Log In Sign Up

Consistent coupling of positions and rotations for embedding 1D Cosserat beams into 3D solid volumes

by   Ivo Steinbrecher, et al.

This article proposes a mortar type finite element formulation for consistently embedding curved, slender beams, i.e. 1D Cosserat continua, into 3D solid volumes. A consistent 1D-3D coupling scheme for this problem type is proposed, which enforces both positional and rotational constraints. Since Boltzmann continua exhibit no inherent rotational degrees of freedom, suitable definitions of orthonormal triads are investigated that are representative for the orientation of material directions in the 3D solid. The rotation tensor defined by the polar decomposition of the deformation gradient is demonstrated to represent these material directions in a L2-optimal manner. Subsequently, objective rotational coupling constraints between beam and solid are formulated and enforced in a variationally consistent framework. Eventually, finite element discretization of all primary fields results in an embedded mortar formulation for rotational and translational constraint enforcement. Based on carefully chosen numerical test cases, the proposed scheme is demonstrated to exhibit a consistent spatial convergence behavior and to offer the up-scaling potential for studying real-life engineering applications such as fiber-reinforced composite materials.


page 5

page 7

page 9

page 10

page 11

page 14

page 15

page 30


A consistent mixed-dimensional coupling approach for 1D Cosserat beams and 2D solid surfaces

The present article proposes a novel computational method for coupling 1...

A mortar-type finite element approach for embedding 1D beams into 3D solid volumes

In this work we present a novel computational method for embedding arbit...

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

Contact and related phenomena, such as friction, wear or elastohydrodyna...

Primal and mixed finite element formulations for the relaxed micromorphic model

The classical Cauchy continuum theory is suitable to model highly homoge...

Solid shell prism elements based on hierarchical, heterogeneous, and anisotropic shape functions

The formulation of a new prism finite element is presented for the nonli...

The Schwarz alternating method for the seamless coupling of nonlinear reduced order models and full order models

Projection-based model order reduction allows for the parsimonious repre...