双材料基本解弹塑性边界元法

提出并研究采用双材料基本解的弹塑性边界元法，得到了内点应力公式中有关奇点塑性应变自由项的完整表达式，并利用非连续边界单元和非连续区域单元解决了当奇点位于界面上时该自由项难于确定，以及计算区域Cauchy主值积分的常塑性应变场法在与界面相连的奇异区域单元上无法实施的困难．采用双材料基本解的弹塑性边界无法针对双材料的结构特点，特别适于分析有关弹塑性双材料界面及界面裂纹问题．

ELASTOPLASTIC BOUNDARY ELEMENT METHOD WITH BIMATERIAL FUNDAMENTAL SOLUTION

The study of problems of bimaterial interface and interface fracture is one of the centralissues of solid mechanics at present. Boundary element method is increasingly manifested to bean effective numerical approach to the study. So an elastoplastic boundary element method withbimaterial fundamental solution, Dundurs-Hetenyi solution, was first proposed by the first authorand is developed in this paper by consideration of the structural features of bimaterial. Becausethe interface conditions of bimaterial are satisfied strictly by this type of fundamental solution, theinterface needs not to be divided into boundary elements during the boundary element analysisof bimaterial body, whiCh ensures more accurate results on or near the interface and improves thecomputational efficiency. The boundary element method of this paper is of some general uses dueto the bimaterial fundamental solution including the fundamental solutions of homogeneous body,i.e. Kelvin solution and that of half-plane body, i.e. Mindlin solution, as its special cases.In the paper, the boundary integral equations of displacements and the formulae of stressincrements of interior point in the elastoplastic boundary element method with bimaterial solutionare presented. The complete analytic expressions of the free terms relevant to the plastic strains inthe formulae of stress increments of interior point are obtained after very complicated derivations.These expressions consummate this method theoretically and are significant to the semi-analyticsolution of Cauchy principal value of singular region integral in the present method. Some difficulties occur when the plastic zone develops onto the interface and when using the approach ofconstant plastic strain field to solve the Cauchy principal values of singular cell connecting on theinterface as singular point lies on interface. These difficulties are overcome by usage of generalquadratic partially discontinuous boundary elements and general quadratic partially discontinuousinterior cells of quadrilateral. The degenerate transforms of local coordinate for solving the singularintegral on partially discontinuous cells are presented in detail as well. The method is illustratedby an example of rectangular bimaterial plate with a circular hole on the interface. It is provedby the numerical results that the present method is especially suitable for the numerical analysisof elastoplastic bimaterial interface or interface crack problems.