Hencky-type discrete model for pantographic structures: numerical comparison with second gradient continuum models

E Turco, F Dell'Isola, A Cazzani, NL Rizzi - Zeitschrift für angewandte …, 2016 - Springer
Hencky (Über die angenäherte Lösung von Stabilitätsproblemen im Raum mittels der
elastischen Gelenkkette. Ph. D. thesis, Engelmann, 1921) proposed a discrete model for …

[HTML][HTML] Linear pantographic sheets: existence and uniqueness of weak solutions

VA Eremeyev, F Dell'Isola, C Boutin, D Steigmann - Journal of Elasticity, 2018 - Springer
The well-posedness of the boundary value problems for second gradient elasticity has been
studied under the assumption of strong ellipticity of the dependence on the second …

Pantographic beam: a complete second gradient 1D-continuum in plane

E Barchiesi, SR Eugster, L Placidi… - Zeitschrift für angewandte …, 2019 - Springer
There is a class of planar 1D-continua which can be described exclusively by their
placement functions which in turn are curves in a two-dimensional space. In contrast to the …

Second-gradient continua as homogenized limit of pantographic microstructured plates: a rigorous proof

JJ Alibert, A Della Corte - Zeitschrift für angewandte Mathematik und …, 2015 - Springer
Since the works by Gabrio Piola, it has been debated the relevance of higher-gradient
continuum models in mechanics. Some authors even questioned the logical consistency of …

Numerical identification procedure between a micro-Cauchy model and a macro-second gradient model for planar pantographic structures

I Giorgio - Zeitschrift für angewandte Mathematik und Physik, 2016 - Springer
In order to design the microstructure of metamaterials showing high toughness in extension
(property to be shared with muscles), it has been recently proposed (Dell'Isola et al. in Z …

Are higher-gradient models also capable of predicting mechanical behavior in the case of wide-knit pantographic structures?

M Spagnuolo, ME Yildizdag… - … and Mechanics of …, 2021 - journals.sagepub.com
The central theme of this study is to investigate a remarkable capability of a second-gradient
continuum model developed for pantographic structures. The model is applied to a particular …

Large deformations of planar extensible beams and pantographic lattices: heuristic homogenization, experimental and numerical examples of equilibrium

F dell'Isola, I Giorgio… - Proceedings of the …, 2016 - royalsocietypublishing.org
The aim of this paper is to find a computationally efficient and predictive model for the class
of systems that we call 'pantographic structures'. The interest in these materials was …

Discrete is it enough? The revival of Piola–Hencky keynotes to analyze three-dimensional Elastica

E Turco - Continuum Mechanics and Thermodynamics, 2018 - Springer
Complex problems such as those concerning the mechanics of materials can be confronted
only by considering numerical simulations. Analytical methods are useful to build guidelines …

Continuation of equilibria and stability of slender elastic rods using an asymptotic numerical method

A Lazarus, JT Miller, PM Reis - Journal of the Mechanics and Physics of …, 2013 - Elsevier
We present a theoretical and numerical framework to compute bifurcations of equilibria and
stability of slender elastic rods. The 3D kinematics of the rod is treated in a geometrically …

Identification of two-dimensional pantographic structure via a linear D4 orthotropic second gradient elastic model

L Placidi, U Andreaus, I Giorgio - Journal of Engineering Mathematics, 2017 - Springer
A linear elastic second gradient orthotropic two-dimensional solid that is invariant under 90^
∘ 90∘ rotation and for mirror transformation is considered. Such anisotropy is the most …