Ensuring Stability in Mechanical Contact and Friction Using Linear Complementarity and Matrix Classes
DOI:
https://doi.org/10.71426/jasm.v1.i1.pp19-23Keywords:
Linear complementarity problem, Contact mechanics, Friction modeling, Matrix-class theory, Game-theoretic stability, Structural equilibriumAbstract
Mechanical systems involving unilateral contact and Coulomb friction exhibit nonsmooth, switching behavior driven by inequality constraints. These features challenge classical linear models and may result in nonphysical penetration, negative contact forces, or solver divergence. The linear complementarity problem (LCP) provides a rigorous representation of contact states through mutually exclusive force–gap relationships. This paper studies stability and solvability guarantees for mechanical contact systems through matrix classes associated with LCPs, including semimonotone matrices, Q- and R0-matrices, and Z-matrices, together with a game-theoretic interpretation of stability. The analysis explains when equilibrium exists and when uniqueness and robustness can be expected. A detailed worked example demonstrates the application of these theoretical tools in evaluating contact stability prior to simulation. The results offer practical guidance for computational mechanics, structural modeling, and contact simulation frameworks.
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