On the Number of Invariants in the Strain Energy Density of an Anisotropic Nonlinear Elastic Material with Two Material Symmetry Directions |
| |
Authors: | Adair Roberto Aguiar Gabriel Lopes da Rocha |
| |
Institution: | 1.Department of Structural Engineering, S?o Carlos School of Engineering,University of S?o Paulo,S?o Carlos,Brazil;2.Programa de Pós-Gradua??o Interunidades em Bioengenharia – EESC/FMRP/IQSC,University of S?o Paulo,S?o Carlos,Brazil |
| |
Abstract: | We determine the minimum number of independent invariants that are needed to characterize completely the strain energy density of a compressible hyperelastic solid having two distinct material symmetry directions. We use a theory of representation of isotropic functions to express this energy density in terms of eighteen invariants, from which we extract ten invariants to analyze two cases of material symmetry. In the case of orthogonal directions, we recover the classical result of seven invariants and offer a justification for the choice of invariants found in the literature. If the directions are not orthogonal, we find that the minimum number is also seven and correct a mistake in a formula found in the literature. An energy density of this type is used to model, on the macroscopic scale, engineering materials, such as fiber-reinforced composites, and biological tissues, such as bones. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|