Nonlinear Viscoelasticity for Short Time Ranges

Approximate constitutive equations for nonlinear viscoelastic incompressible materials under small finite deformation and for short time ranges are derived. The error bound of such a constitutive equation is investigated. Problems of nonlinear stress relaxation and creep are analyzed based on the proposed equation. Also, the problem of a pressurized viscoelastic hollow cylinder bonded to an elastic casing is solved. Numerical solutions, evaluated by assuming particular forms of kernel functions in the constitutive equation, are obtained by means of an inverse interpolation technique and the effects of nonlinearity of material properties are discussed. An experimental procedure is also proposed for measuring kernel functions from uniaxial tension tests for real materials. (Author)