A Caltech Library Service

Impact-Induced Phase Transformations in Elastic Solids: A Continuum Study Including Numerical Simulations for GeO₂


Winfree, Nancy A. (1999) Impact-Induced Phase Transformations in Elastic Solids: A Continuum Study Including Numerical Simulations for GeO₂. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/4dhf-fj83.


This thesis applies recently developed continuum theories of diffusionless phase transformations in solids to the study of impact problems involving materials which can experience such phase changes. Our objective is to compare the theoretical predictions against certain experimental results.

In the experiments of interest, a face-to-face impact occurs between a disk of amorphous germanium dioxide and another material, either tungsten or an aluminum alloy. The GeO₂ is believed to transform to another phase if sufficient compressive stress is achieved.

We model these experiments using one-dimensional finite elasticity. Phase-changing materials are represented by non-convex potential energy functions. This can produce phase boundaries that propagate subsonically or supersonically with respect to the slower longitudinal wave speed of the two phases. When a subsonic phase boundary is possible, it is not uniquely determined by the fundamental field equations and jump conditions. Uniqueness is obtained by invoking a nucleation criterion to control the initiation of the new phase, and a kinetic relation to govern its evolution.

The experiments considered here are sufficiently long in duration (≈ 3 µs) that several reflections and wave interactions occur, and the analysis becomes analytically intractable. Accordingly, a finite-difference method of Godunov type is employed to analyze these experiments numerically. Methods of Godunov type treat adjoining discretized spatial elements as the two sides of a Riemann problem, which is typically solved approximately by linearizing around the initial conditions on each side. Fortuitously, all constitutive models employed in this thesis are such that the required Riemann problems can be solved exactly without too much effort.

Simulations utilizing the numerical method demonstrate that the impact response of a material is sensitive to the kinetic relation that enters the model. It appears the theory may offer a plausible description of the experiments, though the restrictions placed on the constitutive models herein seem too severe to provide a good quantitative match to the experimental results.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Applied Mechanics
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Applied Mechanics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Knowles, James K. (advisor)
  • Ahrens, Thomas J. (co-advisor)
Thesis Committee:
  • Knowles, James K.
  • Ahrens, Thomas J.
Defense Date:13 May 1999
Record Number:CaltechETD:etd-02262008-153435
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:775
Deposited By: Imported from ETD-db
Deposited On:12 Mar 2008
Last Modified:03 May 2021 15:58

Thesis Files

[img] PDF - Final Version
See Usage Policy.


Repository Staff Only: item control page