Recovery of inclusion separations in strongly heterogeneous composites from effective property measurements
An effective property of a composite material consisting of inclusions within a host matrix depends on the geometry and connectedness of the inclusions. This dependence may be quite strong if the constituents have highly contrasting properties. Here, we consider the inverse problem of using effectiv...
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crroyalsociety:10.1098/rspa.2011.0527 2024-06-02T08:14:19+00:00 Recovery of inclusion separations in strongly heterogeneous composites from effective property measurements Orum, Chris Cherkaev, Elena Golden, Kenneth M. 2011 http://dx.doi.org/10.1098/rspa.2011.0527 https://royalsocietypublishing.org/doi/pdf/10.1098/rspa.2011.0527 https://royalsocietypublishing.org/doi/full-xml/10.1098/rspa.2011.0527 en eng The Royal Society https://royalsociety.org/journals/ethics-policies/data-sharing-mining/ Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences volume 468, issue 2139, page 784-809 ISSN 1364-5021 1471-2946 journal-article 2011 crroyalsociety https://doi.org/10.1098/rspa.2011.0527 2024-05-07T14:15:57Z An effective property of a composite material consisting of inclusions within a host matrix depends on the geometry and connectedness of the inclusions. This dependence may be quite strong if the constituents have highly contrasting properties. Here, we consider the inverse problem of using effective property data to obtain information on the geometry of the microstructure. While previous work has been devoted to recovering the volume fractions of the constituents, our focus is on their connectedness—a key feature in critical behaviour and phase transitions. We solve exactly a reduced inverse spectral problem by bounding the volume fraction of the constituents, an inclusion separation parameter and the spectral gap of a self-adjoint operator that depends on the geometry of the composite. We present a new algorithm based on the Möbius transformation structure of the forward bounds whose output is a set of algebraic curves in parameter space bounding regions of admissible parameter values. These results advance the development of techniques for characterizing the microstructure of composite materials. As an example, we obtain inverse bounds on the volume fraction and separation of the brine inclusions in sea ice from measurements of its effective complex permittivity. Article in Journal/Newspaper Sea ice The Royal Society Möbius ENVELOPE(164.217,164.217,-74.633,-74.633) Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 468 2139 784 809 |
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crroyalsociety |
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English |
description |
An effective property of a composite material consisting of inclusions within a host matrix depends on the geometry and connectedness of the inclusions. This dependence may be quite strong if the constituents have highly contrasting properties. Here, we consider the inverse problem of using effective property data to obtain information on the geometry of the microstructure. While previous work has been devoted to recovering the volume fractions of the constituents, our focus is on their connectedness—a key feature in critical behaviour and phase transitions. We solve exactly a reduced inverse spectral problem by bounding the volume fraction of the constituents, an inclusion separation parameter and the spectral gap of a self-adjoint operator that depends on the geometry of the composite. We present a new algorithm based on the Möbius transformation structure of the forward bounds whose output is a set of algebraic curves in parameter space bounding regions of admissible parameter values. These results advance the development of techniques for characterizing the microstructure of composite materials. As an example, we obtain inverse bounds on the volume fraction and separation of the brine inclusions in sea ice from measurements of its effective complex permittivity. |
format |
Article in Journal/Newspaper |
author |
Orum, Chris Cherkaev, Elena Golden, Kenneth M. |
spellingShingle |
Orum, Chris Cherkaev, Elena Golden, Kenneth M. Recovery of inclusion separations in strongly heterogeneous composites from effective property measurements |
author_facet |
Orum, Chris Cherkaev, Elena Golden, Kenneth M. |
author_sort |
Orum, Chris |
title |
Recovery of inclusion separations in strongly heterogeneous composites from effective property measurements |
title_short |
Recovery of inclusion separations in strongly heterogeneous composites from effective property measurements |
title_full |
Recovery of inclusion separations in strongly heterogeneous composites from effective property measurements |
title_fullStr |
Recovery of inclusion separations in strongly heterogeneous composites from effective property measurements |
title_full_unstemmed |
Recovery of inclusion separations in strongly heterogeneous composites from effective property measurements |
title_sort |
recovery of inclusion separations in strongly heterogeneous composites from effective property measurements |
publisher |
The Royal Society |
publishDate |
2011 |
url |
http://dx.doi.org/10.1098/rspa.2011.0527 https://royalsocietypublishing.org/doi/pdf/10.1098/rspa.2011.0527 https://royalsocietypublishing.org/doi/full-xml/10.1098/rspa.2011.0527 |
long_lat |
ENVELOPE(164.217,164.217,-74.633,-74.633) |
geographic |
Möbius |
geographic_facet |
Möbius |
genre |
Sea ice |
genre_facet |
Sea ice |
op_source |
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences volume 468, issue 2139, page 784-809 ISSN 1364-5021 1471-2946 |
op_rights |
https://royalsociety.org/journals/ethics-policies/data-sharing-mining/ |
op_doi |
https://doi.org/10.1098/rspa.2011.0527 |
container_title |
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences |
container_volume |
468 |
container_issue |
2139 |
container_start_page |
784 |
op_container_end_page |
809 |
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1800738122510630912 |