A review of size-dependent continuum mechanics models for micro-and nano-structures

MA Roudbari, TD Jorshari, C Lü, R Ansari… - Thin-Walled …, 2022 - Elsevier
Recently, the mechanical behavior of micro-/nano-structures has sparked an ongoing
debate, which leads to a fundamental question: what steps can be taken to investigate the …

Dynamic problems for metamaterials: review of existing models and ideas for further research

D Del Vescovo, I Giorgio - International Journal of Engineering Science, 2014 - Elsevier
Metamaterials are materials especially engineered to have a peculiar physical behaviour, to
be exploited for some well-specified technological application. In this context we focus on …

At the origins and in the vanguard of peridynamics, non-local and higher-gradient continuum mechanics: an underestimated and still topical contribution of Gabrio …

F Dell'Isola, U Andreaus… - … and Mechanics of Solids, 2015 - journals.sagepub.com
Gabrio Piola's scientific papers have been underestimated in mathematical physics
literature. Indeed, a careful reading of them proves that they are original, deep and far …

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 …

Isogeometric analysis of plane-curved beams

A Cazzani, M Malagù, E Turco - Mathematics and Mechanics …, 2016 - journals.sagepub.com
A curved beam element based on the Timoshenko model and non-uniform rational B-
splines (NURBS) interpolation both for geometry and displacements is presented. Such an …

On effective properties of materials at the nano-and microscales considering surface effects

VA Eremeyev - Acta Mechanica, 2016 - Springer
In the last years, the rapid increase in the technical capability to control and design materials
at the nanoscale has pushed toward an intensive exploitation of new possibilities …

Higher-gradient continua: The legacy of Piola, Mindlin, Sedov and Toupin and some future research perspectives

F Dell'Isola, AD Corte, I Giorgio - … and Mechanics of Solids, 2017 - journals.sagepub.com
Since the first studies dedicated to the mechanics of deformable bodies (by Euler,
D'Alembert, Lagrange) the principle of virtual work (or virtual velocities) has been used to …

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 …

Analytical continuum mechanics à la Hamilton–Piola least action principle for second gradient continua and capillary fluids

N Auffray, F dell'Isola, VA Eremeyev… - … and Mechanics of …, 2015 - journals.sagepub.com
In this paper a stationary action principle is proved to hold for capillary fluids, ie fluids for
which the deformation energy has the form suggested, starting from molecular arguments …

Mechanical response of fabric sheets to three-dimensional bending, twisting, and stretching

DJ Steigmann, F Dell'Isola - Acta Mechanica Sinica, 2015 - Springer
A model for the mechanics of woven fabrics is developed in the framework of two-
dimensional elastic surface theory. Thickness effects are modeled indirectly in terms of …