Equivalences in Material Structures
Creators: Kucera, Kalan Parker
Publisher: name: University of Alberta Library
Year: 2024

<p>Structure dictates every property and behavior of a material. Concepts of structure used within the field of materials science and engineering (MSE) are diverse, ranging from quantum level phenomena, to the practical development of macroscale components. The sheer volume of variables, scales, and models used to represent some aspect of material structure is immense. There is no current framework for bringing all of the concepts of material structure together, outside of a set of four relations, colloquially known as the materials paradigm. The paradigm relates process to structure to properties to performance, and serves as the ontological basis for the consolidated discipline of materials. </p>

<p>Given that general approach, this thesis offers a new framework for the interpretation, analysis, and validation of materials structures by incorporating concepts of general systems from outside of MSE. In this interdisciplinary work, concepts from various systems philosophies, quantum theory, information theory, category theory, and logic are described and selected as desirable components for a fuller notion of material structure. The idea of an enriched material structure leads to the construction of a functional framework for the analysis of aspects of materials systems on the basis of criteria of equivalence. If structure is more generally defined as that which is invariant across change, then equivalence is a natural determinate of shared structure. A multi-component structural equivalence framework is proposed, composed of five different senses of structure: definitional, empirical, informational, categorical, and theoretical.</p>

<p>The proposed structural equivalence framework organizes the different forms of structure which are drawn out of the multivariate analysis offered by each individual form. Through the rigorous definition of each form, models of materials structure in any arrangement can be equated with others, in order to parse out structure. Definitional equivalence can measure how much overlap the vocabularies and foundational concepts two models might share. Empirical equivalence can measure the overlap, or translatability, of the data sets produced by methods within each theory. Informational equivalence can measure the available communication pathways between data (and other) sets within models. Categorical equivalence can compare inherent, or associated, mathematical structures between models. Finally, theoretical equivalence can measure the overlap or translatability of two theories on the basis of the shared structure between the models of those theories (which take the other forms of equivalence into account). This thesis holds that these five senses of equivalence provide a richer version of abstract structural modeling and validation than is currently used.</p>

<p>Using this structural equivalence framework, different aspects of materials structure are investigated including: the general structural form of a conceptual multi-scale bridging technique between atomistic and continuum computational methods; a validation of informational structures produced by variances across X-ray diffraction results for copper samples processed in different manners; a survey of the general structures of creep models for copper; and an analysis of the variable used to represent average grain size in two different creep models for copper. The results of these investigations illustrate the utility—and current boundaries—of the structural equivalence framework when applied directly to concrete materials systems. </p>

<p>The work in this thesis is wide ranging, and offers contributions to multiple fields of study. For those in MSE, it offers new techniques of model validation, model construction, data analysis, and integration of methods from information science and logic. The novel approach of the structural equivalence framework also presents an opportunity for re-evaluation of historical data; a method to recontextualize experiments into the modern ‘vocabulary’ of the discipline. For those outside of MSE, it offers an insight into the approaches, techniques, and a touchpoint for integration of other fields with the vast created knowledge of MSE. Furthermore, this thesis offers an enriched materials ontology, inclusive of multiple structural concepts in an attempt to continue to build towards the goal of an all-encompassing science of materials. </p>