Thermomechanical Variational Principles for Dissipative Materials with Application to Strain Localization in Bulk Metallic Glasses

Citation

Yang, Qiang (2004) Thermomechanical Variational Principles for Dissipative Materials with Application to Strain Localization in Bulk Metallic Glasses. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/6FV2-KV63. https://resolver.caltech.edu/CaltechETD:etd-05282004-152537

Abstract

This thesis is concerned with variational principles for general coupled thermomechanical problems in dissipative materials including finite elastic and plastic deformation, non-Newtonian viscosity, rate sensitivity, arbitrary flow and hardening rule, as well as heat conduction. It is shown that there exists a potential function such that both the conservation of energy and balance of linear momentum are the Euler-Lagrange equations of its first variation. Inspired from the time-discretized version of the variational formulation, we present a procedure for variational thermomechanical update, which generalizes the isothermal approach under a variational thermodynamic framework. This variational formulation then serves as a basis for temperature change as well as constitutive updates.

An important application of the variational formulation is to optimize the shear band thickness in strain localization processes. We show that this optimization takes the form of a configurational-force equilibrium and results in a well-defined band thickness. We further implement displacement discontinuities into a class of strain-localization finite elements. These elements consist of two surfaces, attached to the abutting volume elements, which can separate and slip relative to each other, and thus enable the accurate and efficient simulation of the dynamical formation of stain localization.

The variational formulation also leads to a finite-deformation continuum modeling of bulk metallic glasses. It is shown that the strain softening of bulk metallic glasses is due to the increase of free volume (and thus the decrease of viscosity), while temperature rise accelerates the localization of the deformation. The model reproduces the constitutive behavior of Vitreloy 1 bulk metallic glass at various strain rates and temperatures.

Thesis Files