The Application of Noether Theorem in the Teaching of Fracture Mechanics
J-,L-and M-integrals are the three conservational integrals in fracture me-chanics,which are of great significance for understanding the mechanical behavior of crack tips and achieving singular stress fields at crack tips.The Noether theorem is an impor-tant theorem in theoretical physics.It establishes the intrinsic connection between symme-try and conservation laws.Starting from the Noether theorem,this article constructs Lie groups and infinitesimal transformation corresponding to rigid body translation,rotation,and scale transformations,and derives the mathematic formulations of J-,L-and M-in-tegrals.Through the research in this article,we can attempt to introduce the knowledge of the Noether theorem into fracture mechanics of graduate courses,enabling students to understand the relationship between symmetry and conservation laws,and to recognize the importance to solid mechanics.
Noether theoremfracture mechanicsconservation integralLie group
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