PSI - Issue 81

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ScienceDirect

Procedia Structural Integrity 81 (2026) 129–134

© 2026 The Authors. Copy from the contract: Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of DMDP 2025 organizers Keywords: multilayer plate; periodic system of cracks; bending; crack face contact; intensity factors; limit load. 1. Introduction Multilayer composite materials, including laminated composites and sandwich structures, are extensively used in modern aerospace, automotive, marine, and civil engineering due to their excellent strength-to-weight and stiffness-to-weight ratios (Cherepanov, 1983;Jones, 1999; Reddy, 2004). The ability to tailor material properties by varying layer orientations and thicknesses makes these materials particularly attractive for structural applications where weight reduction is critical (Gibson, 2016; Castanié et al., 2020). Operational loads, manufacturing defects, and environmental factors can lead to crack initiation and propagation in laminated structures, significantly affecting their load-bearing capacity and structural integrity. The mechanical behavior of cracks in multilayer plates differs substantially from that in homogeneous materials due to the mismatch in elastic properties between adjacent layers and complex stress redistribution mechanisms (Suresh and Mortensen, 1998; Delale and Erdogan, 1983). For plate bending, a characteristic feature is the non-uniform stress distribution through the thickness, with tensile stresses on one side and compressive stresses on the other side of the neutral surface. In the compression zone, crack faces can come into contact, leading to stress redistribution and partial crack closure. This phenomenon must be accounted for to obtain correct Abstract The problem of bending of a multilayer plate with a periodic system of collinear through cracks is considered, taking into account the contact interaction of their faces. Based on the classical Kirchhoff plate bending theory and a special line contact model that eliminates the kinematic contradiction of mutual penetration of crack faces, a boundary value problem is formulated for a pair of biharmonic equations with interrelated conditions on the cuts. An analytical solution of the problem in closed form is constructed using the method of singular integral equations with a periodic Hilbert kernel. The influence of the material inhomogeneity profile and mutual arrangement of cracks on the stress and moment intensity factors, as well as on the limit load value according to the energy fracture criterion, is investigated. Numerical analysis is performed for symmetrical three- layer structures with “steel– aluminum –steel” and “aluminum– steel –aluminum” configurations. It is shown that plates with stiffer periphery have higher load-bearing capacity compared to plates with a rigid core. VIII International Conference “In - service Damage of Materials: Diagnostics and Prediction“ (DMDP 2025) A periodic set of collinear closable cracks in a bending multilayer plate Ivan Shatskyi*, Vasyl Petrashchuk Laboratory of Modeling of Damping Systems, Pidstryhach Institute for Applied Problems of Mechanics and Mathematics of the NAS of Ukraine, 3 Mykytynetska Str., Ivano-Frankivsk, 76002, Ukraine

* Corresponding author. Tel.: +38-099-444-4967. E-mail address: ipshatsky@gmail.com

2452-3216 © 2026 The Authors. Copy from the contract: Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of DMDP 2025 organizers 10.1016/j.prostr.2026.03.023