Fusing the Seth–Hill strain tensors to fit compressible elastic material responses in the nonlinear regime. (November 2019)

• Record Type: Journal Article
• Authors: Beex, L.A.A.
• Is Part Of: International journal of mechanical sciences. Volume 163(2019)
• Publication Date: 2019-11
• Subjects: Hyperelasticity -- Seth–Hill strain tensors -- Hencky strain tensor -- Parameter identification -- Isotropy -- Orthotropy -- Data driven modelling; Mechanical engineering -- Periodicals; Génie mécanique -- Périodiques; Mechanical engineering; Maschinenbau; Mechanik; Zeitschrift; Periodicals; 621.05
• DOI: 10.1016/j.ijmecsci.2019.105072
• Languages: English
• ISSNs: 0020-7403

Abstract

Highlights: Strain energy densities employing the Seth–Hill strain tensors can be used to describe isotropic and anisotropic compressible elasticity for moderately large deformations. One parameter distinguishes which member of the Seth–Hill family is employed, but in practice this parameter is not used for fitting in the nonlinear regime. Three generalizations based on the Seth–Hill strain tensors, are proposed to enable a true fitting of the material response in the nonlinear regime. The generalisations reduce to the conventional hyperelasticity if a single strain tensor is used. The generalisations reduce to the isotropic and anisotropic infinitesimal theory for small deformations, meaning that the identification of the Young's moduli, Poisson's ratios and shear moduli remains unaffecteed. Abstract: Strain energy densities based on the Seth–Hill strain tensors are often used to describe the hyperelastic mechanical behaviours of isotropic, transversely isotropic and orthotropic materials for relatively large deformations. Since one parameter distinguishes which strain tensor of the Seth–Hill family is used, one has in theory the possibility to fit the material response in the nonlinear regime. Most often for compressible deformations however, this parameter is selected such that the Hencky strain tensor is recovered, because it yields rather physical stress-strain responses. Hence, the response in the nonlinear regime is in practise not often tailored to match experimental data. To ensure that elastic responses in the nonlinear regime can more accurately be controlled, this contribution proposes three generalisations that combine several Seth–Hill strain tensors. The generalisations are formulated such that the stress-strain responses for infinitesimal deformations remain unchanged. Consequently, the identification of the Young's moduli, Poisson's ratios and shear moduli is not affected. 3D finite element simulations are performed for isotropy and orthotropy, with an emphasis on the identification of the new material parameters.