Homogenized couple stress model of optimal auxetic microstructures computed by topology optimization

• Published in: Zeitschrift für angewandte Mathematik und Mechanik 2018-05, Vol.98 (5), p.696-717
• Main Authors: Ganghoffer, J. F., Goda, I., Novotny, A. A., Rahouadj, R., Sokolowski, J.
• Format: Article
• Language: English
• Subjects: auxetic material; Auxetic materials; Computation; couple stress model; Elasticity; Engineering Sciences; Mathematical models; Mechanical properties; mechanical testing; microstructure design; poisson ratio; Poisson's ratio; topological derivative; Topology optimization
• ISSN: 0044-2267; 1521-4001
• DOI: 10.1002/zamm.201700154

Auxetic materials and microstructures are attracting the attention of a growing community of researchers due to their unusual properties and high mechanical performances, in both the static and dynamic regimes. The topological derivative is used in this contribution to determine microstructures having the most negative in‐plane mean Poisson's ratio. The auxetic nature of the computed microstructures is demonstrated by both numerical and real experiments performed over samples fabricated by additive printing. The effective mechanical properties of these auxetic structures have been computed in the framework of couple stress elasticity, allowing to identify both in‐plane and out‐of plane effective properties. The calculated classical moduli are found independent of the size of the window of analysis and are consequently effective coefficients. In contrast to this, the calculated in‐plane bending moduli show a clear dependency on the auxetic cell size, whereas the out‐of‐plane bending moduli appear to be size‐independent. Auxetic materials and microstructures are attracting the attention of a growing community of researchers due to their unusual properties and high mechanical performances, in both the static and dynamic regimes. The topological derivative is used in this contribution to determine microstructures having the most negative in‐plane mean Poisson's ratio. The auxetic nature of the computed microstructures is demonstrated by both numerical and real experiments performed over samples fabricated by additive printing. The effective mechanical properties of these auxetic structures have been computed in the framework of couple stress elasticity, allowing to identify both in‐plane and out‐of plane effective properties. The calculated classical moduli are found independent of the size of the window of analysis and are consequently effective coefficients. In contrast to this, the calculated in‐plane bending moduli show a clear dependency on the auxetic cell size, whereas the out‐of‐plane bending moduli appear to be size‐independent.