Visco-hyperelastic constitutive modeling of strain rate sensitive soft materials
Visco-hyperelastic constitutive modeling of strain rate sensitive soft materials
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DOI：
10.1016/j.jmps.2019.103777
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发表时间：
2020-02-01
影响因子：
5.3
通讯作者：
Spearot, Douglas
中科院分区：
文献类型：
--
作者：
Upadhyay, Kshitiz;Subhash, Ghatu;Spearot, Douglas
提出了一种新的粘性耗散势用于软材料短时记忆响应的粘-超弹性本构模型，该模型能够在较宽的应变率范围内捕捉线性和非线性大变形行为。建议的潜力是兼容的客观性和连续热力学原理，由物理激励的模型参数，并增加了在小应变制度，这是目前不可能与可用的外部状态变量驱动的粘性耗散潜力的应变率敏感性建模的能力。通过结合建议的粘性耗散潜力与Mooney-Rivlin应变能密度函数，制定了一个粘超弹性关系，并适合于率相关的拉伸应力应变数据的人髌腱，这是以前建模使用现有的粘性耗散潜力。结果表明，该模型提供了改进的拟合精度，并防止可能的热力学不稳定性准静态超弹性模型从腐败的动态响应。此外，模型的简单数学形式和伴随的多步多起点优化过程有助于防止数值不稳定性。多变形模式拟合人脑灰质下的所有三个主要的变形模式（压缩，拉伸和剪切）也被认为是使用一个粘超弹性模型的基础上提出的潜力和半经验的Gent-Gent应变能密度函数。结果表明，粘-超弹性模型的基础上提出的粘性耗散潜力捕捉所有的基本特征的应力-应变数据与独特的最佳模型参数，在单一和多个变形模式的情况下，给予合理的精度。此外，它表明，所提出的模型是稳定和强大的超弹性应变能密度的选择和数据的可用性从多个变形模式。(C)2019爱思唯尔有限公司版权所有。
A novel viscous dissipation potential is proposed for the visco-hyperelastic constitutive modeling of short-time memory responses of soft materials, which can capture both linear and nonlinear large deformation behaviors over a wide range of strain rates. The proposed potential is compatible with objectivity and continuum thermodynamics principles, consists of physically motivated model parameters, and adds the capability of modeling strain rate sensitivity in the small strain regime, which is currently not possible with available external state variable driven viscous dissipation potentials. By combining the proposed viscous dissipation potential with the Mooney-Rivlin strain energy density function, a visco-hyperelastic relation is formulated and fit to the rate-dependent tensile stress strain data of human patellar tendon, which was previously modeled using an existing viscous dissipation potential. It is demonstrated that the proposed model offers improvements in fitting accuracy and prevents possible thermodynamic instabilities in quasi-static hyperelastic models from corrupting the dynamic response. In addition, the uncomplicated mathematical form of the model and the accompanying multi-step multi-start optimization procedure helps prevent numerical instabilities. Multi-deformation mode fitting of human brain gray matter under all three primary deformation modes (compression, tension and shear) is also considered using a visco-hyperelastic model based on the proposed potential and the semi-empirical Gent-Gent strain energy density function. It is shown that visco-hyperelastic models based on the proposed viscous dissipation potential capture all the essential features of the stress-strain data with unique optimal model parameters, giving reasonable accuracy in both single and multiple deformation mode cases. Further, it is demonstrated that the proposed model is stable and robust with respect to both the choice of the hyperelastic strain energy density and the availability of data from multiple deformation modes. (C) 2019 Elsevier Ltd. All rights reserved.