Out‐of‐Plane Tension of Thin Two‐Layered Plates of Cubic Crystals

• Published in: physica status solidi (b) Vol. 258; no. 12
• Main Authors: Gorodtsov, Valentin A., Volkov, Mikhail A., Lisovenko, Dmitry S.
• Format: Journal Article
• Language: English
• Published: 01.12.2021
• Subjects: auxetics; cubic crystals; Poisson's ratios; two-layered plates; Young's moduli
• ISSN: 0370-1972; 1521-3951
• DOI: 10.1002/pssb.202100184

Herein, the theoretical analysis of out‐of‐plane tension of a thin rectangular two‐layered plate of cubic crystals with the same orientation is provided. The dependences of effective Young's modulus and effective Poisson's ratio of the plate on Poisson's ratios of layers, the ratio of Young's moduli, and the thickness ratio are obtained. It is shown that when the ratios between Young's moduli and ratios between Poisson's ratios of the layers are equal, effective Young's modulus and effective Poisson's ratio coincide with Reuss'es means. The rules of mixtures are not fulfilled in the absence of equality of these ratios. In this case, effective Young's modulus can exceed not only Reuss'es mean but also Voigt's mean. It is demonstrated that effective Young's modulus can be larger than Young's moduli of both layers in two‐layered plates of nonauxetic−nonauxetic and auxetic−auxetic type. It is established that the behavior of effective Poisson's ratio of nonauxetic−nonauxetic plates can vary depending on the ratio of the layer thicknesses. At the same time, effective Poisson's ratio of plates from pairs of auxetics cannot be less than Poisson's ratios of both initial auxetic layers. Analysis of out‐of‐plane tension of thin two‐layered plate shows that rules of mixtures are fulfilled only if there are equal ratios of Young's moduli and Poisson's ratios of the layers. Effective Young's modulus E can exceed Reuss'es mean E R, Voigt's mean E V, and Young's moduli of layers (left figure). The effective Poisson's ratio of the plate may be larger than Poisson's ratios of layers (right figure).