Investigation of Structures Featuring Curvilinear Anisotropy: Application to Electrostatic Problem and Mechanical Response

Abstract

This study examines the impact of curvilinear reinforcement in a composite structure. The key areas covered include two main applications: 1) enhancing functional properties in electrostatic problems and 2) improving the mechanical strength and fracture resistance of composite structures. Depending on the arrangement of reinforcement, the conductivity of the composites can be adjusted. The overarching goals towards the electrostatic application are twofold. First, this study aims to provide the computational framework of obtaining optimal fiber configuration maximizing conductivity for structures with finite domain. To that end, an analytical solution of the Poisson equation is derived through conformal mapping, revealing insights such as the optimal alignment of fiber orientation with field lines under specific conditions. The concept of curvilinear transverse isotropy is introduced, and its application to electrostatic problems is demonstrated. This theoretical foundation helps to extends to practical scenarios in finite domains. The finite element method is used to determine the optimal reinforced configuration for a notched specimen. The second objective is to assess the ability of optimal reinforced configuration in the application of damage detection or health monitoring by measuring the change of conductivity. Finite element method is used to compute the change in conductivity at the source after a crack is inserted, representing a breakage of fibers from a localized damage. Subsequently, the investigation on the influence of curvilinear reinforcement on mechanical performance is provided. Isogeometric analysis with spline basis functions for enhanced continuity is employed to evaluate the mechanical performance of composite structures with multiple variants of curvilinear reinforcement on a notched plate. An optimization study with polynomials describing orientation distribution on a given structure is carried on to determine the optimal fiber path that enhances structural properties like stress distribution and stiffness. As a result, the stress concentration factor was reduced to 1.28. This result highlights a substantial 82 % decrease when compared to the conventional longitudinal fiber reinforcement. To extend isogeometric approach suitable for a general types of trimmed surfaces, in-house IGA software is developed which employs LR B splines in a model generation and the numerical analysis. A data-driven optimization approach is used to find the optimial reinforcement configuration for improved damage tolerance. Two types of geometry used in this study are a plate with a semi-circular notch and T-shaped joint structure. A cross-ply layup sequence is assumed for each laminate. As a result for the first optimization study, the maximum principal stress is reduced by a factor greater than 7 for the rectangular plate and is reduced by a factor of 3 for T-joint. The other optimization result highlights the reduction of the energy release rate close to zero which implies that the crack is not likely to form at the notch. Lastly, a new discrete modeling method is proposed to predict damage initiation and progression in fiber-reinforced composites. Fibers are explicitly modeled using Timoshenko beams which are embedded in a tetrahedral conforming mesh that characterizes the matrix. The facet-based formulation enables discrete fracture modeling, and prevents the element erosion. Furthermore, the explicit representation of fibers and matrix allows a simple and distinct definition of material parameters thanks to the constitutive laws grounded in physics rather than in empirical curve fitting.