Auxetic deformations and elliptic curves
| Autor: | Ileana Streinu, Ciprian S. Borcea |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2016 |
| Předmět: |
Auxetics
010102 general mathematics Aerospace Engineering Class (philosophy) Metric Geometry (math.MG) 02 engineering and technology 021001 nanoscience & nanotechnology Topology 01 natural sciences Computer Graphics and Computer-Aided Design Fast algorithm Article Three degrees of freedom Elliptic curve Mathematics - Metric Geometry Natural family Modeling and Simulation Automotive Engineering FOS: Mathematics Cubic form 52C25 74N10 0101 mathematics Computational material science 0210 nano-technology Mathematics |
| Popis: | In materials science and engineering, auxetic behavior refers to deformations of flexible structures where stretching in some direction involves lateral widening, rather than lateral shrinking. We address the problem of detecting auxetic behavior for flexible periodic bar-and-joint frameworks. Currently, the only known algorithmic solution is based on the rather heavy machinery of fixed-dimension semi-definite programming. In this paper we present a new, simpler algorithmic approach which is applicable to a natural family of three-dimensional periodic bar-and-joint frameworks with three degrees of freedom. This class includes most zeolite structures, which are important for applications in computational materials science. We show that the existence of auxetic deformations is related to properties of an associated elliptic curve. A fast algorithm for recognizing auxetic capabilities is obtained via the classical Aronhold invariants of the cubic form defining the curve. Related algorithmic alternatives are also considered. |
| Databáze: | OpenAIRE |
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