An Entropy Dynamics Approach for Deriving and Applying Fractal and Fractional Order Viscoelasticity to Elastomers
An Entropy Dynamics Approach for Deriving and Applying Fractal and Fractional Order Viscoelasticity to Elastomers
复制标题
用于导出分形和分数阶粘弹性并将其应用于弹性体的熵动力学方法
DOI：
10.1115/1.4062389
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发表时间：
2023
期刊：
影响因子：
--
通讯作者：
Oates, William
中科院分区：
文献类型：
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作者：
Pahari, Basanta R.;Stanisauskis, Eugenia;Mashayekhi, Somayeh;Oates, William
熵动力学是一种贝叶斯推理方法，可用于量化随时间变化的后验概率密度，从而指导使用信息理论开发复杂材料模型。在这里，我们将其应用扩展到非高斯过程，以评估分形结构如何影响弹性体的分数超弹性和粘弹性。我们研究了分形聚合物网络变形的运动学约束如何影响介电弹性体等软材料的超弹性本构行为和粘弹性的形式，这在自适应结构的发展中具有应用。建模框架在两种介电弹性体VHB 4910和4949上进行了验证，拉伸率范围很广。研究表明，在恒定拉伸率下，局部分形时间导数与非局部分数时间导数在预测这些材料的粘弹性方面同样有效。我们描述了这种精度的起源，它对模拟大规模问题（如有限元分析）具有影响，因为非局部分数阶导数与局部分形导数的计算效率存在差异。
Entropy dynamics is a Bayesian inference methodology that can be used to quantify time-dependent posterior probability densities that guide the development of complex material models using information theory. Here, we expand its application to non-Gaussian processes to evaluate how fractal structure can influence fractional hyperelasticity and viscoelasticity in elastomers. We investigate how kinematic constraints on fractal polymer network deformation influences the form of hyperelastic constitutive behavior and viscoelasticity in soft materials such as dielectric elastomers, which have applications in the development of adaptive structures. The modeling framework is validated on two dielectric elastomers, VHB 4910 and 4949, over a broad range of stretch rates. It is shown that local fractal time derivatives are equally effective at predicting viscoelasticity in these materials in comparison to nonlocal fractional time derivatives under constant stretch rates. We describe the origin of this accuracy that has implications for simulating large-scale problems such as finite element analysis given the differences in computational efficiency of nonlocal fractional derivatives versus local fractal derivatives.