Linear and nonlinear unified strength theory

Yanshilixue Yu Gongcheng Xuebao/Chinese Journal of Rock Mechanics and Engineering

Volumn 26, Issue 4, 2007, Pages 662-669

  Yu, Maohong ^a  

^a XI'AN JIAOTONG UNIVERSITY   (China)

Author keywords

Beauty of unified strength theory; Failure criteria; Octahedral shear strength theory; Rock and soil mechanics; Single shear strength theory; Twin shear strength theory; Unification of linear criteria and nonlinear criteria; Unified strength theory

Indexed keywords

FAILURE (MECHANICAL); MATHEMATICAL MODELS; ROCK MECHANICS; ROCKS; SHEAR STRENGTH; SOIL MECHANICS; SOILS;

FAILURE CRITERIA; LINEAR CRITERIA; NONLINEAR CRITERIA; OCTAHEDRAL-SHEAR STRENGTH THEORY; ROCK AND SOIL MECHANICS; SINGLE-SHEAR STRENGTH THEORY; TWIN-SHEAR STRENGTH THEORY; UNIFIED STRENGTH THEORY;

STRENGTH OF MATERIALS;

EID: 34248679322     PISSN: 10006915     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (67)

1. ZYCZKOWSKI M. Combined loadings in the theory of plasticity[M]. Warsaw: Polish Scientific Publishers, 1981.
2. CHEN WF. Concrete plasticity: past, present and future[C]//YU M H, FAN S C ed. Strength Theory: Applications, Developments and Prospects for the 21st Century. Beijing: Science Press, 1998: 7-47.
3. CHEN W F, SALEEB A F. Constitutive equations for engineering materials (Vol. 1): elasticity and modeling[M]. Amsterdam: Elsevier, 1994.
4. CHEN W F. Constitutive equations for engineering materials(Vol.2): plasticity and modeling[M]. Amsterdam: Elsevier, 1994.
5. YU Maohong. Advances in strength theories for materials under complex stress state in the 20th Century[J]. Advances in Mechanics, 2004, 34(4): 529-560. (in Chinese)
6. YU Maohong, ZAN Yuewen, FAN Wen, et al. Advances in strength theory of rock in the 20th century-100 anniversary in memory of the Mohr-Coulomb strength theory[J]. Chinese Journal of Rock Mechanics and Engineering, 2000, 19(5): 545-550. (in Chinese)
7. YU Maohong, HE Linan, SONG Lingyu. Twin-shear theory and its generalization[J]. Science in China (Series A), 1985, 28(12): 1113-1121. (in Chinese).
8. YU Maohong. Twin-shear theory and its applications[M]. Beijing: Science Press, 1998. (in Chinese)
9. YU M H, HE L N. A new model and theory on yield and failure of materials under the complex stress state[C]//JONO M, INOUE T ed. Mechanical Behaviour of Materials (ICM-6). Oxford: Pergamon Press, 1991: 841-846.
10. YU Maohong. New system of strength theory[M]. Xi'an: Xi'an Jiaotong University Press, 1992. (in Chinese)
11. YU M H. Unified strength theory and its applications[M]. Berlin: Springer, 2004.
12. MOSTAFA M E. General rock failure criterion[J]. Mining Technology, 2003, 112(1): 64-68.
13. LIU M D, CARTER J P. General strength criterion for geomaterials[J]. Int. J. of Geomechanics, 2003, 3(2): 253-259.
14. AUBERTIN M, LI L. A porosity-dependent inelastic criterion for engineering materials[J]. International Journal of Plasticity, 2004, 20(12): 2179-2208.
15. LI L, AUBERTIN M, SIMON R, et al. Formulation and application of a general inelastic locus for geomaterials with variable porosity[J]. Canadian Geotechnical Journal, 2005, 42(2): 601-623.
16. DAS S K, BASUDHAR P K. Comparison study of parameter estimation techniques for rock failure criterion models[J]. Canadian Geotechnical Journal, 2006, 43(7): 764-771.
