On the dynamics of cracks in three dimensions
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Submission date: 20. Feb. 2002
published in: Journal of the mechanics and physics of solids, 51 (2003) 1, p. 169-185
DOI number (of the published article): 10.1016/S0022-5096(02)00056-X
Keywords and phrases: dynamic fracture, variational principles, crack propagation law
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We introduce a three dimensional dynamic crack propagation law, which is derived from Hamilton's principle. The result is an extension of a previous one obtained, corresponding to the two dimensional case. As a matter of fact, in an orthogonal plane to the crack front, the geometric condition to be satisfied over the path is the same as in two dimensions. The third mode enters only through the energy release rate. The fact that the physics of the problem is locally two dimensional is a consequence of the virtual motions allowed in the set of possible crack configurations.