[hal-01077161] Bifurcations in Piecewise-Smooth Steady-State Problems

The paper presents a local study of bifurcations in a class of piecewise-smooth steady-state problems for which the regions of smooth behaviour permit analytical expressions A system of piecewise-linear equations capturing the essential features of the branching scenarios around points of non-smoothness is derived under the assumptions that i the points lie in the intersection of the boundaries of the regions where the gradients of the respective smooth selections have the full rank ii there is no solution branch whose tangential direction is tangent to the boundary of any of the regions The simplest cases of this system are studied in detail and the most probable branching scenarios are described A criterion for detecting bifurcation points is proposed and a procedure for its realisation in the course of numerical continuation of solution curves of large problems is designed Application of the general frame to discretised plane contact problems with Coulomb friction is explained Simple as well as more realistic model examples of bifurcations are shown



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