Macroscopic behavior and field statistics in viscoplastic
composites
Mr. Martin I. Idiart, Ph.D. Candidate
Advisor: Professor Pedro Ponte Castañeda
Department of Mechanical Engineering and Applied Mechanics
University of Pennsylvania
Abstract
A wide range of man-made as well as natural materials of
interest in engineering and physical sciences are inherently
heterogeneous. Common examples are particle-reinforced composites,
porous materials, and polycrystalline solids such as metals,
ice, and many rocks. A fundamental problem in mechanics
of materials is the estimation of the macroscopic response
of such heterogeneous materials from the properties and
geometrical arrangement (microstructure) of their constituents.
However, under many circumstances, it is also important,
and even essential, to estimate certain statistics of the
spatial distribution of the local fields within the composite.
This is particularly relevant for viscoplastic composites
undergoing large, finite deformations, in which case, certain
knowledge about the spatial distribution of the strain-rate
field (e.g.
phase averages) is necessary to be able to account for the
evolution of the microstructure, which strongly affects
the macroscopic behavior. In addition, information on the
stress distribution can be useful for developing statistical
theories of damage nucleation and evolution in these materials.
To this end, we have developed nonlinear homogenization
methods capable of delivering estimates not only for the
macroscopic behavior but also for the field statistics in
viscoplastic composites. These methods are based on suitably
designed variational principles, which make use of an optimally
chosen ``linear comparison composite''. The variational
structure of these methods is then exploited to obtain estimates
for the field statistics that are entirely consistent with
the corresponding estimates for the effective behavior.
Sample results will be given for two-phase composites with
random particulate microstructures, for which exact results
and numerical simulations are available. Homogenization
estimates are found to be in good agreement with the exact
results, even for high nonlinearities, where the strain-rate
fields are found to become strongly heterogeneous.
Tuesday, May 2nd
305 Towne Bldg.
11:00 – 12:00 noon
