227 research outputs found
Athermal Shear-Transformation-Zone Theory of Amorphous Plastic Deformation II: Analysis of Simulated Amorphous Silicon
In the preceding paper, we developed an athermal shear-transformation-zone
(STZ) theory of amorphous plasticity. Here we use this theory in an analysis of
numerical simulations of plasticity in amorphous silicon by Demkowicz and Argon
(DA). In addition to bulk mechanical properties, those authors observed
internal features of their deforming system that challenge our theory in
important ways. We propose a quasithermodynamic interpretation of their
observations in which the effective disorder temperature, generated by
mechanical deformation well below the glass temperature, governs the behavior
of other state variables that fall in and out of equilibrium with it. Our
analysis points to a limitation of either the step-strain procedure used by DA
in their simulations, or the STZ theory in its ability to describe rapid
transients in stress-strain curves, or perhaps to both. Once we allow for this
limitation, we are able to bring our theoretical predictions into accurate
agreement with the simulations.Comment: 10 pages, 7 figures, second of a two-part series. Reorganized paper
with no substantial changes in conten
Athermal Nonlinear Elastic Constants of Amorphous Solids
We derive expressions for the lowest nonlinear elastic constants of amorphous
solids in athermal conditions (up to third order), in terms of the interaction
potential between the constituent particles. The effect of these constants
cannot be disregarded when amorphous solids undergo instabilities like plastic
flow or fracture in the athermal limit; in such situations the elastic response
increases enormously, bringing the system much beyond the linear regime. We
demonstrate that the existing theory of thermal nonlinear elastic constants
converges to our expressions in the limit of zero temperature. We motivate the
calculation by discussing two examples in which these nonlinear elastic
constants play a crucial role in the context of elasto-plasticity of amorphous
solids. The first example is the plasticity-induced memory that is typical to
amorphous solids (giving rise to the Bauschinger effect). The second example is
how to predict the next plastic event from knowledge of the nonlinear elastic
constants. Using the results of this paper we derive a simple differential
equation for the lowest eigenvalue of the Hessian matrix in the external strain
near mechanical instabilities; this equation predicts how the eigenvalue
vanishes at the mechanical instability and the value of the strain where the
mechanical instability takes place.Comment: 17 pages, 2 figures
Direct Identification of the Glass Transition: Growing Length Scale and the Onset of Plasticity
Understanding the mechanical properties of glasses remains elusive since the
glass transition itself is not fully understood, even in well studied examples
of glass formers in two dimensions. In this context we demonstrate here: (i) a
direct evidence for a diverging length scale at the glass transition (ii) an
identification of the glass transition with the disappearance of fluid-like
regions and (iii) the appearance in the glass state of fluid-like regions when
mechanical strain is applied.
These fluid-like regions are associated with the onset of plasticity in the
amorphous solid. The relaxation times which diverge upon the approach to the
glass transition are related quantitatively.Comment: 5 pages, 5 figs.; 2 figs. omitted, new fig., quasi-crystal discussion
omitted, new material on relaxation time
Harmonic Labeling of Graphs
Which graphs admit an integer value harmonic function which is injective and
surjective onto ? Such a function, which we call harmonic labeling, is
constructed when the graph is the square grid. It is shown that for any
finite graph containing at least one edge, there is no harmonic labeling of
Athermal Shear-Transformation-Zone Theory of Amorphous Plastic Deformation I: Basic Principles
We develop an athermal version of the shear-transformation-zone (STZ) theory
of amorphous plasticity in materials where thermal activation of irreversible
molecular rearrangements is negligible or nonexistent. In many respects, this
theory has broader applicability and yet is simpler than its thermal
predecessors. For example, it needs no special effort to assure consistency
with the laws of thermodynamics, and the interpretation of yielding as an
exchange of dynamic stability between jammed and flowing states is clearer than
before. The athermal theory presented here incorporates an explicit
distribution of STZ transition thresholds. Although this theory contains no
conventional thermal fluctuations, the concept of an effective temperature is
essential for understanding how the STZ density is related to the state of
disorder of the system.Comment: 7 pages, 2 figures; first of a two-part serie
Branching Instabilities in Rapid Fracture: Dynamics and Geometry
We propose a theoretical model for branching instabilities in 2-dimensional
fracture, offering predictions for when crack branching occurs, how multiple
cracks develop, and what is the geometry of multiple branches. The model is
based on equations of motion for crack tips which depend only on the time
dependent stress intensity factors. The latter are obtained by invoking an
approximate relation between static and dynamic stress intensity factors,
together with an essentially exact calculation of the static ones. The results
of this model are in good agreement with a sizeable quantity of experimental
data.Comment: 9 pages, 11 figure
- …