The role of ellipticity and normality assumptions in formulating live-boundary conditions in elasticity
Paolo Podio–Guidugli, G. Vergara-Caffarelli, Epifanio G. Virga · Quarterly of Applied Mathematics · 1987
It is shown that those interactions of an elastic body B with an elastic environment E manifested by local surfacial loadings should be modelled by boundary operators featuring a live system of surfacial forces, i.e., a vector field s, defined over the boundary partial derivative of B and representing the surfacial force per unit area exerted by E over B, which depends functionally in a non-trivial way on the deformation u of B. In addition to the analytical difficulties to be expected, when normality does not hold the mechanical interpretation of boundary conditions fails to be unique. That this is indeed the case is demonstrated by producing an explicit example in linearized elastostatics of a boundary operator condition of traction or as a dead-boundary condition of frictionless contact. Keywords: ellipticity, normality, live-boundary condition of traction.