Abstract
Design and development of fracture-resistant materials is of interest for many different applications in civil, mechanical, and aerospace engineering. While theoretical mean field approaches are generally used to examine the mechanical behavior of homogeneous material the complexities that arise from heterogeneity of the domain cannot be captured through these approaches. It is well known that the microscopic characteristics of materials is a key driver of the effective elastic and fracture properties. The goal of this dissertation is to develop and examine novel techniques for establishing the microtexture and fracture property relationship. We first develop a novel hybrid energy-based approach to efficiently model the fracture behavior in heterogeneous materials. Our model is based on the potential-of-mean-force formulation of the lattice element method and the direct application of the Griffith fracture criteria. The computational efficiency of our approach is achieved through a probing of high energy bonds and quasi-static relaxation leading to near global imposition of the energy-based criteria for crack path resolution. We validate the proposed hybrid approach against results in literature and use it to examine fracture response for different heterogeneous samples including materials with random defects and layered composites. We investigate the effective fracture toughness, its variation and scaling with different mechanical properties of the composite constituent. We then leverage the efficient hybrid approach we developed to evaluate the macroscopic response of random porous materials subject to external loading. We perform statistical analysis on a large set of realizations of two-phase porous materials with the goal of establishing a relationship between microstructural properties and macroscopic response. The effective properties are the effective elastic stiffness, effective fracture energy, and fracture surface, among others. To this end, we define and examine a wide range of geometric descriptors to characterize the micro-texture. These features include the porosity and its local variability, modes of the autocorrelation functions of the random media, and different graph-theoretical features describing the connectivity of the pore network. We use a Bayesian machine learning technique, namely Bayesian Additive Regression Tree to build predictive tools for the macroscopic response of the porous materials. Finally, we leverage the feature selection through BART to determine the key dominant features impacting the elastic and fracture properties.