A discrete, geometrically exact method for simulating nonlinear, elastic and inelastic beams

DOI10.1016/j.cma.2019.112741zbMath1442.74103OpenAlexW2983310758WikidataQ107453263 ScholiaQ107453263MaRDI QIDQ2176927

Claire Lestringant, Dennis M. Kochmann, Basile Audoly

Publication date: 6 May 2020

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

Full work available at URL: https://www.repository.cam.ac.uk/handle/1810/303627

zbMATH Keywords

finite element methodvariational calculusconstitutive modelnonlinear beam theory

Mathematics Subject Classification ID

Rods (beams, columns, shafts, arches, rings, etc.) (74K10) Applications to the sciences (65Z05)

Related Items (7)

A geometrically exact discrete elastic rod model based on improved discrete curvature ⋮ Mixed isogeometric collocation for geometrically exact 3D beams with elasto-visco-plastic material behavior and softening effects ⋮ A novel four-field mixed FE approximation for Kirchhoff rods using Cartan's moving frames ⋮ An efficient displacement-based isogeometric formulation for geometrically exact viscoelastic beams ⋮ On the geometrically exact formulations of finite deformable isogeometric beams ⋮ Natural frequencies of pre-buckled rods and gridshells ⋮ Multiscale modelling and material design of woven textiles using Gaussian processes

Uses Software

• AUTO
• AUTO-07P

Cites Work

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• A discrete geometric approach for simulating the dynamics of thin viscous threads
• Multi-body dynamics simulation of geometrically exact Cosserat rods
• Geometrically exact beam finite element formulated on the special Euclidean group \(SE(3)\)
• A finite strain beam formulation. The three-dimensional dynamic problem. I
• A three-dimensional finite-strain rod model. II. Computational aspects
• On finite element implementation of geometrically nonlinear Reissner's beam theory: Three-dimensional curved beam elements
• The variational formulation of viscoplastic constitutive updates
• A consistent co-rotational formulation for nonlinear, three-dimensional, beam-elements
• Director-based beam finite elements relying on the geometrically exact beam theory formulated in skew coordinates
• A discrete mechanics approach to the Cosserat rod theory-Part 1: static equilibria
• A beam finite element non-linear theory with finite rotations
• Decomposition of the linking number of a closed ribbon: A problem from molecular biology
• Objectivity of strain measures in the geometrically exact three-dimensional beam theory and its finite-element implementation
• Frame-indifferent beam finite elements based upon the geometrically exact beam theory
• FORMULAE FOR THE CALCULATION AND ESTIMATION OF WRITHE
• The Writhing Number of a Space Curve
• Theory of Stress-Strain Relations in Anisotropic Viscoelasticity and Relaxation Phenomena

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