Contact in a multi-material Eulerian finite element formulation

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Using a signed distance function for the simulation of metal forming processes: Formulation of the contact condition and mesh adaptation. From a Lagrangian approach to an Eulerian approach (2009, background): “Developing an Eulerian approach for solving contact problems, remains a numerical challenge, even if a substantial progress has been made recently (see for example [14] and [15]).”
Slope stability analysis based on the Coupled Eulerian-Lagrangian finite element method (2018, methodology): “(11) is decomposed into two equations and solved in sequential steps (Benson and Okazawa 2004): ∂ψ ∂t ¼ S ð12Þ ∂ψ ∂t þ ∇ ⋅Ψ ψ; v; x; tð Þ ¼ 0 ð13Þ During each time increment, Eq.”
Explicit FE-modelling of fluid–structure interaction in hull–water impacts (2006, unknown): “The contact works as a numerical spring-damper sys-tem, where the resisting forces are proportional to the penetration depth, penetration velocity and a user deﬁned contact stiffness, κ D , and contact damping, d [3].”