17. ZIENKIEWICZ O C, PANDE G N. Some useful forms of isotropic yield surfaces for soil and rock mechanics[C]//GUDEHUS G ed. Finite Elements in Geomechanics. London: John Wiley and Sons, 1977: 179-190.
18. ZHENG Yingren, SHEN Zhujiang, GONG Xiaonan. The principles of geotechnical plastic mechanics[M]. Beijing: China Architecture and Building Press, 2002. (in Chinese)
19. SHEN Zhujiang. Science advocates simplicity-some remarks about adopting and adapting methods in geotechnical engineering[J]. Chinese Journal of Geotechnical Engineering, 2004, 26(2): 299-300. (in Chinese)
20. TZANAKIS C. The quest of beauty in research and teaching of mathematics and physics: a historical approach[J]. Nonlinear Analysis, Theory, Methods and Applications, 1997, 30(4): 2097-2105.
21. FAN S C, QIANG H F. Normal high-velocity impact concrete slabs-a simulation using the meshless SPH procedures[C]//VALLIAPPAN S, KHALILI N ed. Computational Mechanics-New Frontiers for New Millennium. Amsterdam: Elsevier, 2001: 1457-1462.
22. ZHANG X S, GUAN H, LOO Y C. UST (unified strength theory) failure criterion for punching shear analysis of reinforcement concrete slab-column connections[C]//VALLIAPPAN S, KHALILI N ed. Computational Mechanics-New Frontiers for New Millennium. Amsterdam: Elsevier, 2001: 299-304.
23. YU M H, YOSHIMINE M, ODA Y, et al. The beauty of strength theories[R]. Cracow, Poland: [s. n.], 2004.
24. SHEN Zhujiang. Review of 'Unified strength theory and its applications'[J]. Advances in Mechanics, 2004, 34(4): 562-563. (in Chinese)
25. TEODORESCU P P. Review of 'Unified strength theory and its Applications'[R]. Berlin: Springer, 2004.
26. MA G W, YU M H, MIYAMOTO Y, et al. Unified plastic limit solution to circular plate under portion uniform load[J]. J. of Structural Engineering, 1995, 41A: 385-392.
27. MA G W, YU M H, IWASAKI S, et al. Unified elastoplastic solution to rotating disc and cylinder[J]. J. of Structural Engineering, 1995, 41A: 79-85.
28. JIANG Mingjing, SHEN Zhujiang. Unified solution to expansion of cylindrical cavity for geomaterials with strain-softening behaviour[J]. Rock and Soil Mechanics, 1996, 17(1): 1-8. (in Chinese)
29. JIANG Mingjing, SHEN Zhujiang. Expansion of cylindrical cavity with elastic-brittle-plastic softening and shear dilatation behaviour[J]. Journal of Hohai University, 1996, 24(4): 65-72. (in Chinese)
30. JIANG Mingjing, SHEN Zhujiang. On expansion of cylindrical cavity with linear softening and shear dilatation behaviour[J]. Chinese Journal of Rock Mechanics and Engineering, 1997, 16(6): 550-557. (in Chinese)
31. MA G W, IWASAKI S, MIYAMOTO Y, et al. Plastic limit analyses of circular plates with respect to unified yield criterion[J]. Int. J. Mech. Sciences, 1998, 40(10): 963-976.
32. MA G W, HAO H, IWASAKI S. Plastic limit analyses of a clamped circular plates with unified yield criterion[J]. Structural Engineering and Mechanics, 1999, 7(5): 513-525.
33. MA G W, HAO H, IWASAKI S. Unified plastic limit analysis of circular plates under arbitrary load[J]. J. Appl. Mechanics, ASME, 1999, 66(2): 568-570.
34. MA G W, IWASAKI S, MIYAMOTO Y, et al. Dynamic plastic behavior of circular plate using unified yield criterion[J]. Int. J. of Solids and Structures, 1999, 36(3): 3257-3275.
