Mathematical Modeling and Computational Mechanics for Heterogeneous or Homogeneous Thin Structures

Dear Colleagues,

In this Special Issue, we invite contributions from all fields of theoretical or applied solid mechanics, focusing on new modelizations for thin structures homogeneous or heterogeneous thin structures (plates, shells, beams, and thin-walled beams) using numerical tests as illustrations.

Mathematical modelization in the linear or the nonlinear setting are being developed recently. For highly heterogeneous thin plate structures, replacing the heterogeneous initial structure with a homogeneous one is rather interesting from a computational point of view. Then, two small parameters appear: the thickness of the plate and the size of heterogeneities. Caillerie-Kohn-Vogelius (Caillerie [1]) provides a theoretical explanation for when both the thickness of the plate and the size of heterogeneities are of the same order of magnitude. However, research on the extension of this theory for other types of constitutive law (nonlinear and growth theory) and higher order theories which include transverse shearing is limited; only a few scholars have focused on these topics (see for example (Lee et al. [2], Kalamkarov et al. [3], Pruchnicki [4]). Additionally, the case when the thickness of the plate and the size are not of the same order of magnitude also remains largely unexplored. Works not related to thin structures are also welcome.

[1] Caillerie, D. Thin and periodic plates. Mathematical Methods in the Applied Science 1984, 6, 159-191.

[2] Lee, C. Y., Yu, W. and Hodges, D.H. Refined modeling of composite plates with in plane heterogeneity. Journal of Applied Mathematics and Mechanics 2014, 94, 85-100.

[3] Kalamkarov, A. L., Tornabaene, F., Pacheco, P. M. C. L., Savi, M. A. and Saha, G. C. Geometrically non-linear elastic model for a thin composite layer with wavy surfaces. Journal of Applied Mathematics and Mechanics 2017, 97, 1381-1392.

[4] Pruchnicki, E. Homogenization of nonlinear heterogeneous thin plate when the plate thickness and in plane heterogeneities are of the same order of magnitude. The Quarterly Journal of Mechanics and Applied Mathematics 2023, 76, 277–295. https://doi.org/10.1093/qjmam/hbad004

Dr. Erick Pruchnicki
Guest Editor

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• mathematical modelization
• theoretical solid mechanics
• applied solid mechanics
• numerical computation
• linear problem
• nonlinear problem
• growth theory
• thin structures
• homogeneous
• heterogeneous