📆 Thursday, October 17, 2024

🕐 5:00 pm CET

📍 OCZ Room, C1 building, 2nd floor, CIMNE Barcelona (UPC Campus Nord)

ABSTRACT

This doctoral thesis presents a novel multiscale theory for the analysis of multilayered plate structures, termed the "Multiscale 2D+ approach" or, simply, "2D+". Based on the formalism of computational homogenization theory, this approach is specifically tailored to account for the mechanical behaviour of multilayered materials, which contain a heterogeneous distribution of thin layers across the thickness and often exhibit substantial non-linear material behavior. After identifying the macroscopic scale as the (2D) reference plane of the plate, the strategy models the through-the-thickness heterogeneity by means of a (1D) meso-scale filament, orthogonal to such plane and spanning the plate depth. At the macro-scale level, classical First Order Shear Deformation Theory (FSDT) kinematics is adopted. At the fine-scale level, the Representative Volume Element (RVE) kinematics is initially derived through the linearization of the macro-scale displacement field along the thickness, in accordance with the first-order computational homogenization theory. The RVE is then endowed with a fluctuating displacement field, which aims to capture the well-known (higher-order) zig-zag displacements observed across the thickness of composite laminates. The Hill-Mandel principle is used to establish the mechanical energy balance across both scales, resulting in a one-dimensional Boundary Value Problem (BVP) to be solved at the meso-scale level in terms of the fluctuating displacement field. Furthermore, the variational RVE-problem allows for the enforcement of an additional condition: the fulfillment of the linear momentum balance (equilibrium) equations at every point across the thickness. This yields a physically meaningful computational setting, in which both scales are represented through simple (degenerated) kinematic descriptions, accounting for the essential mechanical behavior observed at each level yet remaining computationally inexpensive. The Multiscale 2D+ approach can therefore be seen as a modern plate theory, where the through-the-thickness mechanical behavior of the plate is obtained upon the solution of the equilibrium problem of a meso-scale filament. Particularly well-suited for bending-dominated scenarios, it provides accurate stress distributions at the ply-level in non-linear simulations, close to those of full-3D models, at a computational cost similar to that of 2D models. The thesis comprises the development of both the formulation and the corresponding numerical multiscale model within the context of the finite element method. Through a series of representative simulations−including assessments of accuracy, computational performance, and non-linear material modeling− the merits of the 2D+ approach in successfully accounting for the mechanical behavior of multilayered plates are clearly evidenced in this contribution.

Committee

• President: Dr. Albertino Arteiro
• Secretary: Dr. Juan Carlos Cante
• Member: Dr. Pablo J. Sánchez
• PhD advisors: Dr. Francisco J. Oliver & Dr. Oriol Lloberas

PHD CANDIDATE

Mr. Pablo Nicolàs Wierna is a researcher on the multiscale analysis of laminated composite materials at the group on computational design and analysis of engineering materials and metamaterials (COMP-DES-MAT) at CIMNE. He obtained a Bs in Mechanical Engineering from the Universidad Tecnológica Nacional in Córdoba, Argentina, in 2020.