1、考虑材料的塑性，其增量形式的本构关系可表达为(1)pd=(D-)式(1)中， 为弹性矩阵， 为塑性矩阵。Dp弹性矩阵 的形式为(2)42033240330KGKGG D体积模量 ，剪切模量 。3(12)EK2(1)E在应变空间内，塑性矩阵可表达为(3)()TfApD式中， (4)()()TTpfffBD为屈服函数； 为塑性应力， ；fpp(5)1/2()TpTpfBffI； 为塑性功； 为塑性体应变； 为等效塑性应变；10TIp p为反映加载历史的参数。对于 Drucker-Prager 模型，其屈服条件为当 时p当 时当 时p(6)120fIJ， ， 为材料常数。1xyzI2221()xyz
2、xyzxJSS(7)2fJI(8)TxyzxyzxSSS (9)221()3f GKJJDII(10)222()()()9TTTfA K SS1TfpD222 22 221123132221211(3)(3)9 (9)(9)(9)(TTT TTGKJJKGGKJmnlSmSSmnnnlllllSl IIIS112312133232323)()()nSSSl 令 ，4pKGq弹塑性矩阵可表达为 2 1212313222121211123121333233()(pmqnmlSSmSnnnllpllllSGnSlS eppD2)()SG 令 ， ， ， ，12(9)GKJ229Ka12m12n132
3、lS 22222212933(9)()(9)()9x xxxKGKGSSSGJJJGaSmJ pD 222212 2222 2112933(9)()(9)3()9(y xxyx ySSSK KJGJKGJaaSJSmn p222213 222 221132933(9)()(9)3()9(z xxzx zKKSSSGGJJGJaaSJSmlpD22142 121122 22()(9) ()()(9)xyxyx xyKSSKGJGJ SSm pD215 22 121322 223()(9) ()()(9)yz xyzx yzSSJKJGGSSK p216 22 121312 223()(9) ()
4、()(9)zxxzx zxSSJJK SSmGG pD2 22221 222 22112933(9)()()3()99(x yyxx yKKGSJJJaaSSKGJGSmn pD2 22222 2212933(9)()(9)()9y yyyKGKGSSSGJJJGaSnJ pD 222223 222 221132933(9)()(9)3()9(z yyZy zSSSK KJGJKGJaaSJSnlp 22242 121212 22()(9) ()()(9)xyyxy xyKSSKGJGJ SSn pD225 22 121232 223()(9) ()()(9)yz yzy yzSSJKJGGS
5、SnK p226 22 121312223()(9) ()()(9)zxyzxy zxSSJJK SSnGG pD2 22231 222 221132933(9)()()3()99(x z zxx zKKSGJJJaaSSKGJGSml pD2 22232 222 22113293(9)()(9)3()9(y z zyy zKKSSSGJJJaaSKGJGSnl pD2 22223 2213293(9)()(9)()9z z zzKGKGSSSGJJJGaSlJ pD22342 1321122 22()(9 ()()(9)xyzxyz xySKGJKSSlG p235 221321322 22
6、()(9 ()()(9)yz zyz yzSSJJKGSSlK pD236 22 1321312 22()(9 ()()(9)zxzxz zxGSSJJ SSlKG p 22412 121122 223()(9) ()()9xyxyxxyGSSKJJ SSmKG pD242 22 121212223()(9) ()()9xyxyyxySSJGJ SSnK p243 22 132112222()(9) ()()9xyxyzz xyKSSGJJ SSlG pD1224 223()()(9)xy xySSKJKJp123245 222 3()(9)9xyz xyyzGKSSGpD 1213246 2
7、223(9)()xyz xyzxGSSKJKJ p22512 121322 223(9)(9) ()()()yz yzxx yzKGSSKGJJ SSm pD252 22 1212322239(9)()()yz yzy yzSSJKGJGSSnK p253 22132132222(9)(9) ()()yz yzz yzSSJJKGSSlG pD 123254 2223(9)(9)9xyz xyyzKSJKJ p 212325 22 ()()()yz yzKSGpD 132256 2223(9)(9)9yzx yzzxGKS SSJKJG p 22612 121312 22()()3 ()9(9)(9)zxzxx zxKSJGJGSSmK pD262 22 12131222()3)()9(9(9)zxzxyy zxSSJKJGSSnG p263 22 132131222()() ()9(9)(9)zxzxz zxSSKJJK SSlG pD 1321264 2223()()9zxy zxxyGKSJJG p132265 2223 3(9)(9)9zxy zxyzKGGKSSSSJKJGpD21326 22 ()()()zx zxp
