Elastic potentials with best approximation to rubberlike elasticity

Abstract

An explicit approach is proposed to determine elastic potentials of elastomers for the purpose of eliminating the long-standing uncertainty that the applicability may not be assessed for all deformation modes. Toward this goal, a new experimental scheme for testing nonlinear elastic characteristics of elastomers is first designed for obtaining suitable test data, and then, multi-axial elastic potentials are directly constructed via explicit procedures based on these data. For the first time, the error estimate may be established and minimized errors may be achieved for all possible deformation modes by combining Hermite interpolation with Chebyshev’s best approximation. It is demonstrated that each potential thus obtained may with sufficient accuracy represent nonlinearly elastic properties for all deformation modes. It is shown that even the simplest case of the proposed potential, derived from the uniaxial mode alone, may achieve good agreement with a number of test data.