A review on 2D models for the description of pantographic fabrics

L Placidi, E Barchiesi, E Turco, NL Rizzi - Zeitschrift für angewandte …, 2016 - Springer
A review on models for pantographic fabrics, a new promising kind of metamaterials, is
presented. We treat those models that are able to capture the peculiar effects conferred by …

A targeted review on large deformations of planar elastic beams: extensibility, distributed loads, buckling and post-buckling

M Spagnuolo, U Andreaus - Mathematics and Mechanics of …, 2019 - journals.sagepub.com
In this paper, we give a targeted review of the state of the art in the study of planar elastic
beams in large deformations, also in the presence of geometric nonlinearities. The main …

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 …

A strain gradient variational approach to damage: a comparison with damage gradient models and numerical results

L Placidi, E Barchiesi, A Misra - Mathematics and Mechanics of Complex …, 2018 - msp.org
The global response of experimental uniaxial tests cannot be homogeneous, because of the
unavoidable presence of localized deformations, which is always preferential from an …

Strain gradient and generalized continua obtained by homogenizing frame lattices

H Abdoul-Anziz, P Seppecher - Mathematics and mechanics of complex …, 2018 - msp.org
We determine the effective behavior of periodic structures made of welded elastic bars.
Taking into account the fact that flexural and torsional stiffnesses are much smaller than the …

Linear pantographic sheets: asymptotic micro-macro models identification

C Boutin, I Giorgio, L Placidi - Mathematics and Mechanics of Complex …, 2017 - msp.org
In this paper we consider linear pantographic sheets, which in their natural configuration are
constituted by two orthogonal arrays of straight fibers interconnected by internal pivots. We …

Energy approach to brittle fracture in strain-gradient modelling

L Placidi, E Barchiesi - Proceedings of the Royal Society …, 2018 - royalsocietypublishing.org
In this paper, we exploit some results in the theory of irreversible phenomena to address the
study of quasi-static brittle fracture propagation in a two-dimensional isotropic continuum …

Higher-order modeling of anisogrid composite lattice structures with complex geometries

F Tornabene, M Viscoti, R Dimitri, MA Aiello - Engineering Structures, 2021 - Elsevier
The work investigates the vibration behaviour of anisogrid composite lattice shell structures,
typically formed by a system of geodesic unidirectional composite ribs. A homogenization …

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 …

Two-dimensional strain gradient damage modeling: a variational approach

L Placidi, A Misra, E Barchiesi - Zeitschrift für angewandte Mathematik und …, 2018 - Springer
In this paper, we formulate a linear elastic second gradient isotropic two-dimensional
continuum model accounting for irreversible damage. The failure is defined as the condition …