High-Fidelity Stress Fields in Contact Problems using Beam, Plates, and Shells Layer-Wise Models

Structural analysis often involves contact mechanics, as mechanical systems typically feature static or dynamic contact between components. Examples of contact include meshing gears, forming processes, and simulating indentation, with impact analysis of structures being a crucial engineering application of contact. With composite laminated materials being increasingly used, it is essential to study the impact of contact, as it can result in localized damage and delamination, which can severely reduce the mechanical properties of a structure. The numerical modeling of contact is a current challenge in computational mechanics. Over the last few decades, various techniques of varying complexity have emerged, e.g., node-to-node contact and node-to-surface, and surface-based. Such techniques are, then, coupled with structural mechanics models and the Finite Element Method (FEM). For high-resolution results concerning stress and strain fields, 3D FEM is often required; however, the computational overhead of 3D can be prohibitive in many cases, e.g., laminated structures. This work proposes using 1D and 2D models as alternatives to 3D. The Carrera Unified Formulation (CUF) is used to derive such reduced models based on higher-order expansions of the displacement field and ensure 3D-like accuracy for all the components of the stress and strain vectors. The study focuses on normal, frictionless contact using a penalty method to enforce the contact constraints. With a view to the accuracy and the computational time required for analysis, different numerical models, such as higher-order CUF and 3D finite element models, are presented and compared. The results indicate that Layer-Wise CUF models require at least an order of magnitude fewer degrees of freedom and computational time than 3D finite element analysis and can furnish very accurate results regarding stress distribution.