%0 Journal Article
%T UNIQUENESS AND LOCALIZATION BIFURCATION ANALYSIS SOLUTION OF SATURATED POROUS MEDIA<br>饱和多孔介质分析解的唯一性与应变局部化分岔
%A Zhang Hongwu
%A <br>张洪武
%J 力学学报
%D 2000
%I 
%X Strain localization and related material instabilities are of considerable interest because of their importance in failure prediction of materials. A suitable tool for describing localization in solid mechanics is based on the strain rate discontinuity in continuum theory. The basic theory can be found in the works by Mandel (1964) 5 Rudnicki and Rice (1975), Rice (1975, 1976), Vardoulakis (1976) and Rice and Rudnicki (1980). On the other hand, strain localization also means both a non-uniqueness in the incremental elastoplastic response of the deformable continuum and a vanishing speed of the acceleration waves (see Hadamard (1903), Thomas (1961), Rice (1976), Hill (1962) and Mandel (1964)). Some recent works for quite general classes of elastic-plastic solids are given by Ottosen and Runesson (1991), Runesson, Ottosen and Peric (1991), and Bigoni and Hueckel (1991). Most work published so far is related to the behaviour of single phase materials. However, strain localization phenomena are also relevant for elastic-plastic porous solids, the pores of which are filled with a fluid such as water, oil, etc. Strain localization analysis for this problem is generally performed under locally undrained conditions where net inflow or outflow is prevented. Some classical and recent results can be found in the papers by Rice (1975), Rice and Cleary (1976), Rudnicki (1983), Han and Vardoulakis (1991), Runesson, et al. (1996). Rudnicki (1983) and Zhang et al. (1999). Zhang et al. (1999) discussed the relevant localization condition for the more general situation of drained behaviour due to finite permeability of the media, i.e. internal flow is not inhibited. In this paper, the conditions for localization of deformation into a planar (shear) band and loss of uniqueness in the incremental response of elastic-plastic saturated porous media were systematically studied. The critical modulus for shear band localization of undrained condition are studied in terms of the discontinuous bifurcation analysis of the problems. Loss of uniqueness of the response of the coupled problem is investigated by means of the positiveness of the second order work density which has been broadly used in solid mechanics. Based on the general solutions, the explicit solutions of the critical hardening modulus for both kinds of material instability problems, i.e. strain localization and loss of uniqueness, are found in the principle axial space. The existence of the explicit solutions makes it possible to directly inspect possible localization models. Some important results such as that the critical haxdening modulus for strain localization is never positive for associative plasticity and coincides with the critical hardening modulus for zero second order work in saturated porous media, are obtained. It has been shown from the present research that the loss of uniqueness and the critical conditions for strain localization at static undrained conditions are different in quantity with t
%K uniqueness analysis
%K strain localization
%K saturated porous medium
%K undrained
%K condition<br>唯一性分析
%K 应变局部化
%K 饱和多孔介质
%K 非渗流条件
%K 材料
%U http://www.alljournals.cn/get_abstract_url.aspx?pcid=6E709DC38FA1D09A4B578DD0906875B5B44D4D294832BB8E&cid=5D344E2AD54D14F8&jid=4100DA4A1A3BA1B0CE5AD99AE1DFB420&aid=1CD430E96C5A1230&yid=9806D0D4EAA9BED3&vid=9971A5E270697F23&iid=B31275AF3241DB2D&sid=710C005323C0774A&eid=780091CB32840698&journal_id=0459-1879&journal_name=力学学报&referenced_num=7&reference_num=22