基于形状改变比能对M-C准则与 D-P系列准则匹配关系的研究

在一定前提下可导出与Mohr-Coulomb（M-C）屈服准则相匹配的Drucker-Prager （D-P）系列准则。首先解释了基于M-C准则与D-P系列准则匹配关系的能量含义，在此基础上重点研究了 平面内，在Lode角相同的情况下进入M-C屈服面与D-P屈服面所需形状改变比能的差值，并应用最小二乘法，推导了在所有可能的加载方式下到达屈服面所需形状改变比能差值平方和最小时M-C准则与D-P准则的参数匹配关系。结果表明，在此能量偏差极小意义下的匹配与等面积匹配等价，由此给出了等面积匹配的力学意义。

Studies on transformation from M-C criterion to Drucker-Prager criterions based on distortion energy density

Under some hypothesis, the Drucker-Prager(D-P) criterions can be used approximately instead of Mohr-Coulomb(M-C) criterion. The foundation of transformation methods from M-C to D-P from energy view is firstly set forth; and then emphasis is given to investigate the square error of distortion energy density, which are needed for reaching M-C yield and D-P yield respectively, provided the same Lode angle in ? plane. Based on the least square method, the relations of parameters for M-C and D-P are obtained providing minimum of the square error of distortion energy density. The result obtained in the approach is according to the equivalent area’s approach, the interpretation in energy view for the transformation method in equivalent area’s approach is presented.