A Lagrangian–Eulerian formulation for reeling analysis of history-dependent multilayered beams

• A novel beam formulation utilizing Lagrangian–Eulerian kinematics is presented.
• The nearly space-fixed mesh improves the performance of the contact algorithms.
• The same accuracy as offered by the conventional Lagrangian method is achieved.
• Use of non-uniform meshes in elasto-plastic reeling simulations becomes possible.
• The material transport tangent stiffness is crucial for the convergence properties.

This paper presents a novel Lagrangian–Eulerian finite element formulation for reeling analysis of multilayered beams with gross interlayer slippage. In contrast to the conventional Lagrangian approach, the mesh becomes practically fixed in space, which yields significant benefits for the performance of the contact algorithms and the overall computational efficiency. The needed Lagrangian–Eulerian kinematic relations are derived, special attention is given to the convective transport term for the constitutive variables and an implicit update scheme for the elasto-plastic bending model is formulated. The proposed formulation is shown to predict responses with the same accuracy as offered by the conventional Lagrangian formulation.