Obtaining Elastic Potentials For Rubber-like Materials At Large Deformations Via An Explicit, Exact Approach

For its large elastic deformability, rubbery material is a typical representative ofhyperelastic materials. Since synthetic rubber has lots of excellent performance suchas waterproof, airtightness, high and low temperature resisting property, chemicalresistance and so on, rubbery material has extensive application in industry and dailylife. And researching on its constitutive relation has been a major field in solid me-chanics. Differing from the traditional theories, this thesis constructed an explicitelastic potential by a new method.Firstly, some classical models of rubber elastic potential using statistical meth-od and phenomenological method were introduced. Secondly, starting from thermo-dynamics, the rubber’s constitutive relation relying on a scalar function named elas-tic potential was deduced. Adopting logarithmic strain, the deformation modes offour rubber’s benchmark tests were described, and two impotent relations werefound out. By means of spline interpolation, two new one-dimension elastic poten-tial were obtained from benchmark test points. The influence of different boundaryconditions on interpolation result was investigated and we found out that the extrap-olated curve only had a qualitative reference function. Furthermore, based on someinvariants of the logarithmic strain deviator, a new unified multiaxial potential wasconstructed, which matches the test data exactly than Arruda-Boyce’s eight chainmodel.Finally, the new potential was used to predict the results of general biaxial test(Rivlin and Saunders,1951). For first time, good agreement was achieved, whichproved that the new potential was appropriate for other complex deformation.