A non-linear single integral constitutive equation was developed by Wineman and Waldron and for a compressible isotropic viscoelastic solid. Its initial elastic and equilibrium response was given by the generalized Blatz-Ko model for compressible isotropic non-linear elasticity. A reduced time was introduced that causes stress relaxation to be accelerated by volume increases and/or shear deformations. The constitutive equation was used to study circular shear of a hollow cylinder that is bonded to a rigid support at its inner surface and a rigid shell at its outer surface. Two types of boundary conditions were investigated: moment control and rotation control. Circular shear causes the interior cylindrical elements to rotate about the centerline and radially expand or contract. The results showed that the shear stress and strain are greatly influenced by the specific form of dependence on the strain tensors and the volume and/or shear dependence of the reduced time in the constitutive equation.
In the present study, the constitutive equation is incorporated in LS-DYNA® and the problem of circular shear is re-solved. The circular shear problem is also solved using the non-linear viscoelastic constitutive equation provided by LS-DYNA®. The results of these three simulations are compared and differences in the yield-like behaviors are discussed.
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