Meet the editor

Prof. Alexander V. Vakhrushev obtained a Ph.D. in Technical Sciences from Izhevsk Institute of Mechanical Engineering, Russia, in 1982, and a DSc in Physics and Mathematics from the Institute of Continuous Media Mechanics, Ural Branch of the Russian Academy of Sciences in 2003. Currently, he is head of the Department of Nanotechnology and Microsystems Technic, Kalashnikov Izhevsk State Technical University, and head of the

Department of Modeling and Synthesis of Technological Structures, Institute of Mechanics, Udmurt Federal Research Center, Ural Branch of the Russian Academy of Sciences. He has received several awards, including an Academician A. F. Sidorov Prize from the Ural Branch of the Russian Academy of Sciences. He has more than 400 publications to his credit. His research interests include multiscale mathematical modeling of physical-chemical processes into nano-hetero systems.

Contents

**Preface XI**

**Chapter 1 1**

**Chapter 2 13**

**Chapter 3 33**

**Chapter 4 67**

**Chapter 5 91** Synthesis of WO3 Nanostructures and Their Nanocomposites with Graphene

**Chapter 6 105** Ultrasonic and Spectroscopic Techniques for the Measurement of the Elastic

Mode-I and Mode-II Crack Tip Fields in Implicit Gradient Elasticity Based

Mode-I and Mode-II Crack Tip Fields in Implicit Gradient Elasticity Based

Mode-I and Mode-II Crack Tip Fields in Implicit Gradient Elasticity Based

on Laplacians of Stress and Strain. Part I: Governing Equations *by Carsten Broese, Jan Frischmann and Charalampos Tsakmakis*

on Laplacians of Stress and Strain. Part II: Asymptotic Solutions *by Carsten Broese, Jan Frischmann and Charalampos Tsakmakis*

on Laplacians of Stress and Strain. Part III: Numerical Simulations *by Carsten Broese, Jan Frischmann and Charalampos Tsakmakis*

Derivatives via Novel Chemical Approach *by Rhizlane Hatel and Mimouna Baitoul*

Properties of Nanoscale Materials

*by Marco G. Beghi*

Formation of Nanostructures on the Solid Surface

*by Alexander V. Vakhrushev*

## Contents


*by Marco G. Beghi*

Preface

Nanotechnologies and nanomaterials are increasingly used in modern life and largely determine the directions of science and technology development. Therefore, the development of nanomechanics, which is used to describe behavior and properties at different structural levels, is very necessary. Nanomechanics includes different physics and mathematics models, such as quantum mechanics, molecular dynamics, mesodynamics, and continuum mechanics. Because of the multilevel nature of nanotechnological processes, the problems of nanomechanics are very

This book is a collection of six scientific chapters on theoretical and practical advances in nanomechanics at different structural levels. Chapters cover a wide

Chapter 1, "Formation of Nanostructures on the Solid Surface", presents information on the problem of modifying the surface of a solid. It provides a comparative review of different methods of forming nanostructures on the surfaces of solids and mathematical modeling of these processes. It is shown that mathematical modeling makes it possible to predict the structure of the modified surface and determine the

 Chapter 2, "Mode I and Mode II Crack Tip Fields in Implicit Gradient Elasticity based on Laplacians of Stress and Strain. Part I: Governing Equations", provides the governing equations and the required boundary and symmetry conditions for the considered crack problems for the plane strain state. It presents an implicit gradient elasticity model including the Laplacian of stress and the Laplacian of strain. This chapter provides the governing equations and the required boundary and symmetry conditions for the considered crack problems. The development of models of the gradient theory of elasticity is currently important for descriptions of size effects and nonlocal behavior observed in nanostructured materials or composites contain-

In Chapter 3, "Mode I and Mode II Crack Tip Fields in Implicit Gradient Elasticity based on Laplacians of Stress and Strain. Part II: Asymptotic Solutions", the authors develop asymptotic solutions for near-tip fields of Mode I and Mode II crack problems and for model responses reflected by implicit gradient elasticity. Mode I and Mode II crack problems are considered in the setting of plane strain problems. The chapter discusses analytical solutions for near fields using Williams-type asymptotic expansions. The main output of the work is the closed-form analytical solutions predicted by the 3-PG model for Mode I and Mode II fracture problems.

In Chapter 4, "Mode I and Mode II Crack Tip Fields in Implicit Gradient Elasticity based on Laplacians of Stress and Strain. Part III: Numerical Simulations", verification of a resulting finite element model for the square section with a circular hole subjected to displacement-controlled tension loading is considered and discussed. The chapter presents the numerical modeling by the finite element method near tip fields of Mode I and Mode II crack problems. A finite element model for plane strain

complex and require a detailed study by scientists and engineers.

range of research in the field of nanomechanics.

parameters of the technological processes of modification.

ing nanoparticles, carbon nanotubes, and nanofibers.
