FuzzyContact: A generic contact mechanics formulation via a modified penalty method governed by sigmoidal traction law

Conventional contact algorithms struggle to efficiently model stick-slip friction, often relying on complex conditional logic that is sensitive to discretization. This paper introduces FuzzyContact, a generic contact mechanics formulation that implicitly captures this key tribological phenomenon within a unified, continuous framework. The method employs a sigmoidal traction law that defines contact forces based on inter-nodal proximity, eliminating the need for predefined master-slave surfaces. This proximity-based approach ensures a smooth, differentiable transition between stick and slip states, enhancing numerical robustness. The formulation's accuracy and versatility were validated through a series of benchmarks, culminating in a direct comparison with experimental data. Simulated elastic strains in a compressed steel cylinder showed excellent agreement with measurements from in-situ neutron diffraction. The proposed framework provides a robust and scalable solution for generic contact simulations, paving the way for advanced modelling of complex tribological systems involving friction and wear. • A novel proximity-based contact formulation governed by a sigmoidal traction law is proposed. • The formulation implicitly captures stick-slip friction within a unified, continuous penalty framework. • The method eliminates the need for predefined master-slave surfaces and contact pairs. • Simulated elastic strains show excellent agreement with in-situ neutron diffraction data. • The formulation demonstrates robustness and systematic convergence with mesh refinement.