Variational Formulation and Upper Bounds for Degenerate Scales in Plane Elasticity

Alain Corfdir (1) , Guy Bonnet (2)

1 navier umr 8205 - Laboratoire Navier
2 MSME - Laboratoire de Modélisation et Simulation Multi Echelle

Degenerate scales appear when certain plane boundary value problems solved using Boundary Integral Equations do not have a unique solution. The main contribution of this paper is to prove four inequalities that constrain the degenerate scales for plane elasticity. These results are based on a new variational formulation. It is shown that the degenerate scales depend only on Poisson’s ratio. The bounds on the degenerate scales for plane elasticity in a given boundary are obtained mainly from the degenerate scales obtained from the Laplace equation for the same boundary, which are well documented.

Domaines: Sciences de l'ingénieur [physics]; Génie civil; Sciences de l'ingénieur [physics]; Mécanique [physics.med-ph]; Mécanique des solides [physics.class-ph]

Alain Corfdir, Guy Bonnet. Variational Formulation and Upper Bounds for Degenerate Scales in Plane Elasticity. Journal of Elasticity, 2014, 118 (2), pp.207 - 221. ⟨10.1007/s10659-014-9494-1⟩. ⟨hal-01157344⟩