[论文解读] The exponentiated Hencky strain energy in modelling tire derived material for moderately large deformations

Giuseppe Montella, Sanjay Govindjee+1 more|arXiv (Cornell University)|Sep 22, 2015

Elasticity and Material Modeling参考文献 35被引用 5

一句话总结

本文提出了一种基于指数化 Hencky 应变能函数的超-viscoelastic 模型，以精确捕捉轮胎衍生材料（TDM）在中等大变形下的非线性、频率依赖性和振幅依赖性行为。该模型通过一组单一且具有物理解释性的参数，成功预测了压缩和剪切试验中的体积响应与偏量响应，与实验数据高度一致。

ABSTRACT

This work presents a hyper-viscoelastic model based on the Hencky-logarithmic strain tensor to model the response of a Tire Derived Material (TDM) undergoing moderately large deformations. TDM is a composite made by cold forging a mix of rubber fibers and grains, obtained by grinding scrap tires, and polyurethane binder. The mechanical properties are highly influenced by the presence of voids associated with the granular composition and low tensile strength due to the weak connection at the grain-matrix interface. For these reasons, TDM use is restricted to applications concerning a limited range of deformations. Experimental tests show that a central feature of the response is connected to highly nonlinear behavior of the material under volumetric deformation which conventional hyperelastic models fail in predicting. The strain energy function presented here is a variant of the exponentiated Hencky strain energy proposed by Neff et al., which for moderate strains is as good as the quadratic Hencky model and in the large strain region improves several important features from a mathematical point of view. The proposed form of the exponentiated Hencky energy possesses a set of parameters uniquely determined in the infinitesimal strain regime and an orthogonal set of parameters to determine the nonlinear response. The hyperelastic model is additionally incorporated in a finite deformation viscoelasticity framework that accounts for the two main dissipation mechanisms in TDMs, one at the microscale level and one at the macroscale level. The model is capable of predicting different deformation modes in a certain range of frequency and amplitude with a unique set of parameters with most of them having a clear physical meaning. Moreover, by comparing the predictions from the proposed constitutive model with experimental data we conclude that the new constitutive model gives accurate prediction.

研究动机与目标

• 开发一种本构模型，以准确捕捉轮胎衍生材料（TDM）在中等大变形下的高度非线性体积响应。
• 克服传统超弹性模型（如 Mooney-Rivlin、Ogden）在使用单一参数集时无法准确预测 TDM 复杂行为的局限性。
• 在有限变形 viscoelastic 框架中整合微观与宏观耗散机制，以提高预测准确性。
• 确保模型参数具有明确的物理意义，从而简化与基于多项式应变能函数相比的参数识别过程。
• 通过在压缩和剪切模式下，针对不同应变振幅和频率的广泛实验数据，对模型进行验证。

提出的方法

• 采用 Hencky-对数应变张量，以在有限应变下实现体积与偏量行为的解耦。
• 使用具有两组正交参数的指数化 Hencky 应变能函数：一组在无穷小变形范围内唯一确定，另一组用于描述非线性响应。
• 将超弹性模型嵌入有限变形 viscoelastic 框架中，采用两个 Maxwell 元件以表征微观与宏观耗散。
• 将 viscoelastic 应变能定义为超弹性和黏性贡献之和，每种耗散机制均具有频率和振幅依赖的参数。
• 利用在多个频率和振幅下进行的循环压缩和剪切试验的实验数据校准模型参数。
• 通过稳态滞后回线和不同 TDM 样品（500、600、800 kg/m³）每循环的能量耗散，对模型预测进行验证。

实验结果

研究问题

• RQ1 与经典超弹性模型相比，指数化 Hencky 应变能函数是否能更好地捕捉 TDM 的非线性体积响应？
• RQ2 如何通过一组单一且具有物理解释性的参数，描述 TDM 在不同变形模式（压缩、剪切）和加载条件下的行为？
• RQ3 TDM 中两种不同的耗散机制（微观与宏观）在多大程度上贡献于观察到的频率和振幅依赖性刚度与阻尼？
• RQ4 所提出的模型是否能准确预测不同应变振幅和频率下的每循环能量耗散？
• RQ5 该模型能否再现实验中观察到的能量耗散过渡区域，表明存在多种松弛机制？

主要发现

• 所提出的基于指数化 Hencky 的超-viscoelastic 模型，能准确预测在 0.1 Hz 至 25 Hz 频率范围和 10% 与 20% 振幅下，压缩和剪切试验中的稳态滞后曲线。
• 该模型捕捉到了随频率增加而刚度增大的趋势，在图 11 中与实验数据高度一致，显示高频下应力上升。
• 该模型正确再现了振幅依赖的软化行为，较低的压缩应变振幅导致更高的刚度，如图 12 所证实。
• 每循环的能量耗散如图 13 所示，表现出两个明显的过渡区域，验证了在 viscoelastic 模型中采用两个 Maxwell 元件的合理性。
• 微观耗散参数 μ_A 随振幅增加而减小，随后趋于平稳，准确捕捉了 Payne 效应，而 k_A 为频率相关但振幅无关。
• 宏观耗散参数 μ_B 为振幅相关但频率无关，证实了模型中物理机制的分离。