基于非局部理论的Hoek‑Brown软化塑性模型

Hoek Brown Softening Plasticity Model Based on Nonlocal Theory

摘要:

由于缺失材料特征长度，局部应变软化模型在模拟结构层面的失效破坏时，会出现网格依赖性问题，严重影响计算结果的准确性与可靠性。本研究提出了非局部的Hoek-Brown软化塑性模型，该模型基于光滑的 Hoek-Brown强度准则构造屈服函数，并利用过非局部公式将等效塑性剪应变发展为非局部变量，有效规避了结构失效破坏模拟时的网格依赖性问题。利用隐式返回映射应力更新算法求解非局部塑性模型的微分方程组，详细介绍了该模型的有限元实现流程。最后，以经典的缺陷板受压破坏问题和条形基础承载力问题为例，对模型的有效性进行验证。结果表明，在网格细化过程中，非局部Hoek-Brown软化塑性模型的模拟结果对网格尺寸不敏感，预测的剪切带宽度和荷载位移曲线基本不随网格尺寸变化。所提模型可为岩石工程的失效破坏分析提供具有网格客观性的计算工具。

Abstract:

The absence of a material characteristic length in local strain softening models often leads to mesh dependency issues in structural failure simulations, significantly compromising the accuracy and reliability of calculation results. A nonlocal Hoek-Brown softening plasticity model was proposed in this study. This model utilized a smooth Hoek-Brown strength criterion to construct the yield function and transformed the equivalent plastic shear strain into the nonlocal variable using a nonlocal integral formulation, effectively mitigating mesh dependency issues in structural failure simulations. The implicit return mapping algorithm was adopted to solve the differential equations of the nonlocal plasticity model, and the finite element implementation process of the model was detailed. Finally, the validity of the model was verified through two classic examples: the compression failure of an imperfect plate and the bearing capacity problem of a strip foundation. The results showed that during mesh refinement, the simulation results of the nonlocal Hoek-Brown softening plasticity model were insensitive to mesh size. The predicted shear band width and load-displacement curves remained largely unaffected by changes in mesh size. The proposed model can provide a calculation tool with mesh objectivity for failure analysis in rock engineering.