A theory of amorphous solids
undergoing large deformations, with applications to
polymers and metallic glasses


Lallit Anand
Department of Mechanical Engineering
Massachussetts Institute of Technology
Cambridge, MA 02139, USA
anand@mit.edu


Morton E. Gurtin
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA 15213, USA
mg0c@andrew.cmu.edu

Abstract

This paper dvelops a continuum theory for the elastic-viscoplastic deformation of amorphous solids such as polymeric and metallic glasses. Introducing an internal-state variable that represents the local free-volume assocated with certain metastable states, we are able to capture the highly non-linear stres-strain behavior that precedes the yield-peak and gives rise to post-yield strain-softening. Our theory explicitly accounts for the dependence of the Helmholtz free energy on the plastic deformation in a thermodynamically consistent manner. This dependence leads directly to a backstress in the underlying flow rule, and alllows us to model the rapid strain-hardening response after the initial yield-drop in monotonic deformations, as well as the Bauschinger-type reverse-yielding phenomena typically observed in amorphous polymeric solids upon unloading after large plastic deformations. We have implemented a special set of constitutive equations resulting from the general theory in a finite-element computer program. Using this finite-element program, we apply the specialized equations to model the large-deformation response ofthe amorphous polymeric solid polycarbonate, at ambient temperature and pressure. We show numerical results to some representative problems, and compare them against corresponding results from physical experiments.

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