Research On The Theory And The Solution Approach Of Nonlinear Viscoelastic Problems

Material science is the basic subject in natural science field and is substantial foundation of human's production and life. Viscoelastic theory is a boundary science that depends on the development of mechanic and material science, it is one of the important parts of continuum mechanic. At present, many important development on the studies of viscoelastic theory have been made by the efforts of scholars home and abroad, linear viscoelasticity theory has sufficiently developed, while nonlinear viscoelastic theory is still under developed by the reason of difficulties in experiment and mathematics.The aim of this paper is to search for practical nonlinear viscoelastic relations and the solution approach for viscoelastic problems in the range of infinitesimal strain. We have divided the constitutive relation equation into the distortion equation and the dilatation equation and extended elasticity recovery correspondence principle that has one independence material function to the conditions of two independence material functions, a three dimensional nonlinear viscoelastic constitutive relations are also given. According to elasticity recovery correspondence principles and different boundary condition, the solution of a nonlinear viscoelastic problem can be obtained if the solution of the corresponding nonlinear elastic problem is known.According to the double-axis experiment and the uniaxial tension experiment, shear relaxation modulus and bulk relaxation modulus are obtained. Fractional exponent models[23][24][25] are applied to shear relaxation modulus and bulk relaxation modulus.The theory is proved by constant amplitude cyclic strain experiment. Better results are obtained from the comparison of theory curves and experiment results.