Weak formulation of elastodynamics in domains with growing cracks

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dc.contributor.areaMathematicsen_US
dc.contributor.authorTasso, Emanuele
dc.date.accessioned2018-11-22T10:50:29Z
dc.date.available2018-11-22T10:50:29Z
dc.date.issued2018-11
dc.description.abstractIn 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.identifier.urihttps://openscience.sissa.it/handle/1963/35328
dc.language.isoenen_US
dc.miur.area1en_US
dc.publisherSISSAen_US
dc.relation.firstpage1en_US
dc.relation.ispartofseriesSISSA;51/2018/MATE
dc.relation.lastpage22en_US
dc.subjectsecond order linear hyperbolic systemen_US
dc.subjectdynamic fracture mechanicsen_US
dc.subjectcrack-ing domainsen_US
dc.subjectboundary conditionsen_US
dc.subjectbounded deformationen_US
dc.titleWeak formulation of elastodynamics in domains with growing cracksen_US
dc.typePreprinten_US
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