EAGER: Network Sparsification for Atomistic to Continuum Scale Solid Mechanics

Florida State University, Tallahassee FL

Investigators

Abstract

This EArly-concept Grant for Exploratory Research (EAGER) award supports the use of network science tools to predict characteristics of materials. Small imperfections (e.g., defects) in solid materials can have a dramatic impact on their material properties. Models that predict these properties can be extraordinarily challenging due to the physical complexity and computer resources required to solve such problems. To overcome this challenge and advance the understanding of defect mechanics, this award will provide the initial support to formulate and validate a new modeling methodology that leverages novel mathematical tools from network science. While network science has been successfully used to understand global properties of systems associated with friendships, spread of diseases, and information over the Internet, it has not been considered for predicting complex material properties of solids. By uncovering the most important local interactions within a solid, the PIs expect to provide new insights into global material characteristics that take material defects into consideration. This has implications on designing new electronic materials, smart actuator and sensor materials for robotics, and materials for energy applications. The network science tools will also be introduced to graduate and undergraduate students through research experiences and courses. A graph theoretic approach to constitutive model predictions of solids will be applied to bridge the gap between atomic structure calculations and continuum field theory of solids. If successful, this approach will provide unique opportunities in solid mechanics to utilize new tools to provide deeper insight of collective atomic behavior as a continuum with advanced predictive power supported by the properties of the underlying network. The PIs plan to utilize such concepts to understand how local atomic forces govern mesoscale constitutive behavior by projecting material physics onto graphs of varying sparsity. Stochastic estimations of deformation based on the discrete graphs will be utilized within a continuum framework to support quantification of stresses near defects in solids. Utilization of Bayesian uncertainty quantification will be used to provide metrics for judging the efficacy of how changes in the network structure (e.g., defects structures) give rise to changes in mesoscale constitutive behavior. Atomistic calculations of a Lennard-Jones potential in one dimension will be extended to two and three dimensional molecular dynamic simulations. Network structures will be formulated from these models and then used for mesoscale continuum homogenization of deformation to assess validity of the network-based characterization of material defects.