35. SONG Li, ZHANG Yongqiang, YU Maohong. Unified solution to elastoplastic analysis of pressure tunnel[J]. Engineering Mechanics, 1998, 15(4): 57-61. (in Chinese)
36. LI Jianchuan, YU Maohong, FAN Shouchang. A unified solution for limit load of simply supported oblique plates, rhombus plates, rectangle plates and square plates[J]. China Civil Engineering Journal, 2000, 33(6): 76-80. (in Chinese)
37. ZHANG Yongqiang, FAN Wen, YU Maohong. Unified slip line solution of ultimate load of slope[J]. Chinese Journal of Rock Mechanics and Engineering, 2000, 19(Supp.): 994-996. (in Chinese)
38. MA G W, IWASAKI S, MIYAMOTO Y, et al. Dynamic plastic behavior of circular plates using the unified yield criterion[J]. Int. J. of Solids and Structures, 1999, 36(22): 3257-3275.
39. WANG Yanbin, YU Maohong, WEI Xueying, et al. Unified plastic limit analyses of circular plates under uniform annular load[J]. Engineering Mechanics, 2002, 19(1): 84-88. (in Chinese)
40. WANG Xiangqiu, YANG Linde, GAO Wenhua. Calculation of bearing capacity about the strip foundation based on the twin shear unified strength theory[J]. China Civil Engineering Journal, 2006, 39(1): 79-82. (in Chinese)
41. SUN Hongyue, SHANG Yuequan, ZHANG Chunsheng, et al. 3D numerical modeling of possible failure zone with underground excavation[J]. Chinese Journal of Rock Mechanics and Engineering, 2004, 23(13): 2192-2196. (in Chinese)
42. CHEN Lanyun, ZAN Yuewen, WANG Jie, et al. Reinforcement of surrounding rocks of tunnel in landslide area with grouting technology[J]. Chinese Journal of Rock Mechanics and Engineering, 2004, 23(16): 2761-2765. (in Chinese)
43. LI Hangzhou, LIAO Hongjian, SHENG Qian. Study on statistical damage constitutive model of soft rock based on unified strength theory[J]. Chinese Journal of Rock Mechanics and Engineering, 2006, 25(7): 1331-1336. (in Chinese)
44. LUO Zhanyou, XIA Jianzhong, GONG Xiaonan. Unified solution for the expansion of spherical cavity in strain-softening materials with different elastic moduli in tension and compression[J]. Engineering Mechanics, 2006, 23(4): 22-27. (in Chinese)
45. CHEN Qiunan, ZHANG Yongxing, ZHOU Xiaoping. Formula of Rankine passive earth pressure in triaxial state of stress[J]. Chinese Journal of Rock Mechanics and Engineering, 2005, 24(5): 880-882. (in Chinese)
46. HAO Lixia, GU Shuancheng. Discussion on 'Formula of Rankine passive earth pressure in triaxial state of stress'[J]. Chinese Journal of Rock Mechanics and Engineering, 2006, 25(11): 2373-2374. (in Chinese)
47. CHEN Qiunan. Reply to the 'Discussion on 'Formula of Rankine passive earth pressure in triaxial state of stress''[J]. Chinese Journal of Rock Mechanics and Engineering, 2006, 25(11): 2374-2375. (in Chinese)
48. WEI Xueying, YANG Zheng, YU Shu, et al. Solution of axisymmetrical punching strength of concrete slabs with the unified strength theory[J]. Engineering Mechanics, 2002, 19(5): 92-96. (in Chinese)
49. WANG Pengcheng, ZHU Xiangrong. Rigorous similarity solution of cavity expansion in soil taking the effect of intermediate principal stress into account[J]. Journal of Hydraulic Engineering, 2004, (11): 68-73. (in Chinese)
