Periodic auxetics: Structure and design
| Autor: | Ileana Streinu, Ciprian S. Borcea |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Series (mathematics)
Auxetics Applied Mathematics Mechanical Engineering Structure (category theory) FOS: Physical sciences Metric Geometry (math.MG) Articles 02 engineering and technology Mathematical Physics (math-ph) 021001 nanoscience & nanotechnology Condensed Matter Physics 01 natural sciences Ellipsoid Convexity Homothetic transformation Classical mechanics Mathematics - Metric Geometry Mechanics of Materials 0103 physical sciences FOS: Mathematics 52C25 74N10 010306 general physics 0210 nano-technology Mathematical Physics |
| Zdroj: | The Quarterly Journal of Mechanics and Applied Mathematics |
| DOI: | 10.48550/arxiv.1708.03960 |
| Popis: | Summary Materials science has adopted the term of auxetic behavior for structural deformations where stretching in some direction entails lateral widening, rather than lateral shrinking. Most studies, in the last three decades, have explored repetitive or cellular structures and used the notion of negative Poisson’s ratio as the hallmark of auxetic behavior. However, no general auxetic principle has been established from this perspective. In the present article, we show that a purely geometric approach to periodic auxetics is apt to identify essential characteristics of frameworks with auxetic deformations and can generate a systematic and endless series of periodic auxetic designs. The critical features refer to convexity properties expressed through families of homothetic ellipsoids. |
| Databáze: | OpenAIRE |
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