Analytical Mechanics of Fracture and Fatigue
The aim of this paper is to describe the fundamental notions of fracture mechanics (the mechanics of cracked bodies) in the framework of analytical mechanics. The principle of virtual work for systems with unilateral constraints is used. A classification is proposed for states of the system “cracked body — loading” with respect to equilibrium and stability properties. Conditions of equilibrium and stability are stated in terms of generalized forces. The relationship between generalized forces and conventional concepts of fracture mechanics (energy release rate, stress intensity factors, path-independent integrals) is discussed. The fatigue crack growth is also presented in terms of analytical mechanics under the additional assumption that the resistant generalized forces depend on the level of microdamage accumulated near the crack-tips.
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