A Full-Network Rubber Elasticity Model based on Analytical Integration
A Full-Network Rubber Elasticity Model based on Analytical Integration
复制标题
基于解析积分的全网络橡胶弹性模型
DOI：
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发表时间：
2010
期刊：
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通讯作者：
R. Dargazany
中科院分区：
文献类型：
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作者：
M. Itskov;A. E. Ehret;R. Dargazany
全网络橡胶弹性模型通常需要在单位球面上进行数值积分。本文提出了一种基于拉伸方的幂函数级数解析积分方法。该方法既适用于朗之万逆函数，也适用于其四舍五入Padé逼近。在现有的条件下，积分幂函数级数可以快速收敛到解析解，或者基于高分辨率积分格式的数值解。与硅橡胶的实验数据也得到了很好的吻合。还实现了基于Q根运算符的积分过程，以求平均拉伸。这种算子的应用通常是为了在网络模型中引入微观和宏观拉伸之间的非仿射关系。
Full-network rubber elasticity models generally require numerical integration over the unit sphere. In the present paper, a procedure for analytical integration of power series in terms of stretch square is proposed instead. This procedure is applied both to the inverse Langevin function and its rounded Padé approximation. The integrated power series demonstrates fast convergence to the analytical solution so far as it is available or to the numerical one based on a high resolution integration scheme. Good agreement with experimental data on silicone rubber is obtained as well. The integration procedure is also implemented to average the stretch on the basis of a q-root operator. This operator is usually applied in order to introduce a non-affine relation between micro and macro stretches into a network model.