Krakowiak, Konrad J.2022-06-30May 20212021-05May 2021Portions of this document appear in: Nannapaneni, Raj Gopal, Kalyana Babu Nakshatrala, Damian Stefaniuk, and Konrad J. Krakowiak. "Discrete Lattice Modeling of Wave Propagation in Materials with Heterogeneous Microstructures." Journal of Engineering Mechanics 147, no. 10 (2021): 04021075.https://hdl.handle.net/10657/10229With the recent advances in material science and additive manufacturing, there has been an ever-growing trend in developing materials with novel properties. These materials are often heterogeneous composites---with complex microstructures influencing their overall structural behavior. Though non-destructive evaluation using wave propagation can offer the mechanical properties of the composite, experimental methods to gain insights into the relationship between microstructure and mechanical properties can be cumbersome and time-consuming. Hence, researchers prefer computational modeling of materials to trial-and-error experiments. Among the contemporary numerical methods to study heterogeneous materials, discrete lattice models can seamlessly incorporate complex microstructural heterogeneities into the model. However, the available lattice models suffer from numerous deficiencies such as the limitation of Poisson’s ratio, not being isotropic (naïve square lattice), incorporating additional elements or additional degrees of freedom, and not practical for complex domains (equilateral triangle, hexagon lattices). Hence we aim to develop a lattice model that can span the admissible Poisson’s ratio values with a minimum number of elements and degrees of freedom. We use the Lagrangians in continuum and discrete systems, identify the shortcomings in the lattice model and offer a solution to make the lattice isotropic without the limitation of Poisson’s ratio. This model is verified on the benchmark problems and applied to study wave propagation in the heterogeneous microstructure of hydrated cement paste. Furthermore, studying the influence of microstructure on wave propagation in heterogeneous materials needs exploring different material classes with distinct mechanical properties. Given the number of input parameters to operate with, one needs sensitivity analysis to reduce the dimensionality of the input parameter space. One among the many available techniques is the Shapley value---a solution concept from cooperative game theory to identify the marginal contribution of the individual parameters---was recently being used in machine learning to quantify the weights of a neural network. In this work, this technique is applied to rank the input parameters based on their influence on wave attenuation in materials with matrix-inclusion morphology of circular inclusions.application/pdfengThe author of this work is the copyright owner. UH Libraries and the Texas Digital Library have their permission to store and provide access to this work. UH Libraries has secured permission to reproduce any and all previously published materials contained in the work. Further transmission, reproduction, or presentation of this work is prohibited except with permission of the author(s).wave propagationheterogeneous microstructureslattice spring models2022-06-30Thesisborn digital