Contact Mechanics
This tutorial collection demonstrates frictionless slave–master contact in LowLevelFEM using the ContactGap weak-form operator.
The examples cover two-dimensional Hertz-type contact with both penalty and Lagrange-multiplier formulations, as well as a three-dimensional penalty-contact problem. Contact detection is based on closest-point projection in the current configuration, while the contact contribution is assembled directly from the weak form at slave-side Gauss points.
The penalty examples show how the contact tangent can be written compactly as ∫(G ⋅ cn ⋅ G), with G = ContactGap(C), and solved incrementally using prescribed displacement steps. The Lagrange-multiplier example demonstrates the corresponding mixed formulation and the use of a reduced-order multiplier field for stable contact-pressure approximation with higher-order displacement elements.
Examples
2D Hertz contact — penalty method
2D Hertz contact — Lagrange multiplier method