EXPERIMENTAL DETERMINATION OF STRAIN-ENERGY DENSITY FUNCTION OF RUBBER AND THREE-DIMENSIONAL FINITE ELEMENT STRESS ANALYSIS OF RUBBER IN HOSE COUPLING

An experimental setup was designed and fabricated to perform homogeneous biaxial tension tests by the combined extension and inflation of a thin-walled tubular specimen, 1.0 inch internal diameter and made of rubber-like material. This technique enabled higher strains than are obtainable with the customary flat square sheet specimen. From the biaxial stress-strain data, the stain-energy density of the rubber material is plotted against the first two strain invariants, I{dollar}sb1{dollar} and I{dollar}sb2{dollar}, of the Cauchy-Green strain tensor, assuming that the material is isotropic, incompressible and hyper-elastic. A nine parameter fit to this surface is then obtained, to get the strain-energy density function W of the rubber material.; A mixed Galerkin's method is used to formulate the problem of finite deformation from the equations of equilibrium in material coordinates, where the First Piola-Kirchhoff stress tensor and the deformation gradient are the conjugate stress and strain tensors, respectively. The material is assumed to be isotropic, incompressible and hyper-elastic having a general strain-energy density function in terms of the strain invariants. Newton's method is used to solve the resulting non-linear equations. This is a total Lagrangian formulation where the solution is obtained in an iterative manner rather than the conventional incremental approach. A computer code is written in FORTRAN-77, using the simplest eight-noded isoparametric trilinear brick element with an uniform constant pressure. Example problems are solved for bodies with simple geometry and loading conditions. The results are compared with exact solutions and published two-dimensional finite element methods. The comparison indicates the superiority of the present analysis both in accuracy and efficiency.; Finally the computer code is used to analyze the stresses and deformations for the rubber-like material when pressed inside a hose coupling, using the nine parameter constitutive relation, i.e. the strain-energy density function, determined from experiments. Analysis of this nature could be used to improve the design of rubber hose couplings.