The computational modeling of many engineering problems using the Finite Element method involves the modeling of two or more bodies that meet through an interface. The interface can be physical, as in multi-physics and contact problems, or purely numerical, as in the coupling of non-conforming meshes. The most critical part of the modeling process is to ensure geometric compatibility and a complete transfer of surface tractions between the different components at the connecting interfaces. Popular contact modeling techniques rely on geometric projections to detect and resolve overlapping or mass interpenetration between two or more contacting bodies. Such approaches have been shown to have two major drawbacks: they are not suitable for contact at highly nonlinear surfaces and sharp corners where smooth normal projections are not feasible, and they fail to guarantee a complete and accurate transfer of pressure across the interface. This dissertation presents a novel formulation for the modeling of contact problems that possesses the ability to resolve complicated contact scenarios effectively, while being simpler to implement and more widely applicable than currently available methods. We show that the formulation boils down to a node-to-surface gap function that works effectively for non-smooth contact. The numerical implementation using the midpoint rule shows the need to guarantee the conservation of the total energy during impact, for which a Lagrange multiplier method is used. We propose a local enrichment of the interface and a simple stabilization procedure based on the discontinuous Galerkin method to guarantee an accurate transfer of the pressure field. The result is a robust interface formulation for contact problems and the coupling of non-conforming meshes.
Weighted error estimates for transient transport problems discretized using continuous finite elements with interior penalty stabilization on the gradient jumps
Data assimilation in 2D incompressible Navier-Stokes equations, using a stabilized explicit $O(Δt)^2$ leapfrog finite difference scheme run backward in time
A Mortar Finite Element Formulation for Large Deformation Lubricated Contact Problems with Smooth Transition Between Mixed, Elasto-Hydrodynamic and Full Hydrodynamic Lubrication
