Multilayer Shells Interacting Through Friction

Abstract

Abstract The corresponding author had the pleasure of attending an excellent symposium titled “Experimental and Theoretical Micro- and Nano-Mechanics: Honoring the Contributions of Prof. Kyung-Suk Kim” organized by Professors Ashraf Bastawros, Wendy Crone, Yanfei Gao, and Ruike (Renee) Zhao as part of the 2022 Society of Engineering Sciences Annual Technical Meeting held in College Station, TX on October 16–19, 2022. The symposium was held in honor of Prof. Kim’s 70th Birthday and celebrated over 40 years of Prof. Kim’s independent research achievements across several areas of Applied Mechanics. The present paper is dedicated to Prof. Kim, a great colleague at Brown University.We present a new formulation for the multilayer isogeometric Kirchhoff–Love (KL) shells, where the individual layers are assumed to interact through no-penetration and frictional contact. This work is largely motivated by the experiments and analysis presented in Poincloux et al. (2021, “Bending Response of a Book With Internal Friction,” Phys. Rev. Lett., 126(21), p. 218004). We utilize a regularized version of Coulomb’s friction law to model the tangential traction between the contacting shell surfaces. To ensure objectivity (i.e., reference-frame invariance) in the frictional model, we propose two different strategies to extrapolate the velocity vectors of the contact pair at the contact interface: (i) using the underlying KL kinematics of the individual shell layers and (ii) using the Taylor series-based extension from Kamensky et al. (2019, “Peridynamic Modeling of Frictional Contact,” J. Peridyn. Nonlocal Model., 1(2), pp. 107–121). We compare the performance of both approaches through a numerical benchmark example. We then validate our multilayer shell formulation using the “bending response of a book with internal friction” experiments of Poincloux et al. (2021, “Bending Response of a Book With Internal Friction,” Phys. Rev. Lett., 126(21), p. 218004).