Finite Element Formulations for Beam-to-Solid Interaction -- From Embedded Fibers Towards Contact

TL;DR

This paper reviews recent advances in finite element methods for beam-to-solid contact problems, focusing on developing robust formulations for mixed-dimensional interactions from embedded fibers to contact scenarios.

Contribution

It provides an overview of current methods and progress towards a comprehensive 1D-3D beam-to-solid contact formulation in nonlinear mechanics.

Findings

Summarizes state-of-the-art beam-to-beam and solid-to-solid contact algorithms.

Highlights challenges in non-smooth contact conditions and discretization.

Outlines steps towards a general 1D-3D contact formulation.

Abstract

Contact and related phenomena, such as friction, wear or elastohydrodynamic lubrication, remain as one of the most challenging problem classes in nonlinear solid and structural mechanics. In the context of their computational treatment with finite element methods (FEM) or isogeometric analysis (IGA), the inherent non-smoothness of contact conditions, the design of robust discretization approaches as well as the implementation of efficient solution schemes seem to provide a never ending source of hard nuts to crack. This is particularly true for the case of beam-to-solid interaction with its mixed-dimensional 1D-3D contact models. Therefore, this contribution gives an overview of current steps being taken, starting from state-of-the-art beam-to-beam (1D) and solid-to-solid (3D) contact algorithms, towards a truly general 1D-3D beam-to-solid contact formulation.