Scaled Korn-Poincaré inequality in BD and a model of elastic-plastic cantilever. (English) Zbl 0978.74045
Summary: The optimal asymptotic behaviour of the Korn-Poincaré inequality constant due to anisotropic shrinking of an open set is proved in the space of vector fields with bounded deformation (BD). We also describe an elastic-perfectly plastic cantilever as a variational limit of elastic micro-fractured two-dimensional body.
MSC:
74K10 | Rods (beams, columns, shafts, arches, rings, etc.) |
74G10 | Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of equilibrium problems in solid mechanics |
35Q72 | Other PDE from mechanics (MSC2000) |