The construction of a genome from building blocks, termed archetypes, is the archetype-genome exemplar. Archetypes may be crystal lattice unit cells, nano-sized precipitates or inclusions, monomers, turbine blades, or any other substructure in a system of interest. Assemblies may be a polycrystal alloy specimen, nanowire, polymer-matrix composite, jet engine, or any other conformation of component-level archetypes. The entirety of properties of those assemblies are their genomes, such as yield strain, ultimate strength, energy dissipation capacity, fracture toughness, conductivity, permeability, or size effects. Understanding this dependence is at the core of all multiscale methods, mechanism-based or simulation-based constitutive laws, and stochastic micromechanics: pillars of the Modern Era of Mathematical Physics. We will present the mathematical construction and computational implementation of new theories that contain new forms of traditional balance laws and physically consistent constitutive relations that, by rethinking conventional micromechanics, account for each piece of the genome assembly triplet: archetypes, interactions, and their conformation. Continuum theories that consider the entire triplet are rare, but an additional complication arises in the archetype-genome exemplar. Since archetypes and their interactions contain properties difficult to characterize with high fidelity, and since these same archetypes conform randomly after mixing and processing, the material genome is random. The impact of uncertainty and its mathematical formulation on material genome predictions will also be given. The ultimate goal is that the proposed archetype-genome exemplar, which is part of the effort to build virtual material genome database that is integrated into a predictive simulation toolbox, will enable the certification of materials leading to predictable and desired performance at the macroscale. Applications to metallic material systems and polymer matrix composites design will be given.
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