【摘要】 引入一种滞后非线性弹性材料的宏观模型——Preisach-Mayergoyz模型(PM模型),该模型是通过大量分散的滞后细观单元的应力对(σ0,σc)对加载与卸载的响应不是原路可逆的特性,导致在循环荷载作用下多孔饱和岩石具有滞后和离散记忆的特征,以此来描述岩石的滞后和离散记忆的。在PM模型中,岩石的应力-轴向(径向)应变曲线的形状由PM密度空间、应力历史和滞后细观单元的弹性特性所决定,岩石的弹性模量和泊松比与滞后细观单元的平衡长度对和空间密度分布都有密切的关系。通过构造PM空间中不同的密度函数和设定滞后细观单元的弹性特性(平衡长度对)可以模拟性质不同的岩石,PM空间中不同的密度函数在一定程度上反映了岩石在循环载荷下的本构关系响应的不同性质。PM模型也强调了施加于岩石的应力历史在决定岩石的弹性状态时的重要性。通过对岩石离散记忆的模拟,认为多孔饱和岩石的滞后特性是其具有离散记忆特性的原因。同时,还可以利用应力-应变状态方程来模拟实验观测到的饱和岩石的滞后现象。更多还原

【Abstract】 We introduce the macroscopic model of nonlinear elastic materials,Preisach-Mayergoyz model(PMmodel). PM model is founded by the response of the pair of stresses( σ 0 ,σc)of many hysteretic mesoscopicalunits(HMU)versus loading and unloading;and it′s nonreversible through the original path. Porous saturated rockshave characters of hysteresis and discrete memory to describe. Based upon the hypothesis that the macro nonlinearelastic properties of porous rock are caused by an enormous variety of mesoscopical structural features such ascracks,joints and contacts;we have simulated hysteresis and discrete memory in rock by the PM model. Thecurves of stress-axial strain,stress-radial strain in the rock are determined by the space density and elasticproperties of HMU in PM model. The elastic moduli have close relation with distribution of PM space density anda pair of equilibrium length of HMU. The treatment in PM model emphasizes the importance of stress history inthe determination of the elastic state of a rock. The PM space density reflects the constitutive relationship responseof a rock under cyclic loading in some degree. We argue that hysteresis is the cause of discrete memory in rockthrough the simulation of a rock′s discrete memory. We can also use the equation of the stress-strain state to simulate the discrete memory of a rock observing in the experiment.更多还原