Application of finite elastic theory to the behavior of rubber-like materials

摘要

In Part I, methods for determining the strain energy function and the associated constitutive stress-deformation law for rubber-like materials is undertaken and the mechanics of data reduction needed to determine some parameters of the theory are displayed. Experiments were performed in four different stress fields on a foamed polyurethane rubber (dilatable rubber) and on several kinds of continuum rubbers. A new strain energy function and the associated stress-deformation law for a foamed rubber are generated which correlate most of the data to a high degree of accuracy. A parameter appearing in the functional expression for a foam rubber has the same significance as Poisson's ratio in infinitesimal elastic theory. For continuum rubbers, the isotropic Neo-Hookean representations of quasi-static behavior is found to be sufficient over most of the whole range of extension.In Part II, geometrical representations of an isotropic failure surface based on various criteria are depicted both in principal stress and principal stretch spaces for elastic materials. The experimental data are compared with all criteria and the results are discussed.In Part III, finite elastic theory is used to determine the stress and deformation fields around the base of a radial crack in an infinitely long rubber log opened by a facially bonded rigid wedge-shaped bellow.In the last Part, the topology of interstices idealized as closest packed spherical holes (idealized foam structure) is investigated. Equivalent elastic constants are calculated for rubbery interstices of both hexagonal and face-centered cubic closest packings under small displacement.