Variational principles of nonlinear fracture mechanics

SummaryA variational principle of total energy is formulated for finite strain statics of a hyperelastic body whose initial configuration contains a gap. From this principle statical equations and boundary conditions for the gapped body are derived. The equilibrium condition at a gap tip is associated with the well-knownJ-integrals. By including the reaction of inertia and the flux of kinetic energy the principle of total energy is transformed to the variational inequality of evolution for dynamics of a hyperelastic body with a propagating crack. A closed system of dynamical equations, boundary conditions and additional conditions on the unknown contact crack surfaces and crack tip is obtained. As example the antiplane shear of an infinite gapped body is considered.

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