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arXiv · 1504.08015

Macroscopic description of microscopically strongly inhomogenous systems: A mathematical basis for the synthesis of higher gradients metamaterials

Antonio Carcaterra·Francesco dell'Isola·Raffaele Esposito·Mario Pulvirenti
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Abstract

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, called 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.

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Antonio Carcaterra, Francesco dell'Isola, Raffaele Esposito, Mario Pulvirenti. 2015-04-29. Macroscopic description of microscopically strongly inhomogenous systems: A mathematical basis for the synthesis of higher gradients metamaterials. https://doi.org/10.1007/s00205-015-0879-5

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