细观非均匀介质中的耦合波动传播  

Coupled wave propagation in meso-scale heterogeneous medium

作　　者：陆建华 袁良柱 谢雨珊 陈美多 王鹏飞[1] 徐松林[1,2] LU Jianhua;YUAN Liangzhu;XIE Yushan;CHEN Meiduo;WANG Pengfei;XU Songlin(CAS Key Laboratory for Mechanical Behavior and Design of Materials,University of Science and Technology of China,Hefei 230027,Anhui,China;United Laboratory of High-Pressure Physics and Earthquake Science,Institute of Earthquake Forecasting,China Earthquake Administration,Beijing 100036,China)

机构地区：[1]中国科学技术大学中国科学院材料力学行为和设计重点实验室,安徽合肥230027 [2]中国地震局地震预测研究所高压物理与地震科技联合实验室,北京100036

出　　处：《爆炸与冲击》2024年第9期60-74,共15页Explosion and Shock Waves

基　　金：国家自然科学基金(11672286,11872361);高压物理与地震科技联合实验室开放基金(2019HPPES01);中国石油与中国科学院重大战略合作项目(2015A-4812);中央高校基本科研业务费专项资金(WK2480000008)。

摘　　要：非均匀介质在自然界中十分常见,针对细观非均匀介质的波动力学行为和非均匀性描述的研究具有重要意义并充满挑战。建立了反映细观非均匀材料压剪耦合特性的一般压剪耦合本构关系,提出了描述材料非均匀性的耦合系数,并建立了广义波动方程。广义波动方程数值分析表明,耦合系数的正负、取值和组合与应力/应变张量共同影响耦合波动传播过程。作为算例,给出了一阶近似的压剪耦合参数确定的本构关系以及3个压剪耦合特征波速的表达式,并利用有限差分法得到了耦合压缩波和剪切波的传播过程。研究了4个非均匀性耦合系数对应力状态、耦合波速和波传播过程的影响。耦合压缩波速反映了剪切对压缩的耦合效应和体积压实效应2种机制的竞争,耦合剪切波速反映了压缩对剪切的耦合效应和介质持续畸变带来的剪切弱化效应2种机制的竞争。这些机制可通过压剪耦合参数的不同组合来实现。应用真三轴实验系统测量了花岗岩、由砂浆制成的模型材料、具有粗骨料的水泥砂浆制成的材料3种非均匀介质在不同压剪应力下的纵波波速。结果表明,体积压实效应普遍存在,而非均匀程度越高,材料伸缩的同时完成切向的畸变导致压缩波的速度显著降低,剪切对纵波波速的影响越占据主导。理论计算结果与实验结果整体趋势基本一致。本研究可为非均匀材料的波速和动态力学性能研究提供物理机制方面的解释。Heterogeneous media are very common in nature.Due to the complex internal structure,the heterogeneous compressive shear coupled stress field is inside heterogeneous media,which leads to a mutual influence of compression and shear waves.The study of wave mechanics behavior and description of heterogeneity in heterogeneous media is of great significance and full of challenges.This article establishes a general constitutive relationship that reflects the compression shear coupling characteristics of heterogeneous materials,proposes coupling coefficients to describe material heterogeneity,combines momentum conservation law to establish a generalized wave equation,and provides a general method for solving the generalized wave equation.As an example,expressions for the three characteristic wave velocities of compression shear coupling under the first-order compression shear coupling constitutive relationship are provided,and the finite difference method is employed to obtain the propagation process of coupled compression and shear waves.The effects of four heterogeneous coupling coefficients on stress state,coupled wave velocity,and wave propagation process are studied.The positive and negative values of coupling parameters and their combinations reflect the structural characteristics of heterogeneous media and also determine the properties of compression shear coupling waves.For heterogeneous media with high-pressure effects,shear dilation effects,and shear weakening effects,the coupled compression wave velocity is lower than the elastic compression wave velocity corresponding to uniform media,and the coupled shear wave velocity is higher than the elastic shear wave velocity.The effect of shear on compression delays the propagation of compressive stress,while compression promotes the propagation of shear.Coupled compression wave velocity is the result of the competition between the coupling effect of shear on compression and the volume compaction effect.Coupled shear wave velocity is the result of the competition betw

关 键 词：非均匀性 压剪耦合效应 广义波动方程 本构关系 波速 

分 类 号：O347[理学—固体力学]