Predicting Dynamics in Unstable and Active Solids

Syracuse University, Syracuse NY

Investigators

Abstract

NONTECHNICAL SUMMARY This award supports computational and theoretical research and education. Theory and computer simulations will be used in this research to predict how solid-like materials move and fail. It focuses on materials that are disordered – where the constituent parts are all jumbled up – because there is not yet a good understanding of how such materials fail. Examples of such societally important material failure events are everywhere – ranging from rupture of a plastic container or grain silo to avalanches and mudslides. By understanding how these materials behave while they are failing, we will be able to better predict failure events and rationally design materials that resist failure or fail in precise, pre-programmed ways. In addition, a new class of active matter materials, where the constituent parts can move by themselves, are being developed in labs all over the world. However, there are no well-established theories for how those materials flow and fail when the constituent parts are tightly packed together. This project seeks to identify similarities between new active matter solids and non-active solids that are in the process of failing, to better predict the behavior of active solids. An additional goal is to design, or engineer disordered active solids to move in a programmed way to execute tasks. Crowds composed of animals or humans can be thought of as a type of active “solid”. Dense human crowds exhibit many of the features of solid-like materials, including the ability to support waves composed of small changes to crowd density, which are known as sound waves in ordinary materials, as well as dangerous failure events which can lead to crushing. However, since human crowds are actively moving at all times, existing theories for static solids cannot be applied to them. This research will develop a new set of theoretical and computational tools to model failure in active matter crowds. A long-term goal of this work is to understand which types of crowd structures are more likely to lead to local crushing events, and to develop tools to predict and prevent such events. Finally, this project will contribute to the education and professional development of a broad pipeline of interdisciplinary scientists and engineers. It will support ongoing efforts to broaden the participation of under-represented groups, including women, in STEM fields through professional development programming, and support the PI to develop a new “active matter” module for upper-division undergraduate and graduate students in an interdisciplinary Physical Cell Biology class. TECHNICAL SUMMARY This award supports theoretical research and education. The PI aims to develop a broad theoretical and computational framework for predicting the dynamics of unstable and active solids, by exploiting and extending previously developed methods that use vibrational modes to predict deformation in stable disordered materials. The first objective is to use a new computational method to quantify the localized deformations and normal modes of unstable disordered solids during an avalanche or catastrophic failure event. These data will be used to develop an analytic continuum model that predicts brittle and ductile failure and incorporates features of both elasto-plastic and shear transformation zone models. The second objective is to elucidate a nascent connection between sheared particulate matter and active self-propelled particles, using a new computational technique. The third objective is to create a stable active matter simulation, based on “point-of-interest” human crowds, and match it to a non-active simulation with an artificial external potential, as a tractable starting point for extending vibrational mode analysis directly to active systems. This will enable simulations that gradually tune away from the stable active solid in order to generate a theoretical framework that can make accurate predictions about density fluctuations in human crowds and other active matter systems. This project will advance knowledge by identifying new types of material behaviors that are possible for driven or active systems at very high densities. Unlike active gases or fluids, these high density unstable and active solids can transmit shear stresses, exhibit strongly anisotropic behavior, and likely store memories. Preliminary data suggests these new methods can be used to predict dynamics and behavior in active or unstable avalanching systems, which would represent a systematic approach to rationally design active solids to exhibit specified rheological behaviors or accomplish tasks. A second thrust will focus on a new idea for quantitatively comparing sheared particulate systems and active matter, in order to understand which ideas from well-studied sheared systems can be adapted to make prediction for active matter, and also where there are important differences between sheared and active systems that require new theories. Together, this will permit the development of an analytic continuum model for predicting avalanches and instabilities in both sheared and active matter systems. This work is applicable to problems of societal import. Avalanches and catastrophic brittle failure in granular materials and structural glasses are important in industry and nature – the tools developed here to constrain continuum models based on microscopic material properties could improve scientists’ ability to predict earthquake and landslide dynamics, as well as help rationally design better structural materials. This funding would also contribute to a societal goal of broadening participation in STEM, through training and mentoring of female scientists, including a systematic series of women-specific professional development events. As part of this proposal, the PI will also develop an active matter module, with lecture materials, active learning exercises, and a group research project that will be deployed in a course for upper-level undergraduate and graduate students. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.