Automatic image-based adaptive damage analysis (AIBADA) with the scaled boundary finite element method

Abstract

Predicting serviceability and reliability of structures is one of the primary goals in engineering science. In the last few decades Continuum Damage Mechanics (CDM) has risen to prominence providing invaluable insights into the mechanics of deterioration prior to failure. Presently CDM is challenged by poor flexibility and lack of automation in mesh generation, unavailability of Computer Aided Design data, poor solution convergence etc. This thesis presents the development of an Automatic Image-Based Adaptive Damage Analysis (AIBADA) procedure capable of overcoming these difficulties.

Firstly non-linear damage analysis with the Scaled Boundary Finite Element Method (SBFEM) is explored. The SBFE equations are derived incorporating an isotropic thermodynamically congruent elastic damage model. The new simplified damage formulation requires state variable calculations at only one location within a cell. Polygonal (2D) and polyhedral (3D) element formulations are developed for damage analysis. The arbitrary number of edges/faces in these elements assist in meshing complex interfaces. Regularisation is established by exchanging information between model parameters. A line search oriented modified Newton Raphson method with the arc-length technique is adopted to overcome convergence difficulties. The method improves its efficiency by pre-calculating subdomain stiffness matrices, strain modes and weight functions. An adaptive analysis process improves the efficiency and the accuracy of the solution field.

Quadtree and octree image-based mesh generation schemes are utilised to model geometries based on image colour intensities. Mesh balancing limits the number of unique cell patterns reducing the computational burden. Mesh smoothing is carried out by a level set based algorithm. The SBFEM works seamlessly with the pre-processor owing to its inherent compatibility to handle hanging nodes without additional effort. Using these hierarchical meshing algorithms and the SBFE polygonal and polyhedral element formulations mesh automation is achieved.

The computational efficacy, accuracy and the robustness of the proposed fully-automatic framework expands the practical applications of CDM. AIBADA is likely to appeal to engineers and researchers alike in both academia and the industry. Accurate application of the method will enable users to analyse and predict failure with the precursory knowledge on performance deterioration prior to the appearance of macro-cracks.