一种基于Seth应变张量的超弹性模型

New hyperelastic model based on seth strain tensor

为精确表征橡胶类材料在大变形范围内的力学行为,基于Seth应变张量不变量提出了一种适用于橡胶类材料的不可压缩各向同性超弹性模型。为考察其预测能力,分别利用Treloar经典试验数据和某型炭黑填充橡胶试验数据对该模型、Yeoh模型和二阶多项式模型进行了参数识别。结果表明,在同时使用单轴拉伸和等双轴拉伸试验数据情况下,相较于其他两种常用模型,该模型能够更准确地拟合两种橡胶材料的试验数据,并较好地预测纯剪切(或平面拉伸)试验数据。最后,分别基于前述三种超弹性模型对橡胶衬套进行了静刚度仿真计算和试验验证。结果表明,基于所提出的超弹性模型得到的径向刚度和轴向刚度仿真误差分别为6.61%和9.72%,显著小于基于其他两种模型得到的仿真误差。因此,提出的模型在一定误差范围内能够有效适用于橡胶产品的性能分析。该模型仅含4个材料参数,对不同的橡胶材料有较好地适用性,具有良好的工程应用价值。

Based on the Seth strain tensor invariant,a new hyperelastic model for isotropic and incompressible rubber-like materials was proposed,which can describe the mechanical behavior of the rubber-like material over a large range accurately.In order to investigate its applicability and accuracy,the parameters of the proposed model,as well as the Yeoh model and the second-order polynomial model were identified by using Treloar classical data and carbon black filled rubber test data respectively.The results show that only the proposed model can reliably fit the test data of two different rubber-like materials in uniaxial tension and equibiaxial tension tests while others cannot.Finally,based on the three hyperelastic models mentioned above,the finite element analysis and experiment verification on the static stiffness of a rubber bushing were carried out.As compared with experimental data,the simulation errors of radial stiffness and axial stiffness based on the proposed model are 6.61%and 9.72%respectively,which are significantly smaller than those based on other two models.Therefore,the proposed model can be applied to the performance analysis of rubber products.The proposed model merely includes four material parameters,so,it can be used widely for various rubber-like materials and has good engineering value.