Department of Mechanical Engineering and Materials Science , Rice University , Mail Stop 321, PO Box 1892, Houston, TX 77251-1892 , USA.
Philos Trans A Math Phys Eng Sci. 2019 May 6;377(2144):20180067. doi: 10.1098/rsta.2018.0067.
A relatively simple molecular-statistical model for rubber elasticity, similar to the Wang-Guth and the Arruda-Boyce (AB) models, is presented. Discussion of some approximate inverse Langevin functions leads to the selection of a new one as the most attractive balance between accuracy and simplicity. Use of this approximation with the AB model, in particular, yields the logarithmic strain energy introduced by Gent that exhibits limiting chain extensibility. A rather unusual facet of the relationship between the three strain energies is that the new one is the mean of the other two. This article is part of the theme issue 'Rivlin's legacy in continuum mechanics and applied mathematics'.
本文提出了一种与 Wang-Guth 和 Arruda-Boyce（AB）模型类似的相对简单的橡胶弹性分子统计模型。对一些近似逆 Langevin 函数的讨论导致选择了一个新的函数，它在准确性和简单性之间取得了较好的平衡。该近似与 AB 模型的结合，特别是产生了 Gent 提出的具有限制链伸长率的对数应变能。三种应变能之间的关系有一个相当不寻常的特点，即新的应变能是另外两种应变能的平均值。本文是主题为“Rivlin 在连续力学和应用数学中的遗产”的一部分。
