Macroscopic Description of Microscopically Strongly Inhomogenous Systems: A Mathematical Basis for the Synthesis of Higher Gradients Metamaterials

By A. Carcaterra, Francesco dell'Isola, Raffaele Esposito, M. Pulvirenti. 2015

166 citations recorded by the source corpus.

We consider the time evolution of a one dimensional n-gradient continuum. Our aim is to construct and analyze discrete approximations in terms of physically realizable mechanical systems, referred to as microscopic because they are living on a smaller space scale. We validate our construction by proving a convergence theorem of the microscopic system to the given continuum, as the scale parameter goes to zero.

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

View Paper: https://www.semanticscholar.org/paper/38984d8fb4000fff83309e57c9b33fd4d3061933

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In Computational Theory and Mathematics

In Materials Chemistry

In Mechanics of Materials

Citations in the corpus

Designing a light fabric metamaterial being highly macroscopically tough under directional extension: first experimental evidence (2015, unknown): “Of course this micro–macro procedure is needed, and following the ideas presented, for example, in [2,3,77], in [6–8,18,28,62,71,72] in [10] or in [48–50] will be the object of further investigations (see also [63] for a general overview on generalized continua).”
Large deformations of planar extensible beams and pantographic lattices: heuristic homogenization, experimental and numerical examples of equilibrium (2016, background): “Moreover, recent theoretical [30] and numerical [34] evidence shows that also discrete mechanical systems in which the interaction law involves first and second order Lagrangian neighbours may display typical second gradient effects.”
Synthesis of Fibrous Complex Structures: Designing Microstructure to Deliver Targeted Macroscale Response (2015, background): “In particular, the results obtained for 1D systems [135] can be generalized by showing how to synthesize microstructures whose continuous counterparts exhibit “forbidden” frequencies for wave propagation [238], the onset of trapping boundary layers or energy trapping at the microscopic level and con”
Strain gradient and generalized continua obtained by homogenizing frame lattices (2018, background): “Such inverse problem has been addressed in the dynamic case in [27].”
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): “By introducing the dimensionless variables x? = x/L and y? = y/L, we have (the reader is referred for comparison to [40] and [21]):”