分层介质中大变形的建模——Cosserat连续体方法

D. P. Adhikary, Dr. H.-B. Mühlhaus, A. V. Dyskin
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引用次数: 0

摘要

采用连续体近似描述层状材料变形的方法比显式模型具有明显的优势。然而,基于各向异性连续体理论的传统隐式模型在界面滑移和内部不稳定性方面存在一定的困难。这些困难可以通过考虑层的弯曲刚度来弥补。这意味着引入了力矩(耦合)应力和内部旋转,这导致了Cosserat型理论。在本模型中,假设层状材料的行为是线性弹性的;假设界面是弹性完全塑性的。界面处的滑移或无滑移条件由库仑准则检测,张力在零法向应力下被切断。该理论适用于大变形分析。该模型被纳入有限元程序AFENA中,并与层状介质中基本屈曲问题的解析解进行了验证。在高水平原位应力作用下,节理岩体中矩形开挖的顶板和底板的屈曲问题被认为是该理论的主要应用。版权所有©1999 John Wiley&;有限公司。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Modelling the large deformations in stratified media—the Cosserat continuum approach

Methods employing continuum approximation in describing the deformation of layered materials possess a clear advantage over explicit models. However, the conventional implicit models based on the theory of anisotropic continua suffers from certain difficulties associated with interface slip and internal instabilities. These difficulties can be remedied by considering the bending stiffness of the layers. This implies the introduction of moment (couple) stresses and internal rotations, which leads to a Cosserat-type theory. In the present model, the behaviour of the layered material is assumed to be linearly elastic; the interfaces are assumed to be elastic perfectly plastic. Conditions of slip or no slip at the interfaces are detected by a Coulomb criterion with tension cut off at zero normal stress. The theory is valid for large deformation analysis. The model is incorporated into the finite element program AFENA and validated against analytical solutions of elementary buckling problems in layered medium. A problem associated with buckling of the roof and the floor of a rectangular excavation in jointed rock mass under high horizontal in situ stresses is considered as the main application of the theory. Copyright © 1999 John Wiley & Sons, Ltd.

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