科研之友
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摘要
An explicit, direct approach is proposed to obtain multiaxial elastic potentials that exactly match finite strain data of four benchmark tests for incompressible rubberlike materials, including uniaxial, biaxial, plane-strain compression and simple shear tests. This approach is composed of three direct procedures. At first, we utilize a usual interpolating method for single-variable functions to obtain one-dimensional stress-strain relations matching data of uniaxial test and simple shear test, separately, and then obtain two one-dimensional elastic potentials via directly integrating the stress power. After that, we introduce a multiaxial bridging method based on certain invariants of Hencky strain and extend the foregoing two one-dimensional potentials to two potentials for multiaxial cases. Then, we further introduce a multiaxial matching method based also on Hencky invariants and combine the just-mentioned two independent multiaxial potentials to obtain a unified form of multiaxial potential. With two universal relations first disclosed here between the four tests, eventually we demonstrate that each such unified multiaxial potential exactly matches data of four benchmark tests. In particular, we apply the proposed explicit approach with a simple form of rational interpolating function for uniaxial stress-strain relation with two poles and directly from uniaxial stress-strain relation to obtain a new, simple form of multiaxial elastic potential with a limit for strain. It is found that this limit for strain is just a counterpart of the well-known von Mises limit for stress in the theory of elastoplasticity. Also, it is shown that this simple potential accurately matches data of four benchmark tests over the whole range from small to large deformations.
- 出版日期2012-9
- 单位上海大学
