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Award Abstract #0411035
The Response of Composites and Quasiconvexity
| NSF Org: |
DMS
Division of Mathematical Sciences
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| Initial Amendment Date: |
June 25, 2004 |
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| Latest Amendment Date: |
February 27, 2006 |
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| Award Number: |
0411035 |
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| Award Instrument: |
Standard Grant |
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| Program Manager: |
Henry A. Warchall
DMS Division of Mathematical Sciences
MPS Directorate for Mathematical & Physical Sciences
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| Start Date: |
July 1, 2004 |
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| Expires: |
June 30, 2008 (Estimated) |
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| Awarded Amount to Date: |
$312634 |
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| Investigator(s): |
Graeme Milton milton@math.utah.edu (Principal Investigator)
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| Sponsor: |
University of Utah
75 S 2000 E
SALT LAKE CITY, UT 84112 801/581-6903
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| NSF Program(s): |
MSPA-INTERDISCIPLINARY,
MATH PRIORITY SOLICITATION,
APPLIED MATHEMATICS
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| Field Application(s): |
0000099 Other Applications NEC
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| Program Reference Code(s): |
OTHR, 7303, 0000
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| Program Element Code(s): |
7454, 7446, 1266
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ABSTRACT
Proposal: DMS-041103
PI: Graeme W. Milton
Institution: University of Utah
Title: The Response of Composites and Quasiconvexity
ABSTRACT
This work will improve our understanding of creep in composite materials, through establishing bounds on the total creep and identifying microstructures that exhibit the maximum or minimum possible creep. It will also identify microstructures which are best for guiding stress in linear elasticity. These composites should be useful for distributing or concentrating the force in a structure. Additionally, microstructures will be identified with an anomalous Hall coefficient, which could potentially be useful in reducing stray electric fields in circuit design when there is a magnetic field present. In a second part of the work three fundamental problems will be studied: characterizing the surfaces in tensor space associated with sets of effective tensors of hierarchical laminate geometries; exploring the connection between rank-one convexity and quasiconvexity; and developing new tools for bounding the effective moduli of composites and for bounding the quasiconvexification of a function. These problems are important for making progress on the question of what responses of composites are or are not possible. Their solution could, in a wide variety of cases, make numerically tractable the search for the possible macroscopic responses of composites.
A better understanding of the macroscopic response of materials is of central technological importance. This importance stretches across the board, from understanding the macroscopic response of engineered materials (of critical importance to the defence, automative, and aerospace industries), to understanding the macroscopic response of polycrystalline and porous rocks (relevant to earthquake prediction and to the oil industry), to understanding the macroscopic response of sea ice (important to climate modelling), to understanding the macroscopic response of biological materials (such as tissues, bones, shells and tendons). In the past many useful composites were obtained by trial and error, or by mimicking composites found in nature, or by using intuition. In this century we will have greater flexibility to produce designer composites tailor made to meet specific needs. Improving our understanding of the response of composites will facilitate the construction of these designer composites.
PUBLICATIONS PRODUCED AS A RESULT OF THIS RESEARCH
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(Showing: 1 - 10 of 13)
(Showing: 1 - 13 of 13)
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D. Zhang and E. Cherkaev. "Pade approximations for identification of air bubble volume from temperature- or frequency-dependent permittivity of a two-component mixture," Inverse Problems in Science and Engineering, v.16, 2008, p. 425.
G. W. Milton, M. Briane and J. R. Willis. "On cloaking for elasticity and physical equations with a transformation invariant form," New Journal of Physics, v.8, 2006, p. 248.
G.W. Milton and N.A. Nicorovici. "On the cloaking effects associated with anomalous localized resonance," Proceedings Royal Society A, v.462, 2006, p. 3027.
G.W.Milton, N.A.Nicorovici and R.C.McPhedran. "Opaque perfect lenses," Physica B, v.394, 2007, p. 171.
Graeme W. Milton and John R. Willis. "On modifications of Newton's second law and linear continuum elastodynamics," Proceedings Royal Society A, v.463, 2007, p. 855.
Graeme W. Milton, Nicolae-Alexandru P. Nicorovici, Ross McPhedran, and Viktor Podolskiy
Viktor A. Podolskiy. "A proof of superlensing in the quasistatic regime, and limitations of superlenses in this regime due to anomalous localized resonance.," Proceedings of the Royal Society A, v.461, 2005, p. 3999.
H.Kang and G.W.Milton. "Solutions to the Pólya-Szegö Conjecture and the Weak Eshelby Conjecture," Archives for Rational Mechanics and Analysis, v.188, 2008, p. 93.
Hyeonbae Kang and Graeme W. Milton. "On conjectures of Polya-Szego and Eshelby," Contemporary Mathematics, v.408, 2006, p. 75.
M. Briane, D. Manceau, and G.W. Milton. "Homogenization of the two-dimensional Hall effect," Journal of Mathematical Analysis and Applications, v.339, 2008, p. 1468.
N.A.Nicorovici, G.W.Milton, R.C.McPhedran, and L.C.Botten. "Quasistatic cloaking of two-dimensional polarizable discrete systems by anomalous resonance," Optics Express, v.15, 2007, p. 6314.
V. Vinogradov and G. W. Milton. "An accelerated FFT algorithm for thermoelastic and non-linear composites," International Journal for Numerical Methods in Engineering, 2008.
V. Vinogradov and G.W. Milton. "The total creep of viscoelastic composites under hydrostatic or antiplane loading," Journal of the Mechanics and Physics of Solids, v.53, 2005.
Viktor A. Podolskiy, Nicholas A. Kuhta, And Graeme W. Milton. "Optimizing the superlens: Manipulating geometry to enhance the resolution," Applied Physics Letters, v.87, 2005, p. 231113.
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