Applications of an energy-momentum tensor in nonlinear elastodynamics : Pseudomomentum and eshelby stress in solitonic elastic systems

✍ Scribed by Gérard A.Maugin

• Publisher: Elsevier Science
• Year: 1992
• Tongue: English
• Weight: 960 KB
• Volume: 40
• Category: Article
• ISSN: 0022-5096
• DOI: 10.1016/0022-5096(92)90035-z

✦ Synopsis

IK CWTIN;UM mechanics the pseudomomentum is the covariant material momentum whose associated flux in the balance law is Eshelby's "energymomentum"

tensor. The unbalance of pseudomomentum sas previously shown to play a basic role in the formulation of configurational forces and path-independent integrals in the theory of elastic inhomogeneities and brittle fracture. Here, it is further shown to provide a fundamental conservation law for dispersive nonlinear elastic systems which exhibit soliton solutions. This is illustrated by both classical and grade-two clasticily with applications to the sine-Gordon, Boussinesq. sine-G&don~-d'Alcmbert and generalized Zakharov systems encountered in various bulk or surface wave-propagation problems. In these systems the nonconservation of global pseudomomcntum may be used for a perturbational approach to nearly integrable systems so as to study the influence of dissipation and external sources (e.g. defects).