Abstract：The phenomenological constitutive model of incompressible rubber materials is investigated in this paper. The principal of choosing strain-energy function is discussed. The advantages and disadvantages of several models, including the Neo-Hookean formulation, the Mooney formulation, the three-order Rivlin formulation and the Ogden formulation, is mechanically analyzed. Subsequently, an improved form of Rivlin formulation is proposed as , which has three significant advantages: ① in the case of N=1 and small strain, the new function is the same as the strain-energy of the linear elastic incompressible material, and gives a approximately linear shear deformation and a exact linear tension and compression deformation. ②when N≥2, in the condition of small strain, using the new formulation, the strain-energy and shear stress in simple shear experiment are polynomial with γxy as geometric proportion. While using Rivlin formulation, the strain-energy and shear stress τxy under small deformation are polynomial with (γxy)2 as geometric proportion. Besides, when the deformation is small, Rivlin formulation with N=1 provides constant shear module and non-linear relationship in tension and compression. The improved form, compared with the same order Rivlin formulation, shows significant advantages in prediction of test data in single experiment, and has a good performance in the mutual prediction between different tests.
2012, Vol. 33 
