基于Treloar实验数据的超弹性材料完全本构关系研究

COMPLETE CONSTITUTIVE RELATION OF HYPERELASTIC MATERIALS FOR TRELOAR’S EXPERIMENTAL DATA

超弹性材料在航天航空、民用工业等多个领域已得到广泛应用,但因具有的大变形非线性特性,其本构行为异常复杂,本构模型多种多样.本文从超弹性材料的应变能函数出发,在连续介质力学框内开展超弹性材料完全本构关系的理论与应用研究.首先,分析了Treloar针对某硫化橡胶超弹性材料开展的单轴拉伸、等双轴拉伸以及纯剪切3种基本变形模式实验数据的特点;接着,理论分析了这3种变形模式所具有的相同应力条件,从而将3种模式的本构关系均表示为加载方向应力随伸长比的变化,并就I_(1)^(m)和I_(2)^(m)两类幂函数型应变能函数的本构特性进行了研究;然后,将实验曲线分为初始和剩余两个阶段,对初始阶段采用neo-Hookean模型应变能函数、对剩余阶段采用非指定指数的幂函数型应变能函数,在3种变形模式实验数据总体误差泛函最小条件下对模型参数进行识别,最终建立了典型超弹性材料的完全本构关系.对3种基本变形模式下的不同响应进行了重新预测,其结果均优于文献上已发表的多个本构模型.本文工作表明,依据多种不同变形模式下全程变形范围的实验曲线,可建立超弹性材料的完全本构关系,从而为超弹性材料断裂等复杂问题的理论研究与实际应用提供支撑.

Hyperelastic material is a typical one widely used in many fields such as aerospace engineering and civil industrials. However, due to the property of nonlinear large deformation, the constitutive behavior of hyperelastic materials is extremely complex and the models are quite different in form. Starting from the strain energy function, a complete constitutive relation of hyperelastic materials is studied within the theoretical framework of continuum mechanics in this paper. Firstly, the feature is analyzed for the experimental curves under three essential deformation modes like uniaxial tension, equibiaxial tension and pure shear, which are conducted by Treloar for a vulcanized rubber hyperelastic material. Next, the same stress conditions of the three deformation modes are summarized in detail, based on which the constitutive relationship is derived in a same manner in terms of the stress and the principal stretch ratio in the loading direction for the three modes according to the hyperelastic constitutive theory. The constitutive behaviors of two typical power-law strain energy functions, namely I_(1)^(m) and I_(2)^(m), are accordingly studied for the three essential modes. The experimental curves are divided into the initial regime and the remaining regime, and then the neo-Hookean model is adopted for the initial regime while the power-law functions with variable exponents are used for the remaining regime.The complete constitutive model is eventually established after the model parameters are identified by minimizing the overall error functional of the three modes. The responses are re-predicted for the three essential deformation modes, and the results agree better with the experimental than other models available in published literature. The present work indicates that a complete constitutive relation can be obtained for a hyperelastic material in light of the experimental curves with whole deformation range under multiple deformation modes, which is therefore instructive and meaningful to theoretical research and engineering application of complex practical problems such as fracture of hyperelastic materials.