固体力学及其断裂理论的守恒(律)积分扮演着表征材料物理本性的不可或缺的角色。固体的力学过程决定于孪生的两套方程系统，一套是基本物理方程系统，另一套是其通解中独立的任意函数需满足的方程系统。对理论的不完整所提出的挑战是缺失另一套方程系统的非经典守恒(律)积分。应用新发现的获取泛函的普遍性方法，项目将发展和建立三类方程的泛函：场方程通解中的任意函数需满足的方程、某些物理量应满足的方程、以及还未发现Lagrange作用积分的力学方程。力学领域从未丧失对变分原理的兴趣。同时，将新发现的广义Noether恒等式应用于上述三类泛函以获取非经典守恒(律)积分。项目将深入地揭示出固体的新守恒性并将研究经典与非经典守恒(律)积分之间的关系。已获得的个别非经典守恒积分已经展现出无法替代的在固体断裂、缺陷和位错以及在流体和电场等方面的创新应用。完成项目本身是开拓了研究缺陷、位错和裂纹问题的新手段和方法。

Conservation laws or integrals in solids mechanics and its fracture theory play an indispensable role in describing material physical nature. The mechanical process of solids depends on twin sets of equation system, one is basic physical equations, and the other is equations satisfied by independent functions included in general solution. Challenge to the incomplete theory is that non-classical conservation laws or integrals corresponding to the functions included in general solution are lack. By applying new-found universal method, the functionals of three kinds of equations will be established: equations satisfied by the functions in general solution to field equations, equations satisfied by some physical quantities and physical equations without Lagrangian action integral. Mechanics never loses interest in variational principle. At the same time, the new generalized Noether’s identity will be applied to these three kinds of functionals for establishing non-classical conservation laws or integrals. The previously unknown conservativeness will be revealed widely in full and the relationship between classical and non-classical conservation laws or integrals will be found. Innovative application of individual non-classical conservation integral has shown the irreplaceable succeed in the fields of fracture, defects and dislocations as well as fluid mechanics and electric field. The project achievement itself will open up the new means and methods in order to research on defects, dislocations and cracks.