Lattice models in micromechanics
M Ostoja-Starzewski - Appl. Mech. Rev., 2002 - asmedigitalcollection.asme.org
This review presents the potential that lattice (or spring network) models hold for
micromechanics applications. The models have their origin in the atomistic representations …
micromechanics applications. The models have their origin in the atomistic representations …
The postulations á la D'Alembert and á la Cauchy for higher gradient continuum theories are equivalent: a review of existing results
F dell'Isola, P Seppecher… - Proceedings of the …, 2015 - royalsocietypublishing.org
In order to found continuum mechanics, two different postulations have been used. The first,
introduced by Lagrange and Piola, starts by postulating how the work expended by internal …
introduced by Lagrange and Piola, starts by postulating how the work expended by internal …
Homogenization à la Piola produces second gradient continuum models for linear pantographic lattices
In the present work, we show that the linearized homogenized model for a pantographic
lattice must necessarily be a second gradient continuum, as defined in Germain (1973) …
lattice must necessarily be a second gradient continuum, as defined in Germain (1973) …
Linear elastic trusses leading to continua with exotic mechanical interactions
P Seppecher, JJ Alibert, FD Isola - Journal of Physics …, 2011 - iopscience.iop.org
We study the statics of some trusses, ie networks of nodes linked by linear springs. The
trusses are designed in such a way that a few number of floppy modes are present and …
trusses are designed in such a way that a few number of floppy modes are present and …
How contact interactions may depend on the shape of Cauchy cuts in Nth gradient continua: approach “à la D'Alembert”
Abstract Navier–Cauchy format for Continuum Mechanics is based on the concept of contact
interaction between sub-bodies of a given continuous body. In this paper, it is shown how …
interaction between sub-bodies of a given continuous body. In this paper, it is shown how …
Peridynamics as an upscaling of molecular dynamics
Peridynamics is a formulation of continuum mechanics based on integral equations. It is a
nonlocal model, accounting for the effects of long-range forces. Correspondingly, classical …
nonlocal model, accounting for the effects of long-range forces. Correspondingly, classical …
[图书][B] Compendium on gradient materials
A Bertram - 2023 - Springer
Although already suggested in the middle of the 19th century, have material models that
include higher gradients of the kinematical variables become a blossoming field of research …
include higher gradients of the kinematical variables become a blossoming field of research …
From molecular models¶ to continuum mechanics
X Blanc, C Le Bris, PL Lions - Archive for Rational Mechanics and …, 2002 - Springer
We present here a limiting process allowing us to write some continuum mechanics models
as a natural asymptotic of molecular models. The approach is based on the hypothesis that …
as a natural asymptotic of molecular models. The approach is based on the hypothesis that …
The influence of scale size on the stability of periodic solids and the role of associated higher order gradient continuum models
N Triantafyllidis, S Bardenhagen - Journal of the Mechanics and Physics of …, 1996 - Elsevier
Of interest here is the scale size effect on the stability of finitely strained, rate-independent
solids with periodic microstructures. Using a multiple scales asymptotic technique, we …
solids with periodic microstructures. Using a multiple scales asymptotic technique, we …
Linear plane wave propagation and normal transmission and reflection at discontinuity surfaces in second gradient 3D continua
We study plane waves in second gradient solids and their reflection and transmission at
plane displacement discontinuity surfaces. The needed extension of the treatment adopted …
plane displacement discontinuity surfaces. The needed extension of the treatment adopted …