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Variational and Multiscale Modeling of Amorphous Silica Glass


Schill, William Joseph (2020) Variational and Multiscale Modeling of Amorphous Silica Glass. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/B2A9-RQ38.


We develop a critical-state model of fused silica plasticity on the basis of data mined from molecular dynamics (MD) calculations. The MD data is suggestive of an irreversible densification transition in volumetric compression resulting in permanent, or plastic, densification upon unloading. Moreover, this data exhibits dependence on temperature and the rate of deformation. We show that these characteristic behaviors are well-captured by a critical state model of plasticity, where the densification law for glass takes the place of the classical consolidation law of granular media and the locus of constant volume states denotes the critical-state line. A salient feature of the critical-state line of fused silica, as identified from the MD data, that renders its yield behavior anomalous is that it is strongly non-convex, owing to the existence of two well-differentiated phases at low and high pressures. We argue that this strong non-convexity of yield explains the patterning that is observed in molecular dynamics calculations of amorphous solids deforming in shear. We employ an explicit and exact rank-2 envelope construction to upscale the microscopic critical-state model to the macroscale. Remarkably, owing to the equilibrium constraint the resulting effective macroscopic behavior is still characterized by a non-convex critical-state line. Despite this lack of convexity, the effective macroscopic model is stable against microstructure formation and defines well-posed boundary-value problems. We present examples of ballistic impact of silica glass rods by way of the optimal transport meshfree method. We extend the study of the inelastic behavior of silica glass to include the effect of many different temperatures, pressures, and strain rates using MD and maximum entropy atomistics (MXE) calculations. Owing to the temperature dependence of the model, the macroscopic model becomes unstable against adiabatic shear localization. Thus, the material adopts small inter-facial regions where the shear strain is extremely high. We characterize the shear band size, thereby predicting a yield knockdown factor at the macroscale, and compare the results to behavior reported in flyer plate impact experiments.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Engineering mechanics, Amorphous solids, silica glass, Calculus of variations, non-convexity, shear localization, plasticity theory, molecular dynamics, multiscale modeling, microstructure formation, patterning
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Mechanical Engineering
Awards:Centennial Prize for the Best Thesis in Mechanical and Civil Engineering, 2020.
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Ortiz, Michael
Thesis Committee:
  • Bhattacharya, Kaushik (chair)
  • Ortiz, Michael
  • Lapusta, Nadia
  • Stainier, Laurent F.
Defense Date:6 June 2019
Funding AgencyGrant Number
Office of Naval Research (ONR)N000141512453
Philip G. Saffman Endowed Graduate FellowshipUNSPECIFIED
Record Number:CaltechTHESIS:07202019-135213721
Persistent URL:
Related URLs:
URLURL TypeDescription content for Chapter 2.
Schill, William Joseph0000-0003-0950-7433
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:11744
Deposited By: William Schill
Deposited On:23 Jul 2019 20:32
Last Modified:10 Dec 2020 00:00

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