50. SUN J, WANG S J. Rock mechanics and rock engineering in China: developments and current state-of-the art[J]. International Journal of Rock Mechanics and Mining Sciences, 2000, 37(3): 447-465.
51. YU M H, ZAN Y W, ZHAO J, et al. A unified strength criterion for rock material[J]. International Journal of Rock Mechanics and Mining Sciences, 2002, 39(8): 975-989.
52. ZHOU Xiaoping, HUANG Yubin, DING Zhicheng. Influence of intermediate principal stress on formula of Terzaghi ultimate bearing capacity of foundations[J]. Chinese Journal of Rock Mechanics and Engineering, 2002, 21(10): 1554-1556. (in Chinese)
53. DENG Longsheng, CHANG Zheng, LI Guang, et al. Calculation pressure of surrounding rock mass for loosen rock mass based on unified strength theory[J]. Earth and Environment, 2005, 33(Supp.): 32-35. (in Chinese)
54. FAN Wen, YU Maohong, CHEN Liwei, et al. Unified elastoplastic solution for surrounding rocks of openings with consideration of material dilatancy and softening[J]. Chinese Journal of Rock Mechanics and Engineering, 2004, 23(19): 3213-3220. (in Chinese)
55. LIU Jie, ZHAO Minghua. Researches on behaviour of composite foundation with single granular column based on unified twin shear strength theory[J]. Chinese Journal of Geotechnical Engineering, 2005, 27(6): 707-711. (in Chinese)
56. LIAO Hongjian, WU Jianying, HUANG Feiqiang, et al. Determination of dynamic strength parameters of geomaterials based on unified strength theory[J]. Chinese Journal of Rock Mechanics and Engineering, 2003, 22(12): 1994-2000. (in Chinese)
57. ZHOU Annan, LUO Ting, YAO Yangping. Formula of critical edge load of strip foundation under complex stress state[J], Rock and Soil Mechanics, 2004, 25(10): 1599-1602. (in Chinese)
58. SUN Hongyue, SHANG Yuequan, ZHANG Chunsheng. Numerical modeling analysis for surrounding rockmass stability of large underground cavities[J]. Journal of Zhejiang University (Engineering Science), 2004, 38(1): 70-73, 85. (in Chinese)
59. LI Hangzhou, LIAO Hongjian, LAN Xia. Determination of ultimate bearing capacity of rock foundation based on unified strength theory[J]. Chinese Journal of Rock Mechanics and Engineering, 2004, 23(Supp. 1): 4311-4314. (in Chinese)
60. ZHANG Yongqiang, YU Maohong. Discontinuous bifurcations of elastoplastic materials for plane stress[J]. Acta Mechanica Sinica, 2001, 33(5): 706-713. (in Chinese)
61. ZHANG Y Q, LU Y, YU M H. Investigation of strain localization in elastoplastic materials with transversely isotropic elasticity[J]. Int. J. Mech. Sciences, 2003, 45(2): 217-233.
62. WANG Y B, YU M H, YUN X, et al. Dynamic plastic response to circular plate based on unified strength theory[J]. Int. Journal of Impact Engineering, 2005, 31(1): 25-40.
63. ZHANG Y Q, HAO H, YU M H. A unified characteristic theory for plastic plane stress and strain problems[J]. Journal of Applied Mechanics, 2003, 70(5): 649-655.
64. YU M H, FAN W, CHE AL, et al. Application of the unified strength theory in analyzing fracture strength[J]. Key Engineering Materials, 2004, 261-263: 111-116.
65. GONG Jun, LANG Fuyuan, WANG Min, et al. Mixed mode fracture criterion based on unified strength theory[J]. Journal of Mechanical Strength, 2003, 25(3): 347-351. (in Chinese)
66. YU M H, MA G W, QIANG H F, et al. Generalized plasticity[M]. Berlin: Springer, 2006.