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1、第五章：J积分和M积分 J积分 HRR场 J积分的实验测量和数值计算 讨论 M积分 断裂力学中的三个守恒积分 J. K. Knowles, Eli Sternberg, On a class of conservation laws in linearized and finite elastostatics. Archive for Rational Mechanics and Analysis, 44, 187-211 (1972). B. Budiansky and J. R. Rice, Conservation laws and energy-release rates. Journ
2、al of Applied Mechanics, 40, pp. 201-203 (1973). J积分 M积分 L积分 Knowles-Sternberg 2D（线积分） 能量释放率（缺陷相互作用） J积分 J.R. Rice, A path independent integral and the approximate analysis of strain concentration by notches and cracks. J. Appl. Mech. 35, 379-386 (1968). J.D. Eshelby, The force on an elastic singula
3、rity. Phil. Trans. Roy. Soc. London A 244, 87-111 (1951). J.D. Eshelby, The continuum theory of lattice defects. Solid State Physics 3, 79-144 (1956). John Douglas Eshelby James R. Rice G.P. Cherepanov, Crack propagation in continuous media. Journal of Applied Mathematics and Mechanics 31, 503 (1967
4、). G.P. Cherepanov, Cracks in solids. International Journal of Solids and Structures 4, 811-831 (1968). J Integral Emmy Noether (18821935) Noethers Theorem Any differentiable symmetry of the action of a physical system has a corresponding conservation law. The action of a physical system is the inte
5、gral over time of a Lagrangian function (which may or may not be an integral over space of a Lagrangian density function), from which the systems behavior can be determined by the principle of least action. http:/en.wikipedia.org/wiki/Noethers_theorem The homogeneity of the material implies the path
6、 independence of J. The derivation of J as an example of Noethers theorem. 对于J1，显然在l和l段的积分为零，为什么？ J积分的意义 1.具有热力学意义，能够描述流入裂尖端部的能量； 2.具有力学意义，能够描述裂尖场的强度； 3.具有几何学意义，能够反映裂尖的形貌。 J. R. Rice and G. F. Rosengren, “Plane Strain Deformation Near a Crack in a Power Law Hardening Material“, Journal of the Mechanics and Physics of Solids, 16, 1968, pp. 1-12. John W. HutchinsonJames R. Rice Hutchinson, J.W., “ Singular Behavior at the End of a Tensile Crack in a Hardening Material.“ J. Mech. Phys. Solids, 16, 18-31 (1968) 为什么要引入 为什么？
