Dynamic and static response of a slightly compressible hyperelastic solid

Abstract

The paper presents dynamic and static response of a slightly compressible hyperelastic solid. Material models under consideration are obtained by extending incompressible material models which are consistent second and third order approximation of existing stored energy function in terms of a deformation measure, namely MCMV and MCIZ. The problems of a uniaxial compression of a rod and a twisting column are solved using ABAQUS which is a powerful finite element program designed for general use in nonlinear problems. The models are defined with a help of user subroutine UHYPER. In the case of including dynamic effects, an implicit integration scheme available in the software is used. For the twisting column problem, results are compared against available in the ABAQUS library polynomial model where the volumetric stored energy function does not meet basic growth conditions. Experimental data on synthetic rubber neoprene published in the literature is utilized.

Calculation of Strain Energy Density Function Using Ogden Model and Mooney–Rivlin Model Based on Biaxial Elongation Experiments of Silicone Rubber

“…Yamashita et al proposed a more ingenious Formula (8), which is similar to the James-Green-Simpson Formula (7) [47]. Yamashita's equation is devised to satisfy the two Equations ( 7) and (10). Here, C 10 is assumed to be the term due to rubber elasticity, which is entropy elasticity; C 01 is the term due to energy elasticity resulting from the entanglement of the polymer's molecular chains; and C nm , m, and n are energy elastic terms resulting from the elongation of the polymer molecular chains by the addition of reinforcement.…”

“…CAE analysis has become indispensable for the development and design of new products [ 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 ]. Abaqus and Marc are well-known analytical software programs, but recently Ansys and Nastran have also become popular.…”