Treating volumetric inequality constraint in a continuum media with a coupled X-FEM/level-set strategy

Some mechanical problems involve inequality kinematic constraints. This study deals with an original approach to handle those difficult problems. The inequality constraint implies variational inequality since the area where the constraint is active 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.

Research highlights
► We study the problem of a media subjected to a volumetric inequality constraint.
► The inequality constraint induces variational inequality.
► We replace the inequality constraint by an equality constraint over an unknown area.
► This area is found iteratively until it satisfies the configurational equilibrium.