A comparative study of two constitutive models within an inverse approach to determine the spatial stiffness distribution in soft materials
A comparative study of two constitutive models within an inverse approach to determine the spatial stiffness distribution in soft materials
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DOI：
10.1016/j.ijmecsci.2018.03.004
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发表时间：
2018-05-01
影响因子：
7.3
通讯作者：
Goenezen, S.
中科院分区：
文献类型：
--
作者：
Mei, Y.;Stover, B.;Goenezen, S.
对比研究了用两个本构方程求解剪切模量（刚度）分布的弹性反问题：(1)假设小应变理论的线性弹性和(2)采用超弹性新hookean材料模型的有限弹性。假设材料经历了很大的变形，材料非线性可以忽略不计，使用(2)的反解预计会产生比(1)更好的结果。考虑到求解线性弹性模型比求解非线性模型要快得多，并且在数值上更加稳健，我们提出了以下问题：对于经历大变形的试样，我们使用小应变理论在线性弹性模型中映射剪切模量分布的准确性如何？为此，利用数字图像相关系统获取了含两种不同尺寸刚性包裹体的硅基复合材料样品在单轴位移控制拉伸下的实验位移数据。将硅基复合材料建模为无穷小应变下的线性弹性固体和考虑几何非线性有限变形的新胡克超弹性固体。我们观察到，通过求解反问题确定的映射剪切模量对比，与超弹性模型相比，线性弹性模型的夹杂物和背景之间的剪切模量更高。在模拟实验中也观察到类似的趋势，其中产生了综合计算的位移数据，并使用线性弹性模型和neo-Hookean材料模型求解了反问题。此外，我们观察到逆问题的解是包含物大小敏感的，因此，我们引入了一个一维模型来扩大我们对这个问题的理解。这种一维分析表明，使用线性弹性方法，随着外部载荷和目标剪切模量对比的增加，对夹杂物和背景剪切模量对比的高估也会增加。最后，这项研究提供了有价值的信息，证明了利用线性弹性来解决与大变形软固体相关的剪切模量空间分布反问题的假设的有效性。因此，这项工作对于表征聚合物基材料（如橡胶）的机械性能变化或病理组织的弹性成像具有重要意义。(C) 2018 Elsevier Ltd.版权所有。
A comparative study is presented to solve the inverse problem in elasticity for the shear modulus (stiffness) distribution utilizing two constitutive equations: (1) linear elasticity assuming small strain theory, and (2) finite elasticity with a hyperelastic neo-Hookean material model. Assuming that a material undergoes large deformations and material nonlinearity is assumed negligible, the inverse solution using (2) is anticipated to yield better results than (1). Given the fact that solving a linear elastic model is significantly faster than a nonlinear model and more robust numerically, we posed the following question: How accurately could we map the shear modulus distribution with a linear elastic model using small strain theory for a specimen undergoing large deformations? To this end, experimental displacement data of a silicone composite sample containing two stiff inclusions of different sizes under uniaxial displacement controlled extension were acquired using a digital image correlation system. The silicone based composite was modeled both as a linear elastic solid under infinitesimal strains and as a neo-Hookean hyperelastic solid that takes into account geometrically nonlinear finite deformations. We observed that the mapped shear modulus contrast, determined by solving an inverse problem, between inclusion and background was higher for the linear elastic model as compared to that of the hyperelastic one. A similar trend was observed for simulated experiments, where synthetically computed displacement data were produced and the inverse problem solved using both, the linear elastic model and the neo-Hookean material model. In addition, it was observed that the inverse problem solution was inclusion size-sensitive, Consequently, an 1-D model was introduced to broaden our understanding of this issue. This 1-D analysis revealed that by using a linear elastic approach, the overestimation of the shear modulus contrast between inclusion and background increases with the increase of external loads and target shear modulus contrast. Finally, this investigation provides valuable information on the validity of the assumption for utilizing linear elasticity in solving inverse problems for the spatial distribution of shear modulus associated with soft solids undergoing large deformations. Thus, this work could be of importance to characterize mechanical property variations of polymer based materials such as rubbers or in elasticity imaging of tissues for pathology. (C) 2018 Elsevier Ltd. All rights reserved.