Truss Modular Beams with Deformation Energy Depending on Higher Displacement Gradients

By J. Alibert, Pierre Seppecher, Francesco dell'Isola. 2003

597 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Materials Chemistry, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/7c40fa082fd139b4ff8ab3b94a42e83ab302c8ed

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In Computational Theory and Mathematics

In Materials Chemistry

In Mechanics of Materials

Citations in the corpus

Macroscopic Description of Microscopically Strongly Inhomogenous Systems: A Mathematical Basis for the Synthesis of Higher Gradients Metamaterials (2015, unknown): “[11, 26, 19, 1, 24, 29] and references therein).”
Analytical continuum mechanics à la Hamilton–Piola least action principle for second gradient continua and capillary fluids (2013, unknown): “[1], Steinmann et al.”
Designing a light fabric metamaterial being highly macroscopically tough under directional extension: first experimental evidence (2015, background): “The pairs of fields (μ, θ), together with the conditions (16), verify the local condition dμ(ξ) dξ − cos (θ (ξ)) = 0 ∀ξ ∈ [1, 3] .”
Homogenization à la Piola produces second gradient continuum models for linear pantographic lattices (2015, methodology): “…the constituents and impact of strong gradients of the loading); several methods have been developed towards this objective in the literature (see Alibert et al., 2003; Dos Reis & Ganghoffer, 2012a; Forest, 1998, 2002; Hirschberger, Ricker, Steinmann, & Sukumar, 2009; Seppecher, Alibert, &…”
A complete dynamic approach to the Generalized Beam Theory cross-section analysis including extension and shear modes (2014, background): “Furthermore, to the best knowledge of the authors, few references exist, for example [27], on the consequences at the macro-mechanical level of higher displacement gradients, which can lead to interesting developments in the theory of TWBs.”
Second-gradient continua as homogenized limit of pantographic microstructured plates: a rigorous proof (2015, background): “Its judicious use in periodic microstructures (as proposed in [53]) produces naturally a model which cannot be framed in the standard scheme developed by Navier and Cauchy.”
Large deformations of planar extensible beams and pantographic lattices: heuristic homogenization, experimental and numerical examples of equilibrium (2016, background): “[10–15]) some fabrics whose behaviour can be somehow assimilated to the one shown by pantographic micro-structures actually the materials having a pantographic microstructure have been conceived (see [16, 17]) on the basis of purely theoretical considerations aiming to prove the possibility of desig”
On nonconservativeness of Eringen’s nonlocal elasticity in beam mechanics: correction from a discrete-based approach (2014, background): “For instance, higher gradient elasticity theories may be also deduced starting from discrete repetitive truss cells [44].”
Micromechanics based second gradient continuum theory for shear band modeling in cohesive granular materials following damage elasticity (2012, background): “Instead the same effect is obtained in systems in which at microlevel the interaction forces are linear, but strong space variation of elastic properties are observed (Alibert et al., 2003; Seppecher et al., 2011).”
A Two-Dimensional Gradient-Elasticity Theory for Woven Fabrics (2015, background): “In the case of fiber inextensibility, where the stretch gradients vanish identically, Γ also vanishes, yielding the further simplifications κ1 = γ,1 and κ2 = −γ,2, connecting the bending strains to the fiber derivatives of the shear angle (see also [14, 15]).”