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 引用本文: 李锋, 彭天波. 包含Mullins效应的HDR热-超-黏弹性本构模型. 力学学报, 2024, 54(8): 1-9.
Li Feng, Peng Tianbo. An HDR thermal-hyper-viscoelastic constitutive model with mullins effect. Chinese Journal of Theoretical and Applied Mechanics, 2024, 54(8): 1-9.
 Citation: Li Feng, Peng Tianbo. An HDR thermal-hyper-viscoelastic constitutive model with mullins effect. Chinese Journal of Theoretical and Applied Mechanics, 2024, 54(8): 1-9.

## AN HDR THERMAL-HYPER-VISCOELASTIC CONSTITUTIVE MODEL WITH MULLINS EFFECT

• 摘要: 高阻尼橡胶(high damping rubber, HDR)材料具有良好的耗能性能, 在建筑和桥梁抗震设计中得到了广泛应用. 以往研究表明, 其力学行为主要受温度、加载速率和历史幅值等多种因素的影响. 既有HDR本构模型大都只针对其中一种或两种因素进行研究, 且未能综合考虑Mullins效应的影响, 存在一定的缺陷. 针对这种情况, 为研究温度、加载速率和历史幅值对HDR力学行为的影响, 进行了HDR试件的多工况变幅循环压剪试验. 首先将HDR本构模型分解为超弹性部分和黏弹性部分的叠加, 并引入考虑温度影响的时温等效方程、考虑Mullins效应的损伤函数, 最终得到了一种包含Mullins效应的HDR热-超-黏弹性本构模型. 然后使用Python的第三方库Scipy中的optimize模块对试验数据进行非线性最小二乘法的分步拟合, 得到了相应的本构模型参数. 最后, 根据参数变化规律拟合得到参数随温度和应变率变化的公式, 并补充部分试验, 以验证提出的HDR本构模型的有效性和适用性. 结果表明, 提出的本构模型能够较好地描述HDR材料复杂的应力-应变关系, 准确地表述温度、加载速率和历史幅值的影响, 同时具有较好的适用性.

Abstract: High damping rubber material has been widely employed in seismic design of buildings and bridges, primarily due to its exceptional energy dissipation capabilities. This material effectively absorbs and dissipates seismic energy, significantly reducing the potential for structural damage. Previous studies have demonstrated that the mechanical behavior of high damping rubber is primarily influenced by temperature, loading rate, experienced amplitude, and other factors. The majority of existing high damping rubber constitutive models have focused on one or two of these factors, and have been unable to consider the influence of the Mullins effect, which has led to some limitations. In light of the aforementioned considerations, a multi-case variable amplitude cyclic compression-shear test of high damping rubber specimens was conducted with the objective of studying the effects of temperature, loading rate, and experienced amplitude on the mechanical behavior of high damping rubber. The high damping rubber constitutive model was decomposed into the superposition of a hyperelastic part and a viscoelastic part. A time-temperature equivalent equation considering the temperature effect and a damage function considering the Mullins effect are introduced. Finally, a high damping rubber thermal-hyper-viscoelastic constitutive model with Mullins effect is obtained. The optimize module in the third-party library Scipy of Python is then used to fit the test data step by step by nonlinear least square method, and the corresponding constitutive model parameters are obtained. Finally, the variation of parameters is employed to fit the equations of parameters varying with temperature and strain rate. Some experiments are conducted to verify the validity and applicability of the proposed high damping rubber thermal-hyper-viscoelastic constitutive model. The results demonstrate that the proposed high damping rubber thermal-hyper-viscoelastic constitutive model can accurately describe the complex stress-strain relationship of high damping rubber materials, and it can also describe the effects of temperature, loading rate, and experienced amplitude. Furthermore, the model has good applicability.

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