Theoretical and numerical formulation of a molecular based constitutive tube-model of rubber elasticity

The main physical features of the tube-model of rubber elasticity are reviewed. Based on an affine-coupling-hypothesis of network strands between successive entanglements a simple scaling derivation of the non-affine deformation of the lateral tube dimension is presented. The mathematical form of the tube deformation essentially determines the structure of the high elastic potential in a continuum mechanical formulation that is suitable for an efficient implementation into a finite element method. Experimental data from van den Bogert and de Borst are taken for the comparison with numerical results. The material parameters are identified in a uniaxial experiment. Subsequently, a non-homogeneous complex shear experiment is modelled for the comparison in order to assess the predictive character of the finite element simulation. From the numerical part we can conclude that the tube-model can be used to carry out realistic simulations. However, results are sensitive to the material parameters used and parameter identification is of great importance. The tube-model when applied to FEM provides the possibility to relate molecular parameters of the vulcanizate to the properties and behaviour of rubbers under operating conditions.

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