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By Christian Dascalu, Gérard A. Maugin, Claude Stolz, Editors

This quantity provides fresh advancements within the concept of defects and the mechanics of fabric forces. lots of the contributions have been provided on the overseas Symposium on illness and fabric Forces (ISDMM2007), held in Aussois, France, March 25-29, 2007. The mechanics of fabric forces, originated within the works of Eshelby, offer a rational framework for the outline of riding forces on evolving inhomogeneities and structural alterations in continua. the final eshelbian mechanics formula comes up with a unifying remedy of alternative phenomena like fracture and harm evolution, part transitions, plasticity and dislocation movement, and so on. The articles situation either theoretical and computational features of the cloth mechanics of defects. one of the addressed themes are fracture and harm, electromagnetoelasticity, plasticity, disbursed dislocations, thermodynamics, poroelasticity, generalized continua, structural optimization, conservation legislation and symmetries, multiscale techniques, and numerical resolution concepts.

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We can state that (38) must hold on every stage of the propagation process, thus providing the second scalar condition to complete the free boundary problem. On the other hand, it has to be satisfied by other models imposing global minimization of the total energy (see for instance Buliga 1999; Francfort and Marigo 1998). E = −πc12 t − 2π λ c1 c2 t 2 + O(t 3 ). According to (4), in order to check the stability we must take into account the dissipation that is required to open this path. For this purpose we need the evolution of the length of the extended curve.

6 Jk := U n k − σi j u i,k n j ds, (10) where |n| = 1 is normal to C (a Jordan curve surrounding the crack tip), U is the elastic energy density, σi j are the components of the stress tensor and u i is the displacement field. In pure Mode III, (10) reduces to the expression: Jk = U n k − σ3 j u 3,k n j ds ( j, k = 1, 2). C Thus, J1 gives the energy release rate for a straight extension of the preexisting crack. Nevertheless, (9) tells us nothing for other virtual directions of propagation. It should be pointed out that in Rice’s article, the quantity J is not considered as a vectorial force.

On the other hand, if we add a symmetric contribution to the initial field with c2 = 1, we obtain the pattern for the opening displacement shown on the right side of Fig. 6. Notice that for α = −αmax the opening is the lower one. On the other hand, the direction given in (28) is optimal among the three for maximum opening. 1 and c1 (l) = c1 + 2b0 (l)c2 for the expanded crack field (cf. (23)). 4 Arbitrary extensions as virtual paths (29) The contribution of the extra term introduces a singularity in crack curvature at that point.

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