On the efficient and accurate non-linear computational modeling of multilayered bending plates. State of the art and a novel proposal: the 2D+ multiscale approach

After conducting a comprehensive historical review of presently established methods for computational modeling of multilayered bending plates, the present work introduces a novel 2D multiscale strategy, termed the 2D+ approach. The proposed approach is based on the computational homogenization formalism and is envisaged to serve as an appealing alternative to current methodologies for modeling multilayered plates in bending-dominated situations. Such structural elements involve modern and relevant materials, such as laminated composites characterized by the heterogeneous distribution of low-aspect-ratio layers showing substantial non-linear mechanical behavior across their thickness. Within this proposed approach, the 2D plate mid-plane constitutes the macroscopic scale, while a 1D filament-like Representative Volume Element (RVE), orthogonal to the plate mid-plane and spanning the plate thickness, represents the mesoscopic scale. Such RVE, in turn, is capturing the non-linear mechanical behavior throughout the plate thickness at each integration point of the 2D plate-midplane finite element mesh. The chosen kinematics and discretization at the considered scales are particularly selected to (1) effectively capture relevant aspects of non-linear mechanical behavior in multilayered plates under bending-dominated scenarios, (2) achieve affordable computational times (computational efficiency), and (3) provide accurate stress distributions compared to the corresponding high-fidelity 3D simulations (computational accuracy). The proposed strategy aligns with the standard, first-order, hierarchical multiscale setting, involving the linearization of the macro-scale displacement field along the thickness. It employs an additional fluctuating displacement field in the RVE to capture higher-order behavior, which is computed through a local 1D finite element solution of a Boundary Value Problem (BVP) at the RVE. A notable feature of the presented 2D+ approach is the application
The authors gratefully acknowledge the financial support received from the Spanish Ministry of Science and Innovation through the ’Proyectos de Transición Ecológica y Digital 2021’ programme under grant TED2021-129413B-C21, the ’Generación de Conocimiento 2022’ programme under grant PID2022-140249OB-I00 and the Catalan Agency for Management of University and Research Grants through the ’Convocatòria ajuts d’Indústria del Coneixement: Producte, 2021’ under grant PROD 00016. Dr. Oriol Lloberas-Valls gratefully acknowledges the financial support received from he Spanish Ministry of Science and Innovation, through the ’Consolidación Investigadora 2022’ programme under grant CNS2022-135900. CIMNE is a recipient of a “Severo Ochoa Programme for Centers of Excellence in R &D” grant (CEX2018-000797-S) by the Spanish Ministry of Economy and Competitiveness.
Peer Reviewed
Postprint (published version)