A meshfree stabilized collocation method for strongly nonlinear Signorini-Coulomb contact with friction

The Signorini-Coulomb model is widely used in engineering for friction analysis due to its clear physics. Numerical methods that meet normal contact constraints and tangential friction laws are essential for accurately simulating this strongly nonlinear contact behavior. This work employs a stabilized collocation method using the reproducing kernel approximation to solve nonlinear contact problems with friction. The nonlinearity arises mainly from the evolution of the contact area under external load and the uncertainty in both contact state and contact traction. The stabilized collocation approach employs low-order Gaussian quadrature within subdomains to ensure accurate numerical integration, thereby enhancing the conditioning of the resulting discrete matrix. To address the challenges posed by evolving contact boundary conditions, contact information will be directly enforced within the stabilized collocation method framework. The penalty method is implied to enforce the Kuhn-Tucker complementarity conditions, which enables high-precision computation of the normal contact pressure and tangential friction traction governed by Coulomb’s law. To enhance contact accuracy and numerical stability, three compact support construction strategies, including the uniform scheme, four quadrants method and natural neighbor method, are introduced and compared. The aim is to identify a scheme that balances the capture of local nonlinear frictional contact behavior. Numerical examples confirm the flexibility of stabilized collocation method in integration subdomain construction and frictional coefficient, which supports local refinement and reliable detection of contact states. When combined with the natural neighbor method, stabilized collocation method exhibits strong potential for contact analysis applications.