Simple Shearing of Incompressible and Slightly Compressible Isotropic Nonlinearly Elastic Materials |
| |
Authors: | C O Horgan J G Murphy |
| |
Institution: | (1) Department of Civil Engineering, University of Virginia, P.O. Box 400742, Charlottesville, VA, 22904, U.S.A.;(2) Sezione di Ingegneria Industriale, Dipartimento di Ingegneria dell'Innovazione, Università degli Studi di Lecce, 73100 Lecce, Italy |
| |
Abstract: | The classical problem of simple shear in nonlinear elasticity has played an important role as a basic pilot problem involving
a homogeneous deformation that is rich enough to illustrate several key features of the nonlinear theory, most notably the
presence of normal stress effects. Here our focus is on certain ambiguities in the formulation of simple shear arising from
the determination of the arbitrary hydrostatic pressure term in the normal stresses for the case of an incompressible isotropic
hyperelastic material. A new formulation in terms of the principal stretches is given. An alternative approach to the determination
of the hydrostatic pressure is proposed here: it will be required that the stress distribution for a perfectly incompressible
material be the same as that for a slightly compressible counterpart. The form of slight compressibility adopted here is that
usually assumed in the finite element simulation of rubbers. For the particular case of a neo-Hookean material, the different
stress distributions are compared and contrasted. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|