Multiplicative, Non-Newtonian Viscoelasticity Models for Rubber Materials and Brain Tissues: Numerical Treatment and Comparative Studies
Multiplicative, Non-Newtonian Viscoelasticity Models for Rubber Materials and Brain Tissues: Numerical Treatment and Comparative Studies
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橡胶材料和脑组织的乘法非牛顿粘弹性模型：数值处理和比较研究
DOI：
10.1007/s11831-023-09889-x
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发表时间：
2023
影响因子：
9.7
通讯作者：
P. Wriggers
中科院分区：
文献类型：
--
作者：
Alexander Ricker;Meike Gierig;P. Wriggers
在许多方面，弹性体和软生物组织表现出类似的机械性能，例如显著的非线性应力-应变关系和对外部载荷的粘弹性响应。因此，许多模型使用相同的流变框架和材料函数来捕获它们的行为。因此，粘度函数通常假定为常数，相应的自由能函数遵循长期平衡响应之一。这项工作的问题，这一假设，并提出了一个详细的研究弹性体和脑组织的非牛顿粘度函数。粘度函数与几种常用的自由能函数配对，并分别在循环和松弛实验中拟合到两种不同类型的弹性体和脑组织。确定了合适的粘度和自由能函数的不同材料，粘弹性的数值方面的解决。从乘法分解的变形梯度，并确保非负耗散率，四个等效的粘弹性公式推导出，采用不同的内部变量。使用隐式指数映射作为时间积分方案，这四个配方的数值行为相互比较，并确定数值稳健的候选人。拟合结果表明，非牛顿粘度函数显着提高拟合质量。它示出的粘度函数的选择是更重要的比自由能函数的选择和经典的新胡克的方法往往是一个足够的选择。此外，数值研究表明，四个粘弹性配方的优越性，特别是当复杂的有限元模拟进行。
In many aspects, elastomers and soft biological tissues exhibit similar mechanical properties such as a pronounced nonlinear stress–strain relation and a viscoelastic response to external loads. Consequently, many models use the same rheological framework and material functions to capture their behavior. The viscosity function is thereby often assumed to be constant and the corresponding free energy function follows that one of the long-term equilibrium response. This work questions this assumption and presents a detailed study on non-Newtonian viscosity functions for elastomers and brain tissues. The viscosity functions are paired with several commonly used free energy functions and fitted to two different types of elastomers and brain tissues in cyclic and relaxation experiments, respectively. Having identified suitable viscosity and free energy functions for the different materials, numerical aspects of viscoelasticity are addressed. From the multiplicative decomposition of the deformation gradient and ensuring a non-negative dissipation rate, four equivalent viscoelasticity formulations are derived that employ different internal variables. Using an implicit exponential map as time integration scheme, the numerical behavior of these four formulations are compared among each other and numerically robust candidates are identified. The fitting results demonstrate that non-Newtonian viscosity functions significantly enhance the fitting quality. It is shown that the choice of a viscosity function is even more important than the choice of a free energy function and the classical neo-Hooke approach is often a sufficient choice. Furthermore, the numerical investigations suggest the superiority of two of the four viscoelasticity formulations, especially when complex finite element simulations are to be conducted.
影响因子：
5
作者：
Carleo, Francesca;Barbieri, Ettore;Busfield, James J. C.
通讯作者：
Busfield, James J. C.