A paper on ILS : Inequality level set : A new approach to handle inequality constraints

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

N. Bonfils, N. Chevaugeon, N. Moës

(accepted for publication in computer Methods in applied mechanics and engineering).

Abstract
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 intial trial one. Thanks to
numerical tools such as level-set and X-FEM we turn the constrained minimization problem into
a shape equilibrium problem.
1. Introduction