Identification of Material Parameters of a Hyper-Elastic Body With Unknown Boundary Conditions
Identification of Material Parameters of a Hyper-Elastic Body With Unknown Boundary Conditions
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DOI：
10.1115/1.4039170
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发表时间：
2018-02
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影响因子：
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通讯作者：
M. Hajhashemkhani;M. Hematiyan;S. Goenezen
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文献类型：
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作者：
M. Hajhashemkhani;M. Hematiyan;S. Goenezen
近几十年来，人体软组织或类橡胶材料等超弹性材料的材料特性鉴定一直是许多工作的主题。边界条件通常在求解材料识别的反问题中起着重要作用，而边界条件的知识一直被认为是理所当然的。然而，在现实中，边界条件可能不适用于问题域的某些部分，例如工程部件，例如可以建模为超弹性材料的聚合物，安装在系统或体内软组织上。在这些情况下，使用假设的边界条件会产生误导的结果。本文提出了一种考虑部分边界上未知条件的超弹性材料性能表征逆算法。定义了一个基于测量位移和计算位移的代价函数，并使用高斯-牛顿法最小化。采用解析微分法和有限元法进行了灵敏度分析。通过数值算例和实验算例验证了该方法的有效性。用neo-Hookean和Mooney-Rivlin超弹性材料模型对该方法进行了验证。在实验实例中，对边界条件未知的硅基试样的材料参数进行了计算。所有算例均对所得结果进行了验证，结果令人满意、可靠。(DOI: 10.1115/1.4039170)
Identification of material properties of hyper-elastic materials such as soft tissues of the human body or rubber-like materials has been the subject of many works in recent deca-des. Boundary conditions generally play an important role in solving an inverse problem for material identification, while their knowledge has been taken for granted. In reality, however, boundary conditions may not be available on parts of the problem domain such as for an engineering part, e.g., a polymer that could be modeled as a hyper-elastic mate- rial, mounted on a system or an in vivo soft tissue. In these cases, using hypothetical boundary conditions will yield misleading results. In this paper, an inverse algorithm for the characterization of hyper-elastic material properties is developed, which takes into consideration unknown conditions on a part of the boundary. A cost function based on measured and calculated displacements is defined and is minimized using the Gauss–Newton method. A sensitivity analysis is carried out by employing analytic differentiation and using the finite element method (FEM). The effectiveness of the proposed method is demonstrated through numerical and experimental examples. The novel method is tested with a neo–Hookean and a Mooney–Rivlin hyper-elastic material model. In the experimental example, the material parameters of a silicone based specimen with unknown boundary condition are evaluated. In all the examples, the obtained results are verified and it is observed that the results are satisfactory and reliable. [DOI: 10.1115/1.4039170]