A Two-Dimensional Gradient-Elasticity Theory for Woven Fabrics

By Francesco dell'Isola, David J. Steigmann. 2015

214 citations recorded by the source corpus.

Subfields: Materials Chemistry, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/2e26c742b12213f7a8918c84ece1d57b658c220c

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In Materials Chemistry

In Mechanics of Materials

Citations in the corpus

Linear pantographic sheets: Asymptotic micro-macro models identification (2017, background): “Pantographic sheets have an exotic behavior which is not only characterized by their anisotropy as evidenced by (i) their vanishing resistance to shear deformation, and (ii) their significant resistance to elongation along fibers; but also by their capacity to resist to variations in their so-called”
Synthesis of Fibrous Complex Structures: Designing Microstructure to Deliver Targeted Macroscale Response (2015, background): “Poisson effects are generally nonnegligible in woven fabrics due to fiber crimping and decrimping [193,213], but this mechanism is absent in pantographic lattices.”
Continuum and discrete models for structures including (quasi-) inextensible elasticae with a view to the design and modeling of composite reinforcements (2015, background): “Here, we recall that (see dell’Isola and Steigmann, 2014) the compatibility of the first gradient of the deformation is shown to imply a direct connection between the gradient of fiber shear and the fiber bending strains: this effect is associated with the second gradient of deformation.”
Homogenization à la Piola produces second gradient continuum models for linear pantographic lattices (2015, unknown): “…of in-plane displacements: these 2D continua were already investigated in the literature (see e.g. Altenbach, Eremeyev, & Morozov, 2009, 2010, 2012; dell’Isola & Steigmann, 2015; Giorgio, Grygoruk, dell’Isola, & Steigmann, 2015; Pietraszkiewicz, Eremeyev, & Konopińska, 2007; Steigmann &…”
Designing a light fabric metamaterial being highly macroscopically tough under directional extension: first experimental evidence (2015, methodology): “The mathematical continuum model developed in [16,17,81], based on the ideas originated by Rivlin and Pipkin, showed to be an useful tool for design of complex plane pantographic metamaterials.”
Mechanical response of fabric sheets to three-dimensional bending, twisting, and stretching (2015, methodology): “Turning to the boundary terms, a standard integrationby-parts procedure [18] is used to recast the first integral in Eq.”
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]).”
Pantographic metamaterials: an example of mathematically driven design and of its technological challenges (2018, background): “[46], explicit expressions for geodesic and Tchebychev curvatures are provided”
Material symmetry group and constitutive equations of micropolar anisotropic elastic solids (2016, background): “Let us note that modelling of such composite materials can naturally lead to extended models of continua: see for example [45, 46] where the second-gradient models of woven fabrics are discussed.”