Şengül Yasemin
Sabanci University, Faculty of Engineering and Natural Sciences, Tuzla, 34956 Istanbul, Turkey.
Proc Math Phys Eng Sci. 2021 Jan;477(2245):20200715. doi: 10.1098/rspa.2020.0715. Epub 2021 Jan 27.
There are some materials in nature that experience deformations that are not elastic. Viscoelastic materials are some of them. We come across many such materials in our daily lives through a number of interesting applications in engineering, material science and medicine. This article concerns itself with modelling of the nonlinear response of a class of viscoelastic solids. In particular, nonlinear viscoelasticity of strain rate type, which can be described by a constitutive relation for the stress function depending not only on the strain but also on the strain rate, is considered. This particular case is not only favourable from a mathematical analysis point of view but also due to experimental observations, knowledge of the strain rate sensitivity of viscoelastic properties is crucial for accurate predictions of the mechanical behaviour of solids in different areas of applications. First, a brief introduction of some basic terminology and preliminaries, including kinematics, material frame-indifference and thermodynamics, is given. Then, considering the governing equations with constitutive relationships between the stress and the strain for the modelling of nonlinear viscoelasticity of strain rate type, the most general model of interest is obtained. Then, the long-term behaviour of solutions is discussed. Finally, some applications of the model are presented.
自然界中存在一些经历非弹性变形的材料。粘弹性材料就是其中的一部分。通过工程、材料科学和医学中的许多有趣应用，我们在日常生活中会遇到许多这样的材料。本文关注一类粘弹性固体非线性响应的建模。特别地，考虑了应变率型非线性粘弹性，它可以通过一个不仅依赖于应变而且依赖于应变率的应力函数本构关系来描述。这种特殊情况不仅从数学分析的角度来看是有利的，而且基于实验观察，了解粘弹性性质的应变率敏感性对于准确预测不同应用领域中固体的力学行为至关重要。首先，给出了一些基本术语和预备知识的简要介绍，包括运动学、材料框架无关性和热力学。然后，考虑用于应变率型非线性粘弹性建模的应力与应变之间具有本构关系的控制方程，得到了最一般的感兴趣模型。接着，讨论了解的长期行为。最后，给出了该模型的一些应用。
