Nonlinear dynamics of uniformly loaded Elastica: Experimental and numerical evidence of motion around curled stable equilibrium configurations
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Publication:6145895
DOI10.1002/zamm.201800121OpenAlexW2940805330WikidataQ118359308 ScholiaQ118359308MaRDI QIDQ6145895
Emilio Turco, L. A. Igumnov, Djebar Baroudi, Antonio Battista, Ivan Giorgio
Publication date: 9 January 2024
Published in: ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1002/zamm.201800121
Thin bodies, structures (74Kxx) Dynamical problems in solid mechanics (74Hxx) Generalities, axiomatics, foundations of continuum mechanics of solids (74Axx)
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Cites Work
- Unnamed Item
- On the whole spectrum of Timoshenko beams. I: A theoretical revisitation
- Mechanical response of fabric sheets to three-dimensional bending, twisting, and stretching
- Simplified analysis of a generalized bias test for fabrics with two families of inextensible fibres
- Identification of multiple open and fatigue cracks in beam-like structures using wavelets on deflection signals
- Comment to ``Hypertractions and hyperstresses convey the same mechanical information`` by Prof. Podio-Guidugli and Prof. Vianello and some related papers on higher gradient theories
- Geometrically nonlinear higher-gradient elasticity with energetic boundaries
- The complete works of Gabrio Piola: Volume I. Commented English translation of the original Italian works, published between 1825 and 1856
- A unified computational framework for bulk and surface elasticity theory: a curvilinear-coordinate-based finite element methodology
- Computational aspects of growth-induced instabilities through eigenvalue analysis
- An energy-based method to determine material constants in nonlinear rheology with applications
- A review on 2D models for the description of pantographic fabrics
- Hencky-type discrete model for pantographic structures: numerical comparison with second gradient continuum models
- Macroscopic description of microscopically strongly inhomogenous systems: a mathematical basis for the synthesis of higher gradients metamaterials
- On the constitutive equations of viscoelastic micropolar plates and shells of differential type
- Identification of higher-order elastic constants for grain assemblies based upon granular micromechanics
- Designing a light fabric metamaterial being highly macroscopically tough under directional extension: first experimental evidence
- Variational theory for spatial rods
- A second gradient material resulting from the homogenization of an heterogeneous linear elastic medium
- The complete works of Gabrio Piola: Volume II. Commented English translation of the original Italian works
- Modelling size-dependent bending, buckling and vibrations of 2D triangular lattices by strain gradient elasticity models: applications to sandwich beams and auxetics
- Forms of the dissipation function for a class of viscoplastic models
- Bias extension test for pantographic sheets: numerical simulations based on second gradient shear energies
- Strain gradient and generalized continua obtained by homogenizing frame lattices
- Variational formulations and isogeometric analysis for the dynamics of anisotropic gradient-elastic Euler-Bernoulli and shear-deformable beams
- On the validity range of strain-gradient elasticity: a mixed static-dynamic identification procedure
- Form II of Mindlin's second strain gradient theory of elasticity with a simplification: for materials and structures from nano- to macro-scales
- Discrete is it enough? The revival of Piola-Hencky keynotes to analyze three-dimensional \textit{Elastica}
- A Ritz approach for the static analysis of planar pantographic structures modeled with nonlinear Euler-Bernoulli beams
- Free vibrations of finite-memory material beams
- How contact interactions may depend on the shape of Cauchy cuts in \(N\)th gradient continua: approach ``à la d'Alembert
- Dynamics of a flexible beam and a system of rigid rods, with fully inverse (one-sided) boundary conditions
- Locking-free variational formulations and isogeometric analysis for the Timoshenko beam models of strain gradient and classical elasticity
- Flexural-torsional flutter and buckling of braced foil beams under a follower force
- On the possible effective elasticity tensors of 2-dimensional and 3-dimensional printed materials
- Anisotropic and dispersive wave propagation within strain-gradient framework
- A two-dimensional gradient-elasticity theory for woven fabrics
- Extensional \textit{Elastica} in large deformation as \(\Gamma \)-limit of a discrete 1D mechanical system
- On a thermodynamic theory of rods with two temperature fields
- A revisitation of the paradox of discontinuous trajectory for a mass particle moving on a taut string
- On one-dimensional finite-strain beam theory: the plane problem
- Consistent tangent operator for an exact Kirchhoff rod model
- Cosserat-Type Rods
- Analytical continuum mechanics à la Hamilton–Piola least action principle for second gradient continua and capillary fluids
- Director-based beam finite elements relying on the geometrically exact beam theory formulated in skew coordinates
- Hencky Bar-Chain Model for Buckling and Vibration of Beams with Elastic End Restraints
- Kirchhoff’s problem for nonlinearly elastic rods
- A lumped parameter method in the nonlinear analysis of flexible multibody systems
- Un résultat d'homogénéisation pour un matériau élastique renforcé périodiquement par des fibres élastiques de très grande rigidité
- Truss Modular Beams with Deformation Energy Depending on Higher Displacement Gradients
- Homogenization of periodic graph-based elastic structures
- Convergence of Hencky-Type Discrete Beam Model to Euler Inextensible Elastica in Large Deformation: Rigorous Proof
- Continuum modelling of pantographic sheets for out-of-plane bifurcation and vibrational analysis
- Equilibria of a clamped Euler beam (Elastica) with distributed load: Large deformations
- A displacement-based approach to geometric instabilities of a film on a substrate
- Variational formulation of generalized interfaces for finite deformation elasticity
- Mechanical metamaterials: a state of the art
- A targeted review on large deformations of planar elastic beams: extensibility, distributed loads, buckling and post-buckling
- Variational formulations, model comparisons and numerical methods for Euler–Bernoulli micro- and nano-beam models
- A locking-free model for Reissner–Mindlin plates: Analysis and isogeometric implementation via NURBS and triangular NURPS
- Higher-gradient continua: The legacy of Piola, Mindlin, Sedov and Toupin and some future research perspectives
- On the use of the multiple scale method in solving ‘difficult’ bifurcation problems
- Nonlinear hysteretic damping effects on the post-critical behaviour of the visco-elastic Beck’s beam
- The postulations á la D’Alembert and á la Cauchy for higher gradient continuum theories are equivalent: a review of existing results
- Wave propagation in pantographic 2D lattices with internal discontinuities
- At the origins and in the vanguard of peridynamics, non-local and higher-gradient continuum mechanics: An underestimated and still topical contribution of Gabrio Piola
- A CRITICAL EXAMINATION OF THE REPRESENTATION OF MASSIVE AND ELASTIC BODIES BY SYSTEMS OF RIGD MASSES ELASTICALLY CONNECTED
- Cauchy tetrahedron argument applied to higher contact interactions
- An analytical assessment of finite element and isogeometric analyses of the whole spectrum of Timoshenko beams
- On the effect of shear stiffness on the plane deformation of linear second gradient pantographic sheets
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