A new family of strain tensors based on the hyperbolic sine function

Abstract

This work introduces a new family of strain tensors based on the hyperbolic sine function: The Generalized Hyperbolic Sine (GHS). This family is obtained by using any given strain measure as an argument in a normalized hyperbolic sine function. Particularly, this paper adopts the Seth-Hill family as an argument and shows how some drawbacks of the classical strain measures can be overcome by means of the proposed strain family. A broad analytical study of pure deformation modes (simple axial extension, equi-biaxial loading and simple shear) is presented to show the behavior of the proposed strain family and investigate the physical coherence of their responses. Obtained results are promising as the GHS family proved itself capable of enhancing the physical behavior of the Seth-Hill strain measures and providing versatility with the addition of just one material constant with clear physical meaning. Materials investigated in the article are isotropic and homogeneous. The proposed Hookean-type hyperelastic models can be applied for both incompressible and compressible materials without additional strain energy density function changes.