# The archetype-genome exemplar in molecular dynamics and continuum mechanics

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## Abstract

We argue that 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, this work presents the mathematical ingredients and computational implementation of theories in solid mechanics that are (1) molecular and (2) continuum manifestations of the assembly process. Both coarse-grained molecular dynamics (CGMD) and the archetype-blending continuum (ABC) theories are formulated then applied to polymer nanocomposites (PNCs) to demonstrate the impact the components of the assembly triplet have on a material genome. CGMD simulations demonstrate the sensitivity of nanocomposite viscosities and diffusion coefficients to polymer chain types (archetype), polymer–nanoparticle interaction potentials (interaction), and the structural configuration (conformation) of dispersed nanoparticles. ABC simulations show the contributions of bulk polymer (archetype) properties, occluded region of bound rubber (interaction) properties, and microstructural binary images (conformation) to predictions of linear damping properties, the Payne effect, and localization/size effects in the same class of PNC material. The paper is light on mathematics. Instead, the focus is on the usefulness of the archetype-genome exemplar to predict system behavior inaccessible to classical theories by transitioning mechanics away from heuristic laws to mechanism-based ones. There are two core contributions of this research: (1) presentation of a fundamental axiom—the archetype-genome exemplar—to guide theory development in computational mechanics, and (2) demonstrations of its utility in modern theoretical realms: CGMD, and generalized continuum mechanics.

## Keywords

Materials genome Archetype Coarse-graining Continuum mechanics Molecular dynamics Polymer## Notes

### Acknowledgments

This work is supported by NSF CMMI Grants 0823327 and 0928320, as well as by NSF IDR CMM Grant I 1130948. M. Steven Greene warmly thanks the National Science Foundation GRFP for its support. Y. Li acknowledges financial support from Ryan Fellowship and Royal E. Cabell Terminal Year Fellowship at Northwestern University. W.K. Liu was also supported by the World Class University Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science, and Technology. The authors would also like to thank Assistant Professor Khalil Elkhodary at the American University in Cairo, Egypt and Professor Shan Tang at Chongqing University in China for their challenging discussions and assistance with clarifying many of the concepts presented herein.

## Supplementary material

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