The nonlinear viscoelastic response of suspensions of rigid inclusions in rubber: I—Gaussian rubber with constant viscosity
The nonlinear viscoelastic response of suspensions of rigid inclusions in rubber: I—Gaussian rubber with constant viscosity
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橡胶中刚性夹杂物悬浮液的非线性粘弹性响应：恒粘度I-高斯橡胶
DOI：
10.1016/j.jmps.2021.104544
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发表时间：
2021
影响因子：
5.3
通讯作者：
Lopez-Pamies, Oscar
中科院分区：
文献类型：
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作者：
Ghosh, Kamalendu;Shrimali, Bhavesh;Kumar, Aditya;Lopez-Pamies, Oscar
本文对橡胶中刚性夹杂悬浮体在有限准静态变形下的宏观或均匀化粘弹性响应进行了数值和解析研究。重点是在原型情况下的随机各向同性悬浮液的等轴夹杂物牢固地嵌入各向同性不可压缩高斯橡胶具有恒定的粘度。从数值的角度来看，一个强大的计划被引入到解决管理的初边值问题的基础上符合Crouzeix-Raviart有限元离散的空间和高精度显式龙格库塔离散的时间，这是特别适合于处理有限变形和橡胶的不可压缩性约束所带来的挑战。该计划部署在各种负载条件下的相同（单分散）的大小的球形夹杂物的悬浮液的基本情况下产生的样品解决方案。从互补的角度来看，解析解是在以下极限下得出的：（i）小变形，（i i）无限小缓慢或无限快施加的有限变形，以及（i i i）当橡胶失去其储存弹性能量的能力并减少到牛顿流体时。引人注目的是，尽管下面的橡胶基质具有恒定的粘度的事实，解决方案表明，粘弹性响应的悬浮液表现出有效的非线性粘度的剪切稀化类型。该解决方案进一步表明，粘弹性响应的悬浮液具有相同类型的短程记忆行为，而不是通常预期的长程记忆行为，作为底层橡胶。在渐近解析结果和数值解的指导下，提出了一种简单而精确的悬架宏观粘弹性响应的近似解析解。
A numerical and analytical study is made of the macroscopic or homogenized viscoelastic response of suspensions of rigid inclusions in rubber under finite quasistatic deformations. The focus is on the prototypical case of random isotropic suspensions of equiaxed inclusions firmly embedded in an isotropic incompressible Gaussian rubber with constant viscosity. From a numerical point of view, a robust scheme is introduced to solve the governing initial–boundary-value problem based on a conforming Crouzeix–Raviart finite-element discretization of space and a high-order accurate explicit Runge–Kutta discretization of time, which are particularly well suited to deal with the challenges posed by finite deformations and the incompressibility constraint of the rubber. The scheme is deployed to generate sample solutions for the basic case of suspensions of spherical inclusions of the same (monodisperse) size under a variety of loading conditions. From a complementary point of view, analytical solutions are worked out in the limits:(i) of small deformations,(i i) of finite deformations that are applied either infinitesimally slowly or infinitely fast, and (i i i) when the rubber loses its ability to store elastic energy and reduces to a Newtonian fluid. Strikingly, in spite of the fact that the underlying rubber matrix has constant viscosity, the solutions reveal that the viscoelastic response of the suspensions exhibits an effective nonlinear viscosity of shear-thinning type. The solutions further indicate that the viscoelastic response of the suspensions features the same type of short-range-memory behavior—as opposed to the generally expected long-range-memory behavior—as that of the underlying rubber. Guided by the asymptotic analytical results and the numerical solutions, a simple yet accurate approximate analytical solution for the macroscopic viscoelastic response of the suspensions is proposed.
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DOI：
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发表时间：
1975
期刊：
影响因子：
--
作者：
B. Halphen;Q. Nguyen
通讯作者：
Q. Nguyen
粘弹性流体中粒子运动的数值模拟
影响因子：
5.3
作者：
Howard H. Hu
通讯作者：
Howard H. Hu
影响因子：
5.3
作者：
L. Brinson;W. Knauss
通讯作者：
W. Knauss
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影响因子：
9.9
作者：
M. M. Cross
通讯作者：
M. M. Cross
通过粘弹性复合材料中的平均场均匀化来简化模型。
DOI：
10.1098/rspa.2020.0869
发表时间：
2021
期刊：
Proceedings of the Royal Society A
影响因子：
--
作者：
N. Lahellec;M. I. Idiart;P. Suquet
通讯作者：
P. Suquet