General Finite-Element Framework of the Virtual Fields Method in Nonlinear Elasticity
General Finite-Element Framework of the Virtual Fields Method in Nonlinear Elasticity
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DOI：
10.1007/s10659-021-09842-8
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发表时间：
2021-06-16
影响因子：
2
通讯作者：
Avril, Stephane
中科院分区：
文献类型：
--
作者：
Mei, Yue;Liu, Jiahao;Avril, Stephane
本文提出了一种用虚场法(VFM)求取识别本构模型参数的虚场的方法。VFM是一种利用在给定目标体积上测量的变形场来识别未知本构参数的方法。用VFM解决识别问题的一般原则是首先从测量的变形场中推导出参数应力场，其中任何点处的应力分量取决于未知的本构参数。将虚功原理应用到参数应力场中，可以写出未知参数的标量方程，并求解得到的方程组，从而推导出未知参数的值。然而，在与非线性弹性有关的识别问题中，还没有提出选择虚场的规则，并且有多种可能的策略可以产生不同的结果。在这项工作中，我们提出了一种系统的、稳健的和自动的方法来重构标量方程组。这种方法非常适合于有限元实现，并且可以应用于任何问题，只要有感兴趣的体积上的全场变形数据。通过多个数值算例，成功地证明了该方法的可行性。所提出的方法在生物医学工程中有许多潜在的应用，在生物医学工程中，成像技术通常用于观察软组织，并且材料特性的改变是疾病状态的标志。
This paper presents a method to derive the virtual fields for identifying constitutive model parameters using the Virtual Fields Method (VFM). The VFM is an approach to identify unknown constitutive parameters using deformation fields measured across a given volume of interest. The general principle for solving identification problems with the VFM is first to derive parametric stress field, where the stress components at any point depend on the unknown constitutive parameters, across the volume of interest from the measured deformation fields. Applying the principle of virtual work to the parametric stress fields, one can write scalar equations of the unknown parameters and solve the obtained system of equations to deduce the values of unknown parameters. However, no rules have been proposed to select the virtual fields in identification problems related to nonlinear elasticity and there are multiple strategies possible that can yield different results. In this work, we propose a systematic, robust and automatic approach to reconstruct the systems of scalar equations with the VFM. This approach is well suited to finite-element implementation and can be applied to any problem provided that full-field deformation data are available across a volume of interest. We also successfully demonstrate the feasibility of the novel approach by multiple numerical examples. Potential applications of the proposed approach are numerous in biomedical engineering where imaging techniques are commonly used to observe soft tissues and where alterations of material properties are markers of diseased states.