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Weak formulation of elastodynamics in domains with growing cracks

Show simple item record Tasso, Emanuele 2018-11-22T10:50:29Z 2018-11-22T10:50:29Z 2018-11
dc.description.abstract In this paper we formulate and study the system of elastodynamics on domains with arbitrary growing cracks. This includes homogeneous Neumann conditions on the crack sets and mixed general Dirichlet-Neumann conditions on the boundary. The only assumptions on the crack sets are to be (n − 1)-rectifiable with finite surface measure, and increasing in the sense of set inclusions. In particular they might be dense, hence the weak formulation must fall outside the usual context of Sobolev spaces and Korn's inequality. We prove existence of a solution both for the damped and undamped systems, while in the damped case we are also able to prove uniqueness and an energy balance. en_US
dc.language.iso en en_US
dc.publisher SISSA en_US
dc.relation.ispartofseries SISSA;51/2018/MATE
dc.subject second order linear hyperbolic system en_US
dc.subject dynamic fracture mechanics en_US
dc.subject crack-ing domains en_US
dc.subject boundary conditions en_US
dc.subject bounded deformation en_US
dc.title Weak formulation of elastodynamics in domains with growing cracks en_US
dc.type Preprint en_US
dc.miur.area 1 en_US
dc.contributor.area Mathematics en_US
dc.relation.firstpage 1 en_US
dc.relation.lastpage 22 en_US

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