A Multiaxial Elastic Potential With Error-minimizing Approximation

Soft materials with their remarkable physical and mechanical properties, such as highly elastic deformations at relatively low stress levels, have been found wide applications in many engineering fields. The study for soft materials is concerned with relevant scientific branches including physics, chemistry and biology. For reasonable design and efficient applications in engineering, it is of much significance to obtain multiaxial stress-strain relations for highly elastic behavior.Many classical models, such as those proposed by Ogden, Arruda and Boyce are in current use, which are involved in complicated numerical calculations for parameter identification, as well as the impossibility of estimating the error. In this article, based on a pair of conjugate logarithmic strain modes, the Hermite interpolation with Chebyshev nodes has been employed in a new, explicit approach to derive the elastic potential of the rubberlike materials for all possible deformation modes. Compared to the usual studies, the advantages and features of the new method are as follows, for the first time errors may be estimated and rendered minimal for all possible deformation modes and, in addition, failure behavior may be incorporated. Numerical examples verify that the new model predictions are in excellent agreement with Treloar’s well-known data and the benchmark test data of some hyper-elastic gels, such as biological gelatin gels and extremely soft polymer gels.