Geometry of constraint manifolds and wave propagation in internally constrained elastic bodies

The implications of the non-Euclidean structure of constraint manifolds on differentiation of the stress in internally constrained elastic bodies are examined, and the equations governing propagation of acceleration waves in such bodies are deduced differentiating the reactive stress consistently wi...

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Bibliographic Details
Published inMeccanica (Milan) Vol. 46; no. 4; pp. 651 - 669
Main Author Lembo, Marzio
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 01.08.2011
Subjects
Amplitudes
Automotive Engineering
Civil Engineering
Classical Mechanics
Constraints
Differentiation
Elastic bodies
Manifolds
Mathematical analysis
Mechanical Engineering
Original Article
Physics
Physics and Astronomy
Stresses
Wave propagation
Riemannian manifolds
Wave propagation
Internal constraints
Nonlinear elasticity
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Summary:The implications of the non-Euclidean structure of constraint manifolds on differentiation of the stress in internally constrained elastic bodies are examined, and the equations governing propagation of acceleration waves in such bodies are deduced differentiating the reactive stress consistently with the assumption that it does no work in any admissible motion. This yields a treatment of the subject in which the presence of internal constraints imposes restrictions on the set of possible amplitudes of waves but the condition for local existence of waves, that amplitudes must satisfy, is of the same type as that for bodies free from internal constraints, in the sense that it depends on the properties of the response map of the material and is independent of reactive stress.
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ISSN:0025-6455
1572-9648
DOI:10.1007/s11012-010-9328-6