目 錄
上 冊
第 1章 小變形彈塑性本構關係 ······································································1
1.1經典彈塑性本構關係 ·········································································1
1.2 J2流動理論 ······················································································· 13
1.2.1各嚮同性硬化 ······································································· 13
1.2.2 混閤硬化 ··············································································· 16
1.3 J2形變理論及其與 J2流動理論（各嚮同性硬化）的比較 ············ 27
1.3.1 J2形變理論 ··········································································· 27
1.3.2 J2形變理論與 J2流動理論的比較 ······································· 33
1.4奇異屈服麵塑性理論 ······································································· 35
1.4.1 Sanders理論 ········································································· 35
1.4.2 Koiter理論············································································ 41
1.5 Tresca流動理論（混閤硬化） ························································ 49
1.6塑性基本假設 ··················································································· 63
1.6.1 Drucker假設········································································· 64
1.6.2 Ilyushin假設········································································· 68
1.6.3 對 J2形變理論的重新評價··················································· 70
1.7 J2角點理論 ······················································································· 74
1.7.1塑性應變率勢 ······································································· 74
1.7.2 W p()80..為凸函數的條件························································
1.7.3逆塑性本構關係 ··································································· 88
1.7.4 J2角點理論 ··········································································· 93
1.7.5應變率勢理論 ······································································· 98
1.8壓力敏感及塑性膨脹模型 ····························································· 102 習題 1 ······································································································ 107
第 2章 連續介質力學概述 ·········································································· 117
2.1變形幾何 ························································································· 117
2.1.1 F的極分解 ········································································· 121
2.1.2綫元、麵元與體元的變換 ·················································· 126
2.1.3 Hill應變度量與 Seth應變度量 ········································· 129
高等固體力學（上冊）
2.1.4應變張量通過位移矢量錶示 ·············································· 131
2.1.5在參考構形 R與即時構形 r中梯度運算的轉換關係 ········ 134
2.2變形運動學 ····················································································· 138
2.2.1速度梯度、變形率、鏇率 ·················································· 138
2.2.2 各種鏇率 ············································································· 145
2.2.3 Hill應變度量、 Seth應變度量的率 ··································· 147
2.3應力理論 ························································································· 152
2.3.1 Cauchy應力，第一類與第二類 P-K應力························· 152
2.3.2 動量方程 ············································································· 157
2.3.3 變形功率 ············································································· 161
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2.3.4 與E，En功共軛的應力度量··········································· 162
2.4質量與能量的守恒或平衡律 ·························································· 164
2.4.1質量守恒律 ········································································· 165
2.4.2機械能平衡律 ····································································· 166
2.4.3能量平衡律 ········································································· 167
2.4.4熵不等式，熵平衡律 ························································· 168
2.5本構理論的客觀性原理 ································································· 170
2.5.1 客觀量 ················································································· 171
2.5.2張量的客觀率（或客觀導數） ·········································· 180
2.5.3本構理論的客觀性原理 ····················································· 183
2.6 Lagrange嵌入（或隨體）麯綫坐標，張量的轉移 ······················ 187
2.6.1 Lagrange嵌入麯綫坐標係 ················································· 187
2.6.2張量的轉移 ········································································· 191
2.6.3張量的四個客觀導數 ························································· 195
2.6.4 Lagrange嵌入麯綫坐標 XA與 Euler麯綫坐標 xi··············· 198
2.7小變形彈塑性本構關係形式上的推廣 ·········································· 199
2.7.1彈性本構關係（率形式） ·················································· 200
2.7.2各嚮同性硬化 Prandtl-Reuss彈塑性本構方程 ·················· 202
2.7.3 混閤硬化 ············································································· 203
2.7.4 J2形變理論 ········································································· 205
2.8局限性····························································································· 205 習題 2 ······································································································ 210
第 3章 大變形彈性本構關係及應用 ····························································· 227
3.1彈性本構關係與熱傳導 ································································· 227
3.1.1彈性本構關係 ····································································· 227
目錄
3.1.2 一個特例 ············································································· 231
3.1.3 熱傳導 ················································································· 237
3.1.4率形式彈性本構關係 ························································· 239
3.2彈性張量必須滿足的條件 ····························································· 242
3.3各嚮同性材料大變形彈性本構關係 ·············································· 246
3.4彈性大變形典型問題解 ································································· 252
3.4.1材料的內部約束 ································································· 253
3.4.2各嚮同性彈性材料的典型問題解 ······································ 255
3.5彈性大變形邊值問題 ····································································· 278
3.5.1運動或平衡方程 ································································· 279
3.5.2 邊界條件 ·············································································· 282
3.5.3各嚮同性彈性體的本構關係 ·············································· 284
3.5.4材料的內部約束（續） ····················································· 287
3.5.5各嚮同性彈性材料的應變能函數 W·································· 290 習題 3 ······································································································ 293
第 4章 大變形彈塑性本構關係 ···································································· 301
4.1彈性變形與塑性變形 ······································································ 301
4.2彈性變形率 de與塑性變形率 dp ···················································· 307
4.2.1 Moran-Ortiz-Shih定義 ······················································· 308
4.2.2 Green-Naghdi與 Simo-Ortiz的定義 ·································· 314
4.2.3 Rice與 Hill的定義 ····························································· 316
4.2.4三種定義的比較及卸載構形剛性轉動 .的影響 ·············· 322
4.3 Rice-Hill大變形彈塑性理論 ·························································· 324
4.3.1率形式本構關係 ································································· 326
4.3.2內變量的演化，正交法則 ·················································· 332
4.4度量相關性 ····················································································· 364
4.4.1 應變度量 E及率 E.，應力度量 T及率 T. ····················· 364
4.4.2度量不變量 ········································································· 368
4.4.3對應於不同度量函數的本構關係 ······································ 370
4.4.4應變率與應力率的彈塑性分解 ·········································· 371
4.4.5正交法則的對偶性與度量不變性 ······································ 375
4.5 Simo-Ortiz大變形彈塑性本構理論 ··············································· 377
4.5.1 一般關係 ············································································· 377
4.5.2各嚮同性硬化（等嚮硬化）情況 ······································ 380
高等固體力學（上冊）
4.6 中間構形彈塑性本構理論之一 ——Moran-Ortiz-Shih大變形彈塑性本構理論 ··························· 389
4.6.1 彈性響應 ············································································· 391
4.6.2塑性響應，率形式本構關係 ·············································· 393
4.6.3虛位移原理 ········································································· 404
4.7 中間構形彈塑性本構理論之二 ——Van der Giessen大變形彈塑性本構理論 ······························ 406
4.7.1熱力學討論 ········································································· 410
4.7.2 熱傳導 ················································································· 413
4.7.3塑性變形率 dp與塑性鏇率 wp············································ 414
4.7.4內變量理論 ········································································· 418
4.7.5持續各嚮同性介質 ····························································· 422
4.7.6機動與混閤硬化 ································································· 426
4.7.7各嚮異性硬化 ····································································· 432 習題 4 ······································································································ 433
附錄 A 張量分析 ··························································································· 439
A.1矢量與張量的概念 ········································································· 439
A.2張量代數 ························································································ 443
A.3張量的微積分 ················································································ 449
附錄 B ABAQUS軟件的理論基礎 ······························································· 456
B.1塑性大變形 ····················································································· 456
B.2彈性大變形 ····················································································· 472
參考文獻 ········································································································· 483
下 冊
第 1章晶體的大變形彈塑性理論
第 2章 應變梯度塑性理論
第 3章納米管的力學
第 4章柔性可伸展電子元件的力學
VIII
· · · · · · (收起)