This paper discusses the problem of macroscopic modeling a knitted technical fabric with the aim to determine a constitutive law for adequately modeling the material response under real-life load. As phenomenological, hyperelastic material laws reveal different parameters due to different test modalities used to identify such parameters, an optimization scheme is proposed to determine an objective solution. The study is conducted for three medical textiles which are differentiated by anisotropy ratios and designed to cover abdominal hernia. The optimization parameters are defined by a constitutive law and the bi-axial test modality. State variables are taken from ex-vivo reference tests on ‘operated’ hernia models subjected to simulated real-life loads generated by post-operative coughs. The objective function is different for isotropic and anisotropic mesh. However, in both cases a numerical model of a mesh placed in the abdominal wall with different variants of the constitutive law is used. The model is constructed according to the finite element method framework. The objective function for isotropic mesh is defined by the variance of reaction forces in mesh fixation points, calculated in the numerical model, while for anisotropic mesh, it is generated by the difference between angles which determine the position of maximal reaction force in the numerical and experimental reference models. Three constitutive laws and five modalities of bi-axial tests are considered. This analysis proves the need for a constitutive model, itself validated by a suitable reference test, instead of an arbitrary decision on bi-axial test modality selected to identify the material law parameters. These conclusions may help to increase the reliability of numerical modeling of operated hernia and increase the effectiveness of hernia treatment.

中文翻译：

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针织物客观数值建模本构定律的优化


本文讨论了针织技术织物的宏观建模问题，旨在确定在实际载荷下对材料响应进行充分建模的本构定律。由于现象学上的超弹性材料定律揭示了由于用于识别这些参数的测试模式不同而导致的不同参数，因此提出了一种优化方案来确定客观解。该研究针对三种医用纺织品进行，这些纺织品通过各向异性比率进行区分，旨在覆盖腹疝。优化参数由本构定律和双轴测试模态定义。状态变量取自对“手术”疝气模型的离体参考测试，这些模型受到术后咳嗽产生的模拟真实负荷的影响。各向同性和各向异性网格的目标函数不同。然而，在这两种情况下，都使用了放置在腹壁上的网格的数值模型，该模型具有不同的本构定律变体。该模型是根据有限元方法框架构建的。各向同性网格的目标函数由数值模型中计算的网格固定点中的反作用力方差定义，而对于各向异性网格，它由决定数值和实验参考模型中最大反作用力位置的角度差生成。考虑了双轴测试的三种本构定律和五种模式。该分析证明了需要一个本构模型，该模型本身由合适的参考测试验证，而不是武断地决定选择双轴测试模式来识别材料定律参数。 这些结论可能有助于提高手术疝数值建模的可靠性，提高疝治疗的有效性。