Collaborative Research: Connecting Atomistic and Continuum Amorphous Solid Mechanics via Non-equilibrium Thermodynamics

Harvard University, Cambridge MA

Investigators

Abstract

NONTECHNICAL SUMMARY This award supports computational and theoretical research, and education on materials deformation. The objective of this collaborative research project is to develop computational models to predict the deformation and failure of a class of materials known as amorphous solids, particularly focusing on structural metallic glasses. The atoms in amorphous solids are arranged in a highly disordered structure unlike crystals in which atoms are arranged into a regular repeating structure. The current research seeks to go beyond directly simulating the atomic scale behavior using techniques like molecular dynamics simulations. While molecular dynamics simulation has been groundbreaking, this technique is computationally intensive and cannot be scaled up to model structures on scales of typical practical engineering interest. This research will focus on translating information from molecular dynamics simulations to computationally efficient models at larger scales. In doing so, comparisons will be made between atomic scale representations and larger scale theories to ensure that the larger scale theories are statistically consistent and adequately verified. Particular attention will be paid to testing whether they capture the mechanisms governing material behavior and the inherent variability that results from the disordered atomic configurations. This verification will permit the use of these models for testing theories of large-scale material behavior, particularly failure and fracture; successful theories will help to enable the design of amorphous materials wherein the structure of a material is chosen to meet certain performance objectives, and permitting the assessment of the reliability of engineering materials. The insights gained and methods employed in this research have the potential to transform the way in which length-scales are spanned in the study of the mechanics of materials beyond those with amorphous structure. This award also supports educational initiatives at both Johns Hopkins University and Harvard University. These will address the critical need to integrate computational methods into the core Materials Science and Engineering curriculum while also engaging elementary school students in high-need urban schools through the NSF funded STEM Achievement in Baltimore Elementary Schools project. TECHNICAL SUMMARY This award supports computational and theoretical research, and education on nonequilibrium properties of materials with a focus on deformation. Atomistic mechanisms govern both a material's kinetics and the manner in which its structure evolves during the inherently nonequilibrium process of deformation and failure. The need to establish numerically tractable continuum descriptions of viscoplasticity that incorporate atomistic mechanisms in ways that retain their essential aspects presents a grand challenge at the intersection of physics and mechanics. The strategy employed in this research for reducing the operative degrees of freedom is to extend thermodynamic concepts beyond their common equilibrium application. The configurational entropy will be deployed in the context of the shear transformation zone theory to make quantitative predictions of deformation and failure processes in amorphous solids. This study will utilize molecular dynamics simulation to parameterize a highly optimized fully Eulerian implementation of the shear transformation zone theory that permits investigation of very large strains such as those that arise in failure processes like strain localization and fracture. This will require development and analysis of new numerical projection methods for viscoplasticity. The shear transformation zone constitutive law differs from existing relations insofar as it makes reference to a configurational effective temperature that quantifies the structure. These structural parameters can be independently measured in molecular dynamics to cross-validate the predictions of the numerical implementations of the constitutive theory. Rigorous statistical comparisons will be made through a novel stochastic framework that establishes a random field representation of the atomic potential energy that is translated to a continuum effective temperature. This work will validate predictions of the mechanical response of metallic glasses, emerging structural materials, both during homogeneous flow near the glass temperature and during the development of plastic localization and fracture at lower temperatures in a manner that accounts for inherent fluctuations and correlations associated with the material's amorphous structure. This will lead to a greatly increased understanding of deformation and failure in materials with varying degrees of disorder and predictive numerical schemes suitable for large strains that can be rigorously analyzed and deployed in engineering contexts. This award also supports educational initiatives at both Johns Hopkins University and Harvard University. These will address the critical need to integrate computational methods into the core Materials Science and Engineering curriculum while also engaging elementary school students in high-need urban schools through the NSF funded STEM Achievement in Baltimore Elementary Schools project.