拟合橡胶类材料非等双轴变形数据的显式超弹性势

基于样条插值的直接方法,构造精确符合单轴和等双轴拉伸数据以及剪切数据的大变形超弹性势,给出显式表达式,避免了现有各方法寻求待定参数组达到近似拟合的复杂计算过程;推导了一般变形情形下的应力应变关系,对非等双轴拉伸实验进行了预测,并与Rivlin和Saunders的非等双轴拉伸实验数据进行了对比,预言结果与实验数据一致．     

Further study of rubber-like elasticity： elastic potentials matching biaxial data＊

By virtue of the rational interpolation procedure and logarithmic strain, a direct approach is proposed to obtain elastic potentials that exactly match uniaxial data and shear data for elastomers. This approach reduces the determination of multiaxial elastic potentials to that of two one-dimensional potentials, thus bypassing usual cumbersome procedures of identifying a number of unknown parameters. Predictions of the suggested potential are derived for a general biaxial stretch test and compared with the classical data given by Rivlin and Saunders(Rivlin, R. S. and Saunders, D. W. Large elastic deformation of isotropic materials. VII: experiments on the deformation of rubber. Phill. Trans. Royal Soc. London A, 243, 251–288(1951)). Good agreement is achieved with these extensive data.