UC San Diego

Fiber-reinforced composite materials have become increasingly popular in the past few decades for lightweight applications, in particular in the aerospace industry where high strength-to-weight and high stiffness-to-weight ratio are considered key design parameters. At the same time, new computational technologies are required to support the design process of increasingly complex structural components and to predict damage growth under non-standard loading conditions. However, the development of accurate and computationally efficient analysis tools, capable of predicting the response of laminated composite structures from the elastic regime to the failure point and beyond, is a complex task. Difficulties stem from the inherent heterogeneous nature of fiber-reinforced polymer composite materials and from their multi-modal failure mechanisms. Composite structures optimized for low weight applications are often laminates, consisting of several layers of fiber-reinforced material, called laminae, bonded together. Intra-laminar damage may occur within a given lamina, and inter-laminar damage, or delamination, may occur when bonds between laminae break down. The unique challenges associated with modeling damage in these structures may be addressed by means of thin-shell formulations which is naturally developed in the context of Isogeometric Analysis.

This dissertation presents a novel multi-layer modeling framework based on Isogeometric Analysis, where each ply or lamina is represented by a Non-Uniform Rational B-Spline (NURBS) surface, and it is modeled as a Kirchhoff-Love thin shell. A residual stiffness approach is used to model intra-laminar damage in the framework of Continuum Damage Mechanics. A new zero-thickness cohesive interface formulation is introduced to model delamination as well as permitting laminate-level transverse shear compliance. The gradient-enhanced continuum damage model is then introduced to regularize material instabilities, which are typically associated with strain-softening damage models. This nonlocal regularization technique aims to re-establish mesh objectivity by limiting the dependence of damage predictions on the choice of discrete mesh. To account for the anisotropic damage modes of laminae, the proposed formulation smooths a tensor-valued strain field by solving an elliptic partial differential equation system on each lamina.

The proposed approach has significant accuracy and efficiency advantages over existing methods for modeling impact damage. These stem from the use of IGA-based Kirchhoff-Love shells to represent the individual plies of the composite laminate, while the compliant cohesive interfaces enable transverse shear deformation of the laminate. Kirchhoff-Love shells give a faithful representation of the ply deformation behavior, and, unlike solids or traditional shear-deformable shells, do not suffer from transverse-shear locking in the limit of vanishing thickness. This, in combination with higher-order accurate and smooth representation of the shell midsurface displacement field, allows to adopt relatively coarse in-plane discretizations without sacrificing solution accuracy. Furthermore, the thin-shell formulation employed does not use rotational degrees of freedom, which gives additional efficiency benefits relative to more standard shell formulations.