An isogeometric finite element formulation for frictionless contact of Cosserat rods with unconstrained directors

TL;DR

This paper introduces an isogeometric finite element method for nonlinear Cosserat rods with frictionless contact, utilizing NURBS basis functions for accurate surface representation and efficient contact analysis.

Contribution

It develops a novel isogeometric formulation for Cosserat rods with unconstrained directors, incorporating a surface-to-surface contact algorithm and active set strategy.

Findings

Accurate contact pressure distribution matching brick element results

Reduced degrees-of-freedom compared to traditional methods

Validated efficiency and accuracy through numerical examples

Abstract

This paper presents an isogeometric finite element formulation for nonlinear beams with impenetrability constraints, based on the kinematics of Cosserat rods with unconstrained directors. The beam cross-sectional deformation is represented by director vectors of an arbitrary order. For the frictionless lateral beam-to-beam contact, a surface-to-surface contact algorithm combined with an active set strategy and a penalty method is employed. The lateral boundary surface of the beam is parameterized by its axis and cross-sectional boundary curves with NURBS basis functions having at least $C^2$-continuity, which yields a continuous surface metric and curvature for the closest point projection. Three-dimensional constitutive laws of hyperelastic materials are considered. Several numerical examples verify the accuracy and efficiency of the proposed beam contact formulation in comparison to brick element solutions. The lateral contact pressure distribution of the beam formulation is in excellent agreement with the contact pressure of the brick element formulation while requiring much less degrees-of-freedom.