基于有理插值方法模拟可压缩类橡胶材料多轴变形行为

Modeling multi-axial deformation of compressible rubber-like material based on rational interpolation

提出一个多轴应变能函数来模拟可压缩类橡胶材料在载荷作用下的大变形行为。首先,基于对数应变构造三个不变量,使得应变能函数分别具备可压缩功能、多轴有效功能以及适用于多个变形模式的功能;其次,利用有理插值方法构造单轴形函数,并结合前面引入的三个不变量,通过哈密顿插值方法构建统一的应变能函数;最后,在单轴情况下,应变能函数通过对Hencky应变求导,可以得到对应变形模式下的应力-应变关系。本文通过调节泊松比的大小来控制体积变化从而实现模型的可压缩性;此应变能函数可以模拟单轴拉伸压缩、平面应变以及等双轴拉伸等至少三个基准试验。新方法得到的伸长比-应力关系、伸长比-体积比关系与经典试验数据结果作比较,进而证明方法的准确性和有效性。

A new multi-axial strain energy function for rubber-like material is proposed to simulate the large deformation behavior by considering the compressible situation.Firstly,three invariants based on the Hencky strain are constructed to make the strain energy function compressible,multi-axial effective and suitable for multiple deformation modes.Secondly,a unified potential is proposed via Hamiltonian interpolation by three invariants combined with uniaxial shape functions,which are constructed by rational interpolation.Thirdly,stress-strain relationships in uniaxial cases can be deduced from the unified potential by derivative of this with respect to the Hencky strain.Towards realize the compressible property,a compressible invariant related to the Poisson’s ratio is introduced to control the volume changes.The proposed new method can simulate at least three benchmark tests,that is to say,uniaxial tension-compression,equi-biaxial tension and plain strain tension.The elongation ratio-stress relationships and elongation ratio-volume ratio relationships deduced from the new method can exactly match the classical test data.