A metamaterial is any material engineered to have a property that is not found in naturally occurring materials. Most famous properties in the context of waves include cloaking, super-resolution, negative refraction or prohibited propagation bands. The purpose of this course is to provide an introduction to the modeling of metamaterials. By using modern techniques based on asymptotic homogenization, transformation optics and modal methods, we aim to explain the the extraordinary properties of these metamaterials and their underlying mechanisms that allow to control waves according to our desires. Particular attention will be paid to present practical applications that illustrate the effectiveness of metamaterials to control waves on topical issues in acoustics, elastodynamic and electromagnetism.
The 8 lectures will covered the following topics :
- Homogenization theory for microstructured media and application to metamaterials
- Surface (guided) waves and application to Spoof Surface Plasmons
- Invisibility cloak and transformation optics
- Phononic cristals, locally resonant resonant metamaterial and application to band gaps and negative refraction
Final examination will consist in a written exam.
Background and motivation: The generic phenomenon of phase transformation underlies a variety of intriguing material behaviors that include (i) the superelasticity of shape-memory alloys, (ii) the mechanically-driven formation and evolution of complex microstructures in shape-memory alloys and ferroelectrics, and (iii) lithiation of (i.e., the insertion of lithium into) silicon electrodes in Li-ion batteries.
With the variety of material behaviors governed by phase transformation comes a wide range of applications. For instance, the superelasticity of shape-memory alloys, which emanates from a displacive (martensitic) phase transformation, finds applications in mechanical dampers (for earthquake-resistant buildings and anti-vibration devices in vehicles and jet engines) and in biomedical components (as self-expanding devices). Further, the evolution of microstructure in metallic alloys, which is often governed by a diffusive phase transformation, is at the core of a spectrum of industrial processes such as casting, additive manufacturing, and other thermomechanical treatments aimed at optimizing material properties through a target microstructure. Finally, recent technological advances and research on Li-ion batteries have brought a particular interest in silicon electrodes, which during the functioning of such batteries undergo a phase transformation which is governed by the interplay between the diffusion of lithium and the mechanical stresses inside the solid electrode.
