平面应变问题非连续分叉统一解

UNIFIED SOLUTION OF DISCONTINUOUS BIFURCATION FOR PLANE STRAIN PROBLEMS

运用统一强度理论 ,对弹塑性材料的非连续分叉现象进行了研究 ,获得了非关联弹塑性材料在平面应变条件下非连续分叉的起始方位角以及相应的硬化模量的统一解析解形式。由于考虑了材料的非关联流动以及拉压异性 ,此解可适用于岩土类材料以及其它类别的弹塑性材料。已有文献中的非连续分叉起始方位角结果为本文统一解的特例或线性逼近。研究表明 ,材料的拉压异性以及所受的中间主应力对非连续分叉有较大影响。同时指出不同强度准则对于弹塑性材料非连续分叉的影响以及正确选择符合所研究材料的强度准则在非连续分叉的研究中是重要的。进一步分析表明 ,对于平面应变情形 ,剪切带同滑移线本质上是一致的。通过与实验结果比较 ,验证了统一非连续分叉理论的合理性和正确性。

Using the Unified Strength Theory in studying the discontinuous bifurcation phenomenon of elasto-plastic materials,hence the unified explanatory solution of the initial direction angle of discontinuous bifurcation and the corresponding value of the hardening modulus under plane strain condition for non-associate elasto-plastic materials have been obtained.Owing to taking account of the non-associate mobility and the strength differential effect of materials,then the unified solution can be adopted to rock-soil type matarials and other kinds of elasto-plastic materials.The results of the initial direction angles of discontinuous bifurcation,which had been shown in the reference documents,are the special case or linear approack for the unified solution in the paper.It is shown that the influence of the strength differential effect and the suffered intermediate principal stress of materials on the discontinuous bifurcation are comparatively large.Meantime,in the study of discontinuous bifurcation that the importance to the influence of different yield criteron on discontinuous bifurcation of elasto-plastic materials and the accurate selection of yield criterion to fit the used materials are pointed out.Furthermore,from the analytical results indicate that the shear band mode of discontinuous bifurcation is essentially identical with slip line in the plane strain condition.Finally,the correctness and rationalization of the unified discontinuous bifurcation theory is verified by the results of experiment.