Optimization of constitutive law for objective numerical modeling of knitted fabric

Abstract

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.