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 λ, 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 λ → ∞. 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.

中文翻译：

---

粘弹性与弹性的关系

经受大变形的软材料表现出极其丰富的现象学，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描述中，人们通常遵循固体力学路线（拉格朗日描述）或流体力学路线（欧拉描述）。这篇综述的目的是强调粘弹性理论和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。我们回顾了控制粘弹性液体模型的原则，例如柔性聚合物的解决方案。此类材料的特征在于弛豫时间 λ，在该弛豫时间上应力松弛。我们回忆大变形的运动学和弹性响应，并显示哪些聚合物模型可以（哪些不可以）对应于极限 λ → ∞ 中的非线性弹性固体。有了这个见解，我们将弹性应力所做的功分解为可逆和耗散部分，并建立总能量守恒定律的一般形式。弹性对应可以为范围广泛的问题提供一个有见地的工具；作为示例，我们展示了弹性极限的存在与否如何决定毛细管不稳定期间弹性线的命运。弹性对应可以为范围广泛的问题提供一个有见地的工具；作为示例，我们展示了弹性极限的存在与否如何决定毛细管不稳定期间弹性线的命运。弹性对应可以为范围广泛的问题提供一个有见地的工具；作为示例，我们展示了弹性极限的存在与否如何决定毛细管不稳定期间弹性线的命运。