A finite strain framework for the simulation of polymer curing. Part II. Viscoelasticity and shrinkage
A finite strain framework for the simulation of polymer curing. Part II. Viscoelasticity and shrinkage
复制标题
DOI：
10.1007/s00466-010-0479-z
复制
发表时间：
2010-02
影响因子：
4.1
通讯作者：
M. Hossain;G. Possart;P. Steinmann
中科院分区：
文献类型：
--
作者：
M. Hossain;G. Possart;P. Steinmann
一个现象学的启发，elasticfinite应变框架来模拟聚合物的固化已被开发和讨论的第一部分（Hossain等人。in Comput Mech 44（5）：621-630，2009）。目前的贡献提供了一个扩展以前的模拟概念对考虑的粘弹性效应和固化收缩现象。所提出的方法特别独立于自由能密度的类型，即可以利用任何基于现象学或微机械的粘弹性聚合物模型。对于这两种情况下，相同的代表已被用于弹性固化模型，即新胡克模型和21链微球模型，相应地进行了审查和扩展。的控制方程推导以及相应的切线算子内的有限元方法的数值实现所必需的。此外，我们研究了两种不同的方法-收缩应变函数和变形梯度的乘法分解-捕捉固化收缩的现象，即由聚合反应引起的体积减小，这可能会导致显着的残余应力和应变在完全固化的材料。一些有代表性的数值例子总结了这项工作，并证明了我们的方法能够正确捕捉正在经历固化过程的聚合物的非弹性行为和收缩效应。
A phenomenologically inspired,elasticfinite strain framework to simulate the curing of polymers has been developed and discussed in the first part (Hossain et al. in Comput Mech 44(5):621–630, 2009) of this work. The present contribution provides an extension of the previous simulation concept towards the consideration ofviscoelasticeffects and the phenomenon ofcuring shrinkage. The proposed approach is particularly independent of the type of the free energy density, i.e. any phenomenologically or micromechanically based viscoelastic polymer model can be utilised. For both cases the same representatives that have been used for the elastic curing models, i.e. the Neo-Hookean model and the 21-chain microsphere model, are reviewed and extended accordingly. The governing equations are derived as well as the corresponding tangent operators necessary for the numerical implementation within the finite element method. Furthermore, we investigate two different approaches—a shrinkage strain function and a multiplicative decomposition of the deformation gradient–to capture the phenomenon of curing shrinkage, i.e. the volume reduction induced by the polymerisation reaction which may lead to significant residual stresses and strains in the fully cured material. Some representative numerical examples conclude this work and prove the capability of our approach to correctly capture inelastic behaviour and shrinkage effects in polymers undergoing curing processes.