A discrete formulation of Kirchhoff rods in large-motion dynamics

Giorgio, Ivan

doi:10.1177/1081286519900902

Cited by 64 publications

(28 citation statements)

References 80 publications

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“…There are different possibilities found in the literature to overcome these difficulties. On the one hand minimal formulated spatial Euler-Bernoulli beam models [9][10][11][12] or different constrained Euler-Bernoulli beam theories that explicitly ensure the vanishing shear deformations [61,62] can be used. On the other hand, so-called intrinsically locking-free Timoshenko beam formulations [38,63] have to be extended from the planar case to the spatial one.…”

Section: Discussionmentioning

confidence: 99%

Finite element formulations for constrained spatial nonlinear beam theories

Harsch

Capobianco

Eugster

2021

Mathematics and Mechanics of Solids

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A new director-based finite element formulation for geometrically exact beams is proposed by weak enforcement of the orthonormality constraints of the directors. In addition to an improved numerical performance, this formulation enables the development of two more beam theories by adding further constraints. Thus, the paper presents a complete intrinsic spatial nonlinear theory of three kinematically different beams which can undergo large displacements and which can have precurved reference configurations. Moreover, the hyperelastic constitutive laws allow for elastic finite strain material behavior of the beams. Furthermore, the numerical discretization using concepts of isogeometric analysis is highlighted in all clarity. Finally, all presented models are numerically validated using exclusive analytical solutions, existing finite element formulations, and a complex dynamical real-world example.

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Section: Discussionmentioning

confidence: 99%

Finite element formulations for constrained spatial nonlinear beam theories

Harsch

Capobianco

Eugster

2021

Mathematics and Mechanics of Solids

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“…In the analysis of large deformations, the mesh of elements undergoes excessive distortion, which results in the necessity to sometimes undertake multiple adaptive remeshing of the domain. These problems can be overcome by meshless methods [145,146].…”

Section: Meshless Methodsmentioning

confidence: 99%

Multiphysics Modeling and Numerical Simulation in Computer-Aided Manufacturing Processes

Trzepieciński

Dell’Isola

Lemu

2021

Metals

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The concept of Industry 4.0 is defined as a common term for technology and the concept of new digital tools to optimize the manufacturing process. Within this framework of modular smart factories, cyber-physical systems monitor physical processes creating a virtual copy of the physical world and making decentralized decisions. This article presents a review of the literature on virtual methods of computer-aided manufacturing processes. Numerical modeling is used to predict stress and temperature distribution, springback, material flow, and prediction of phase transformations, as well as for determining forming forces and the locations of potential wrinkling and cracking. The scope of the review has been limited to the last ten years, with an emphasis on the current state of knowledge. Intelligent production driven by the concept of Industry 4.0 and the demand for high-quality equipment in the aerospace and automotive industries forces the development of manufacturing techniques to progress towards intelligent manufacturing and ecological production. Multi-scale approaches that tend to move from macro- to micro- parameters become very important in numerical optimization programs. The software requirements for optimizing a fully coupled thermo-mechanical microstructure then increase rapidly. The highly advanced simulation programs based on our knowledge of physical and mechanical phenomena occurring in non-homogeneous materials allow a significant acceleration of the introduction of new products and the optimization of existing processes.

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“…Pantographic fabrics have been proposed recently as a metamaterial which is well described at the macroscopic scale by second gradient continuum theories [34]. Fibers can be modeled as beams, possibly subjected to large deformations [11,54]. Pioneering papers [20,47,62,69,94] recognized the importance of understanding microscale mechanics in order to deduce macroscale behavior of continuum models.…”

Section: Literature Reviewmentioning

confidence: 99%

Research perspective on multiphysics and multiscale materials: a paradigmatic case

Ciallella

2020

Continuum Mech. Thermodyn.

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Pantographic fabrics are presented as a paradigmatic example to discuss the research perspective on multiphysics and multiscale materials. Reduced-order modeling, obtained by introducing higher-gradient or microstructured continua, shows much smaller computational needs than those required by full-scale 3D modeling calculations and by equivalent discrete spring systems. Researches already available in the literature compare theoretical predictions with results obtained in real experiments, analyzing both in-plane and outof-plane deformations possibly induced by local buckling phenomena. The goal is to achieve three major objectives: (1) formulate coarse-scale nonlinear higher-gradient continuum models describing a more general class of pantographic metamaterials, based on finer-scale descriptions, through homogenization techniques;(2) implement finite element analyses with shape functions possessing higher regularity or employing mixed formulations to perform simulations with the above-formulated models; and (3) validate and verify the derived models through the acquisition and analysis of experimental data. These goals would likely push toward the improvement of 3D printing protocols to enhance the quality of the pantographic prototypes and DIC as experiments measurement technique. It can be also conjectured that many macroscopic deformation energies can be synthesized by using as elementary elements, inside periodicity cells, some pantographic modules.

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A discrete formulation of Kirchhoff rods in large-motion dynamics

Cited by 64 publications

References 80 publications

Finite element formulations for constrained spatial nonlinear beam theories

Finite element formulations for constrained spatial nonlinear beam theories

Multiphysics Modeling and Numerical Simulation in Computer-Aided Manufacturing Processes

Research perspective on multiphysics and multiscale materials: a paradigmatic case

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