Abstract Building on the existing model, an improved constitutive model for rock is proposed and extended in three dimensions. The model can avoid the defect of non-zero dynamic stress at the beginning of impact loading, and the number of parameters is in a suitable range. The three-dimensional expansion method of the component combination model is similar to that of the Hooke spring, which is easy to operate and understand. For the determination of model parameters, the shared parameter estimation method based on the Levenberg–Marquardt and the Universal Global Optimization algorithm is used, which can be well applied to models with parameters that do not change with confinement and strain rates. According to the established dynamic constitutive equation, the stress–strain curve of rock under the coupling action of the initial hydrostatic pressure load and constant strain-rate impact load can be estimated theoretically. By comparing the theoretical curve with the test data, it is shown that the dynamic constitutive model is suitable for the rock under the initial pressure and impact load.

中文翻译：

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岩石受初始应力的动态三轴本构模型

摘要 在现有模型的基础上，提出了一种改进的岩石本构模型，并在三个维度上进行了扩展。该模型可以避免冲击加载开始时动应力非零的缺陷，参数个数在合适的范围内。组件组合模型的三维展开方式与虎克弹簧的展开方式类似，易于操作和理解。模型参数的确定采用了基于Levenberg-Marquardt和通用全局优化算法的共享参数估计方法，可以很好地应用于参数不随约束和应变率变化的模型。根据建立的动态本构方程，在初始静水压力载荷和恒定应变率冲击载荷的耦合作用下，岩石的应力-应变曲线可以从理论上估计。通过理论曲线与试验数据对比，表明该动力本构模型适用于初始压力和冲击载荷作用下的岩石。