How contact interactions may depend on the shape of Cauchy cuts in Nth gradient continua: approach “à la D’Alembert”

By Francesco dell'Isola, Pierre Seppecher, A. Madeo. 2012

318 citations recorded by the source corpus.

Subfields: Biomedical Engineering, Materials Chemistry, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/5a5160ceec1350a355cbcc8f9431b03752028e25

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Biomedical Engineering

In Materials Chemistry

In Mechanics of Materials

Citations in the corpus

Second-gradient continua as homogenized limit of pantographic microstructured plates: a rigorous proof (2015, background): “, [6–14]; for a general theoretical framework in which is discussed the link between n-th gradient models and the variational formulation, see [15]).”
Reflection and transmission of plane waves at surfaces carrying material properties and embedded in second-gradient materials (2014, unknown): “[28], [29], [30], [34], [8],[11], [13], [9],[7],[12], [38], [39], [37], [36], [42], [44]).”
Hencky-type discrete model for pantographic structures: numerical comparison with second gradient continuum models (2016, background): “, [59–62] or [63–65] for 2D or 1D generalized continua characterized by a specific microstructure).”
Linear pantographic sheets: Asymptotic micro-macro models identification (2017, background): “In particular, when there is a high contrast (see [18, 77, 59, 16, 25]) in the physical properties at micro-level then it may become necessary at macro level to introduce higher order continua (see [43, 39]).”
Analytical continuum mechanics à la Hamilton–Piola least action principle for second gradient continua and capillary fluids (2013, methodology): “ · N. (14) On the contrary, new diﬃculties appear when calculating the ﬁrst variation δ∇FA. However, the techniques developed by Mindlin, Green, Rivlin, Toupin and Germain (see also dell’Isola et al. [54]) allow us to treat this term eﬃciently and elegantly. Starting from (the comma indicates partia”
On some fundamental misunderstandings in the indeterminate couple stress model. A comment on recent papers of A.R. Hadjesfandiari and G.F. Dargush (2016, background): “As it is well known from differential geometry, the projectors 1− n⊗ n and n⊗ n allow to split a given vector or tensor field in a part projected on the plane tangent to the considered surface and in another part projected on the normal to such surface (see also [5, 41, 4] for details)).”
Exegesis of the Introduction and Sect. I from “Fundamentals of the Mechanics of Continua”** by E. Hellinger (2017, methodology): “Here, Hellinger anticipates the structure theorems later proven by Laurent Schwartz (see [88]) for distributions which has been later explicitly considered in [33] and [28,30,32].”
A Two-Dimensional Gradient-Elasticity Theory for Woven Fabrics (2015, background): “The derivation of the Euler equations and boundary conditions in second gradient elasticity is well known [24–29].”