基于单轴数据决定橡胶类材料多轴刚性化有界超弹性势

BOUNDED MULTI-AXIAL ELASTIC POTENTIALS WITH STRAIN-STIFFENING EFFECTS FOR RUBBERY MATERIALS BASED ON UNIAXIAL DATA

指出表征橡胶类材料应变刚化效应的现有超弹性模型涉及应变能无穷发散困难,提出新方法解决该困难.基于对数应变不变量的多轴扩张和多轴匹配步骤,建议直接构造橡胶类材料大变形弹性势的显式直接方法.该方法从单轴应力-应变关系直接得到多轴弹性势,所得结果避免了现有各方法决定待定参数组的复杂数值计算,能够准确描述应变刚性化效应,且给出有界弹性应变能,从而避免了前述发散困难.数值结果表明,从单轴数据所得到的弹性势可同时很好的拟合平面应变拉伸(剪切)数据以及等双轴拉伸数据.

It is indicated that the existing elasticity models with strain-stiffening effects for rubbery materials are involved in an issue concerning unbounded strain energy. Toward a solution to this issue, an explicit,straightforward approach is proposed to obtain multi-axial elastic potentials for incompressible rubberlike materials. Such potentials are derived directly from one-dimensional elastic potentials for uniaxial case by means of explicit procedures and,as such, bypass usual tedious numerical calculations in estimating a set of unknown parameters. It is shown that these potentials based solely on uniaxial data may accurately match data of four benchmark tests over the whole stretch range from small to large deformations. Also, they not only can well describe strain-stiffening effects, but can always give rise to bounded strain energy. Numerical examples are presented in fitting Treloar＇s classical data.