Mechanics and Physics of Solids, Uncertainy, and the Archetype-Genome Exemplar.

다국어 초록 (Multilingual Abstract)

This dissertation argues that the mechanics and physics of solids rely on a fundamental exemplar: the apparent properties of a system depend on the building blocks that comprise it. Building blocks are referred to as archetypes and apparent system properties as the system genome. Three entities are of importance: the archetype properties, the conformation of archetypes, and the properties of interactions activated by that conformation. The combination of these entities into the system genome is called assembly.
To show the utility of the archetype-genome exemplar, the dissertation presents the mathematical construction and computational implementation of a new theory for solid mechanics that is a continuum manifestation of the assembly process. The so-called archetype-blending continuum theory aligns the form of globally valid balance laws with physics evolving in a material's composite constitutive response so that, by rethinking conventional micromechanics, the theory accounts naturally for each piece of the genome assembly triplet: archetypes, interactions, and their conformation. With the pieces of the triplet isolated in the theory, materials genome design concepts that separately control microstructure and property may be gleaned from exploration of the constitutive parameter space. A suite of simulations that apply the new theory to polymer nanocomposite materials demonstrate the ability of the theory to predict a robust material genome that includes damping properties, modulus weakening, local strain amplification, and size effects.
The dissertation also presents a theoretical assessment of the importance of uncertainty propagation in the archetype-genome exemplar. The findings from a set of computational experiments on instances of a general class of microstructured materials suggest that when overlap occurs between the size of the system geometry and the features of the conformation, material genomes become less certain. Increasing nonuniformity of boundary conditions and the size of random field correlation lengths exacerbate this conclusion. These criteria are combined into a scalar metric used to assess the impact of archetype-level uncertainties on the material genome for general scenarios in solid mechanics. Exemplary benchmark problems include bending in elastoplasticity and instability-induced pattern transition in porous elastomer.
The contributions of this dissertation are threefold: (1) the mathematical construction of a new continuum theory for mechanics and physics of solids, (2) implementation of the theory, and (3) theoretical assessment of the scenarios in which material genomes deviate from determinism.