Field fluctuations and macroscopic properties for nonlinear composites |
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| Institution: | 3. Department of Bioengineering, University of California, San Diego, La Jolla, California 92093;6. Department of Pharmacology, University of California, San Diego, La Jolla, California 92093;12. Institute of Engineering in Medicine, University of California, San Diego, La Jolla, California 92093,;4. NORLUX Neuro-Oncology Laboratory, Department of Oncology, Luxembourg Institute of Health, 1526 Luxembourg, Luxembourg,;5. Luxembourg Centre for Systems Biomedicine, University of Luxembourg, 4362 Esch-Belval, Luxembourg;1. Navarrabiomed-Hospital Universitario de Navarra (HUN)-Universidad Pública de Navarra (UPNA), Pamplona, Spain;2. Departamento de Estadística, Universidad Pública de Navarra (UPNA), Pamplona, Spain;3. Red de Investigación en Servicios Sanitarios y Enfermedades Crónicas (REDISSEC), Bilbao, Spain;4. Instituto de Investigación Sanitaria de Navarra (IdiSNA), IdiSNA, Pamplona, Spain;5. Dirección de Salud Pública y Adicciones, Departamento de Sanidad, Gobierno Vasco, Vitoria, Spain;6. Departamento de Ciencias de la Salud, Universidad Pública de Navarra (UPNA), Pamplona, Spain;1. Lenfest Center for Sustainable Energy, Earth Institute, Department of Earth and Environmental Engineering, Columbia University, 500 West 120th Street, Mudd 918, New York, NY 10027, USA;2. Center for Negative Carbon Emissions, School of Sustainable Engineering and the Built Environment, Ira A. Fulton Schools of Engineering, Arizona State University, Tempe, AZ 85287, USA;1. Nomads UAB, Grai?iūno 8, LT-02241 Vilnius, Lithuania;2. Institute of Biotechnology of Vilnius University, Grai?iūno 8, LT-02241 Vilnius, Lithuania;3. Nomad Bioscience GmbH, Biozentrum Halle, Weinbergweg 22, D-06120 Halle (Saale), Germany;4. LUHS Veterinary Academy, Til??s 18, LT-47181 Kaunas, Lithuania;1. Department of Critical Care Medicine, Children’s Hospital of Pittsburgh, Safar Center for Resuscitation Research, University of Pittsburgh School of Medicine, Pittsburgh, PA, USA;2. Department of Pharmacology and Chemical Biology, University of Pittsburgh School of Medicine, Pittsburgh, PA, USA |
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| Abstract: | A recently introduced nonlinear homogenization method J. Mech. Phys. Solids 50 ( 2002) 737–757] is used to estimate the effective behavior and the associated strain and stress fluctuations in two-phase, power-law composites with aligned-fiber microstructures, subjected to anti-plane strain, or in-plane strain loading. Using the Hashin–Shtrikman estimates for the relevant “linear comparison composite,” results are generated for two-phase systems, including fiber-reinforced and fiber-weakened composites. These results, which are known to be exact to second-order in the heterogeneity contrast, are found to satisfy all known bounds. Explicit analytical expressions are obtained for the special case of rigid-ideally plastic composites, including results for arbitrary contrast and fiber concentration. The effective properties, as well as the phase averages and fluctuations predicted for these strongly nonlinear composites appear to be consistent with deformation mechanisms involving shear bands. More specifically, for the case where the fibers are stronger than the matrix, the predictions appear to be consistent with the shear bands tending to avoid the fibers, while the opposite would be true for the case where the fibers are weaker. |
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