Simulation of deformation and fracture in very large shell structures

Abstract

Although advances in computing have increased the limits of three-dimensional computational solid mechanics, structural elements remain essential in the practical design of very large thin structures such as aircraft fuselages, ship hulls, automobiles, submarines, and pressure vessels. In many applications, fracture is a critical design concern, and thus the ability to numerically predict crack propagation in shells is a highly desirable goal. There are relatively few tools devoted to computational shell fracture, and of the existing approaches, there are two main defects: First, the existing methods are not scalable, in the sense of parallel computing, and consequently simulation of large structures remains out of reach. Second, while the existing approaches treat in-plane tensile failure, fracture due to transverse shearing has largely been ignored. In this thesis, a new computational framework for simulating deformation and fracture in large shell structures is presented that is well-suited to parallel computation. The scalability of the framework derives from the combination of a discontinuous Galerkin (DG) finite element method with an interface element-based cohesive zone representation of fracture. This representation of fracture permits arbitrary crack propagation, branching, and merging, without on-the-fly mesh topological changes. Furthermore, in parallel computing, this propagation algorithm is indifferent to processor boundaries. The adoption of a shear-flexible shell theory is identified as a necessary condition for modeling transverse shear failure, and the proposed method is formulated accordingly. Locking is always an issue that emerges in numerical analysis of shear-flexible shells; here, the inherent flexibility afforded by DG methods in the choice of approximation spaces is exploited to prevent locking naturally, without recourse to mixed methods or reduced integration. Hence, the DG discretization elegantly solves both the problems of scalability and locking simultaneously. A stress resultant-based cohesive zone theory is proposed that considers transverse shear, as well as bending and in-plane membrane forces. The theory is quite general, and the specification of particular constitutive relations, in the form of resultant traction-separation laws, is independent of the discretization scheme. Thus, the proposed framework should be extensible and useful for a variety of applications. A detailed description of the implementation strategy is provided, and numerical examples are presented which demonstrate the ability of the framework to capture all of the relevant modes of fracture in thin bodies. Finally, a numerical example of explosive decompression in a commercial airliner is shown as evidence that the proposed framework can successfully perform shell fracture simulations of unprecedented size.