Topics in the Mathematical Modelling of Composite Materials

• Corporate Author: SpringerLink (Online service)
• Other Authors: Cherkaev, Andrej V. (Editor, http://id.loc.gov/vocabulary/relators/edt), Kohn, Robert (Editor, http://id.loc.gov/vocabulary/relators/edt)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Birkhäuser, 2018.
• Edition: 1st ed. 2018.
• Series: Modern Birkhäuser Classics,
• Subjects: Mathematical models.; Applied mathematics.; Engineering mathematics.; Computer mathematics.; Mathematical Modeling and Industrial Mathematics.; Applications of Mathematics.; Computational Science and Engineering.

Over the past several decades, we have witnessed a renaissance of theoretical work on the macroscopic behavior of microscopically heterogeneous materials. This activity brings together a number of related themes, including: (1) the use of weak convergence as a rigorous yet general language for the d...

Table of Contents:

• 1. On the Control of Coefficients in Partial Differential Equations
• 2. Estimations of Homogenized Coefficients
• 3. H- Convergence
• 4. A Strange Term Coming from Nowhere
• 5. Design of Composite Plates of Extremal Rigidity
• 6. Calculus of Variations and Homogenization
• 7. Effective Characteristics of Composite Materials and the Optimal Design of Structural Elements
• Appendix: Local distribution of a MHD Channel in the case of optimal distribution of the resistivity of the working medium
• 8. Microstructures of Composites of Extremal Rigidity and Exact Bounds on the Associated Energy Density.