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 引用本文: 魏志刚, 陈海波. 一种新的橡胶材料弹性本构模型[J]. 力学学报, 2019, 51(2): 473-483.
Zhigang Wei, Haibo Chen. A NEW ELASTIC MODEL FOR RUBBER-LIKE MATERIALS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(2): 473-483.
 Citation: Zhigang Wei, Haibo Chen. A NEW ELASTIC MODEL FOR RUBBER-LIKE MATERIALS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(2): 473-483.

## A NEW ELASTIC MODEL FOR RUBBER-LIKE MATERIALS

• 摘要: 橡胶类材料本构关系对于科学研究和工程应用具有重要意义,但已有的橡胶模型的拟合能力和可靠性需要进一步提高.为解决此问题,本文提出了一种新的橡胶材料的各向同性、不可压缩柯西弹性模型.研究了橡胶材料本构关系的模型形式,基于平面应力变形状态,提出了一种以较大的两个伸长率为自变量、适用于一般变形状态的橡胶材料弹性本构模型形式;研究了橡胶材料在侧面受约束条件下的变形规律,分析了橡胶材料本构关系需要满足的约束条件;在此基础上,结合一个可以通过实验确定的描述平面拉伸变形状态下的橡胶材料力学特性函数,提出一种将该函数拓展为平面应力状态一般模型的方法,并给出了一个具体的函数形式,形成了一个新的不可压缩、各向同性的橡胶材料弹性本构模型.使用5组包含3种类型实验的数据和一组较全面的双轴测试数据对该模型进行了参数拟合,结果表明：该模型具有很好的拟合精度和更高的可靠性,仅用一种类型实验数据,如单轴拉伸或者平面拉伸等,也能获得较好的拟合结果.

Abstract: The constitutive relation of rubber-like materials is important for scientific study and engineering application. However, the fitting ability and reliability of the existing models don't satisfy the requirement. To solve this problem, a new incompressible isotropic constitutive model for the elasticity of the rubber-like materials was proposed in this paper. The form of the constitutive model was studied and a new model was proposed based on plane stress deformation state. This model is an isotropic incompressible model which is defined in terms of the first and second principal stretches and is applicable to describe the elasticity of rubber-like materials in general deformation state. The deformation rules of the material subjected to a lateral constraint was studied and the constraints which this model should satisfy were studied. With a proposed function for stress-strain relation of rubber-like materials under plane stress deformation, a method and a function was proposed to extend the function for plane stress deformation states to a general one for arbitrary three-dimensional deformation states. Thus, a new general incompressible isotropic elastic constitutive model for rubber-like materials was derived. The model was fitted to five groups of test data which all include three types of test and a biaxial test data which covers a broad range of deformation state. The results show that this model fits the test data very well and has a better reliability than the existing models. Besides, the model can predict the material's response well even with a type of test data such as the uniaxial tension test.

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