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"Nonlinear Physics Seminar: The geometry and mechanics of growth and defects in amorphous materials" | The Racah Institute of Physics

"Nonlinear Physics Seminar: The geometry and mechanics of growth and defects in amorphous materials"

Date: 
Wed, 10/06/201512:00-13:30
Location: 
Danciger B building, Seminar room
Lecturer: Mr. Michael Moshe
Affiliation: Racah Institute of Physics,
The Hebrew University of Jerusalem
Abstract:
In my talk I will address two main
topics that are related to plastic
deformations and growth of
amorphous materials, in effectively
2D systems. I will use the geometric
formalism of incompatible elasticity
in order to describe these processes
and solve for the stress states of the
bodies.
The first topic concerns the
challenge of describing the intrinsic
geometry of defects in amorphous
materials. We argue that defects can
be defined as local deviations of the
material's reference metric field,
from a Euclidian metric. This
definition allows the description of
intrinsic defects in amorphous, as
well in crystalline materials, and
allows for the formulation of the
non-linear elastic problem. The
reference metrics that describe
isolated defects are obtained via
multipole expansion of the reference
Gaussian curvature field, leading to a
hierarchy of defects. I will show the
equivalence of the monopole and
dipole cases to known defects in
crystals. Finally, I will focus on the
quadrupole terms that describe
localized deformations, reminiscent
of Eshelby inclusions, and on the
way in which an ensemble of defects
is described in the formalism.
In the second part of the talk I will
present a new analytical method that
allows the calculation of the
equilibrium stress field in residually
stressed bodies. The method, which
is a generalization of the stress
function approach, enables the
calculation of the solution to the non-
linear incompatible elastic problem.
Using geometric compatibility
conditions, the method provides
exact equations for the
“Incompatible Stress Function” (ISF)
for arbitrary material’s constitutive
law. The relevant equations can be
solved in a controlled level of
linearization. Application of the ISF
method to cases of bodies that
contain defects (as defined earlier)
allows the derivation of quantitative
expressions for the interaction
energies of any kind of defects with
each other and with external fields. I
will demonstrate the relevance of
these results to the development of
geometrical modeling of plasticity in
amorphous materials and for elastic
meta-materials.