extremely rich phenomenology, with properties lying in between those of simple fluids and those of elastic solids. In the continuum description of these systems, one typically follows either the route of solid mechanics (Lagrangian description) or the route of fluid mechanics (Eulerian description). The purpose of this review is to highlight the relationship between the theories of viscoelasticity and of elasticity, and to leverage this connection in contemporary soft matter problems. We review the principles governing models for viscoelastic liquids, for example solutions of flexible polymers. Such materials are characterized by a relaxation time , over which stresses relax. We recall the kinematics and elastic response of large deformations, and show which polymer models do (and which do not) correspond to a nonlinear elastic solid in the limit → ∞. With this insight, we split the work done by elastic stresses into reversible and dissipative parts, and establish the general form of the conservation law for the total energy. The elastic correspondence can offer an insightful tool for a broad class of problems; as an illustration, we show how the presence or absence of an elastic limit determines the fate of an elastic thread during capillary instability.
承受大变形的软材料展现出极为丰富的现象学，其性质介于简单流体和弹性固体之间。在对这些系统的连续介质描述中，人们通常遵循固体力学的路径（拉格朗日描述）或流体力学的路径（欧拉描述）。本综述的目的是突出粘弹性理论与弹性理论之间的关系，并在当代软物质问题中利用这种联系。我们回顾了支配粘弹性液体模型的原理，例如柔性聚合物溶液。这类材料的特征在于一个松弛时间，应力在该时间内松弛。我们回顾大变形的运动学和弹性响应，并展示哪些聚合物模型在极限→∞时对应（以及哪些不对应）非线性弹性固体。有了这一见解，我们将弹性应力所做的功分为可逆部分和耗散部分，并建立总能量守恒定律的一般形式。弹性对应关系可为一大类问题提供有见地的工具；作为例证，我们展示了弹性极限的存在与否如何决定弹性细丝在毛细不稳定性过程中的命运。
