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Mechanical contact between solids is almost exclusively modeled in Lagrangianframeworks. While these frameworks have been developed extensively and appliedsuccessfully to numerous contact problems, they generally require complexalgorithms for contact detection and resolution. These challenges becomeparticularly important when contact appears between solids with evolvingboundaries, such as in systems where crystals grow in a constrained space. Inthis work, we introduce a fully Eulerian finite element framework for modelingcontact between elastic solids tailored towards problems including evolving andintricate surfaces. The proposed approach uses a phase-field method thatinvolves a diffuse representation of geometries on a fixed mesh, simplifyingthe modeling of evolving surfaces. Our methodology introduces a novelvolumetric contact constraint based on penalty body forces, efficientlyresolving the interpenetration of solids. We showcase the validity andversatility of our method through numerical examples, highlighting its abilityto accurately capture complex solid-solid interactions. The Eulerianphase-field formulation greatly simplifies contact detection and itsresolution. Furthermore, the framework can be straightforwardly coupled withother physical phenomena through the inclusion of multiple energy terms in theevolution of the phase-field. This enables multiphysics modeling, potentiallyproviding a valuable tool for a wide range of applications involving chemicallyor physically evolving deformable solids in contact, as they commonly occur indeterioration processes of porous media.

Eulerian framework for contact between solids represented as phase fields