Event-Driven Asymptotic Continuation and Regular Branch Decomposition for Signorini Contact

Hamdaoui, Mohamed

doi:10.22055/jacm.2026.49691.6165

Event-Driven Asymptotic Continuation and Regular Branch Decomposition for Signorini Contact

Articles in Press

Document Type : Research Paper

Author

Mohamed Hamdaoui

Université de Lorraine, LEM3, UMR CNRS 7239, 7 rue Félix Savart, 57070 Metz, France

10.22055/jacm.2026.49691.6165

Abstract

Each opening or closure of a unilateral contact changes the smooth equations being followed. The

proposed procedure therefore continues one fixed-contact stratum with the asymptotic numerical method,

corrects the predicted transition to a single nonlinear event state, and then examines the admissible post-event

supports. The local proof uses the standard implicit-function theorem. The contribution lies instead

in organizing the regular, strictly complementary outgoing half-branches by feasible support rays at the

corrected event, while sharing the large tangent calculation and keeping branch existence separate from the

later choice of traversal direction. In the symmetric seven-node truss, a simultaneous two-contact opening

produces three forward children. A sparse finite-element strip is used to check that the same event treatment

carries over to assembled equations. The results reported here concern quasistatic, frictionless contact with

fixed normals and regular event groups of one or two contacts.

Keywords

Signorini contact

asymptotic numerical method

nonlinear continuation

complementarity

branch switching

Subjects