This book discusses the theoretical foundations of the structural modeling method applied to metamaterials. This method takes into account the parameters of the crystal lattice, the size of the medium particles, as well as their shape and constants of force interactions between them. It provides mathematical models of metamaterials that offer insights into the qualitative influence of the local structure on the effective elastic moduli of the considered medium and into performing theoretical estimations of these quantities. This book is useful for researchers working in the fields of solid mechanics, physical acoustics, and condensed matter physics, as well as for graduate and postgraduate students studying mathematical modeling methods.
Shows the influence of size effects on the physical and mechanical properties of a material
Presents mathematical models of metamaterials
Describes the propagation and interaction of nonlinear waves in generalized continua
Prof. Dr. Erofeev Vladimir Ivanovich is the Director of the Mechanical Engineering Research Institute of the Russian Academy of Sciences. His scientific interests include structural modeling of advanced material, nonlinear wave dynamics of microstructured solids, and acoustic testing of microstructured materials.He is a member of the Russian Acoustical Society and the Russian National Committee on Theoretical and Applied Mechanics.Prof. Dr. Pavlov Igor Sergeevich is the Vice-Director of the Mechanical Engineering Research Institute of the Russian Academy of Sciences, and a Professor at the Radiophysics Department of Lobachevsky State University of Nizhny Novgorod, Russia. His scientific interests include structural modeling of advanced materials, nonlinear wave dynamics of microstructured solids, and acoustic testing of microstructured materials. He is a member of the Russian Acoustical Society and the Russian National Committee on Theoretical and Applied Mechanics.
Chapter 1. Theoretical basis of the structural modeling method
Chapter 2. A 2D lattice with dense packing of the particles
Chapter 3. A 2D lattice with non-dense packing of the particles
Chapter 4. Application of the 2D models of media with dense and non-dense packing
of the particles for solving the parametric identification problems
Chapter 5. Nonlinear models of microstructured media
Chapter 6. Propagation and interaction of nonlinear waves in generalized continua
Discussion of the results ..