Continuum modelling of pantographic sheets for out-of-plane bifurcation and vibrational analysis
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Publication:4646903
DOI10.1098/rspa.2017.0636zbMath1404.74064OpenAlexW2768120143WikidataQ118359325 ScholiaQ118359325MaRDI QIDQ4646903
Nicola Luigi Rizzi, Ivan Giorgio, Emilio Turco
Publication date: 28 December 2018
Published in: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1098/rspa.2017.0636
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Uses Software
Cites Work
- Unnamed Item
- 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
- Solitons in elastic solids (1938--2010)
- Mechanics of generalized continua
- Geometrically nonlinear higher-gradient elasticity with energetic boundaries
- An implicit \(G^1\) multi patch B-spline interpolation for Kirchhoff-Love space rod
- The complete works of Gabrio Piola: Volume I. Commented English translation of the original Italian works, published between 1825 and 1856
- Hencky-type discrete model for pantographic structures: numerical comparison with second gradient continuum models
- Numerical identification procedure between a micro-Cauchy model and a macro-second gradient model for planar pantographic structures
- On natural strain measures of the non linear micropolar continuum
- Isogeometric analysis of 2D gradient elasticity
- Nonlinear microstrain theories
- Macroscopic description of microscopically strongly inhomogenous systems: a mathematical basis for the synthesis of higher gradients metamaterials
- Second-gradient continua as homogenized limit of pantographic microstructured plates: a rigorous proof
- Designing a light fabric metamaterial being highly macroscopically tough under directional extension: first experimental evidence
- Gedanken experiments for the determination of two-dimensional linear second gradient elasticity coefficients
- Plane deformations of nets with bending stiffness
- Variational theory for spatial rods
- A second gradient material resulting from the homogenization of an heterogeneous linear elastic medium
- Problems of identification of mechanical characteristics of viscoelastic composites
- Equilibrium of elastic lattice shells
- Wave dynamics and composite mechanics for microstructured materials and metamaterials
- Bias extension test for pantographic sheets: numerical simulations based on second gradient shear energies
- A two-dimensional gradient-elasticity theory for woven fabrics
- An efficient blended mixed B-spline formulation for removing membrane locking in plane curved Kirchhoff rods
- Finite gradient elasticity and plasticity: a constitutive thermodynamical framework
- A mixture model with evolving mass densities for describing synthesis and resorption phenomena in bones reconstructed with bio-resorbable materials
- Hencky Bar-Chain Model for Buckling and Vibration of Beams with Elastic End Restraints
- Equilibrium of elastic nets
- Remodelling in statistically oriented fibre-reinforced materials and biological tissues
- Truss Modular Beams with Deformation Energy Depending on Higher Displacement Gradients
- Identification of Two-Dimensional Pantographic Structures with a Linear D4 Orthotropic Second Gradient Elastic Model Accounting for External Bulk Double Forces
- Dynamic fiber reorientation in a fiber-reinforced hyperelastic material
- The Method of Virtual Power in Continuum Mechanics. Part 2: Microstructure
- 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
- Exegesis of Sect. II and III.A from “Fundamentals of the Mechanics of Continua” by E. Hellinger
- Exegesis of the Introduction and Sect. I from “Fundamentals of the Mechanics of Continua”** by E. Hellinger