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讨论大变形拟不可压缩橡胶类材料的本构关系及有限元分析方法.采用乘法分解,将变形梯度表示成等容和体积变形两部分,在此基础上,推导了克希荷夫应力和格林应变表示的Yeoh 形式应变能橡胶类材料的本构关系及数值处理方法.为处理不可压缩问题,采用三场变分原理,其中静水压力,体积膨胀,以及位移均作为独立变量进行处理.并指出该变分原理同胡鹫津广义变分原理的联系.变形采用相容等参插值,压力及体积膨胀采用低阶插值,推导了详细的有限元列式.最后给出了两个数值算例,结果表明了该方法的有效与可靠.为这类材料的精确的有限元分析打下了良好的基础.
The constitutive relation and finite element analysis method of non-compressible rubber materials with large deformation are discussed.Using multiplicative decomposition, the deformation gradient is expressed as two parts of equal volume and volume deformation, on the basis of which, Kirschhof stress and Green Three-field variational principle is adopted to deal with incompressible problems, in which hydrostatic pressure, volume expansion, and displacement are all treated as independent variables. It is also pointed out that the constitutive relations and numerical methods of strain- The principle of variational principle is related to the generalized variational principle of Hu Qiu Jin.The deformation is solved by the method of compatible isoparametric interpolation, pressure and volume expansion using low - order interpolation, and the detailed finite element formulation is derived.Finally, two numerical calculations The results show that this method is effective and reliable, which lays a good foundation for the accurate finite element analysis of these materials.