Determination of the Closure of the Set of Elasticity Functionals

By M. Camar-Eddine, Pierre Seppecher. 2003

121 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Computational Theory and Mathematics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/0f6dab3a37d626d86e98e4e3987ff9552ce1439a

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In Civil and Structural Engineering

In Computational Theory and Mathematics

In Mechanics of Materials

Citations in the corpus

Homogenization à la Piola produces second gradient continuum models for linear pantographic lattices (2015, background): “…the strict assumption of the scale separation, short range micro-interactions or absence of high contrast of physical and geometrical properties at micro-level (see, Camar-Eddine & Seppecher, 2003; Pideri & Seppecher, 1997; Trinh & Forest, 2010; Trinh, Jänicke, Auffray, Diebels, & Forest, 2012).”
On cloaking for elasticity and physical equations with a transformation invariant form (2006, methodology): “The model of figure 3 can be used to achieve any desired tensor ρ′, and Milton and Cherkaev [35] show how to achieve any positive definite tensor C′ satisfying the symmetries of elasticity tensors (see also chapter 30 of [10] for an essentially complete proof in the 2D case, and also see Camar-Eddin”
Continuum and discrete models for structures including (quasi-) inextensible elasticae with a view to the design and modeling of composite reinforcements (2015, background): “…microstructured continua, multipolar continua, enhanced continuum models and so on (see e.g. dell’Isola et al., in press; Pideri and Seppecher, 1997; Camar-Eddine and Seppecher, 2002, 2003; Bouchet and Brechet, 2009; Auffray et al., 2010; Auffray et al., in press; Svendsen et al., 2009; Neff and…”
Hencky-type discrete model for pantographic structures: numerical comparison with second gradient continuum models (2016, background): “On the other hand, the particular class of microstructured mechanical systems which present high contrast in microscopic properties once homogenized has been shown to produce generalized continua in [46–53].”