Treating volumetric inequality constraint in a continuum media with a coupled X-FEM/Level-Set strategy

Nicolas Bonfils (1) , Nicolas Chevaugeon (1) , Nicolas Moes (1)

1 GeM - Institut de Recherche en Génie Civil et Mécanique

Some mechanical problems involve inequality kinematic constraint. This study deals with an original approach to handle those difficult problems. The main issue is the treatment of the variational inequalities due to the fact that the constrained area is a priori unknown. The method, introduced here, is to find the exact constrained area iteratively starting from an initial trial one. Thanks to numerical tools such as level-set and X-FEM we turn the constrained minimization problem into a shape equilibrium problem.

Mots clés: inequality constraint; X-FEM; Configurational equilibrium; Variational inequality; ILS; level set

Domaines: Mécanique des solides [physics.class-ph]; Mécanique des solides [physics.class-ph]; Mécanique des structures [physics.class-ph]; Mécanique des structures [physics.class-ph]

Nicolas Bonfils, Nicolas Chevaugeon, Nicolas Moes. Treating volumetric inequality constraint in a continuum media with a coupled X-FEM/Level-Set strategy. Computer Methods in Applied Mechanics and Engineering, 2012, 205, pp.16-28. ⟨10.1016/j.cma.2011.02.012⟩. ⟨hal-00569557⟩