Advertisement

Microstructured Materials: Inverse Problems

  • Jaan Janno
  • Jüri Engelbrecht

Part of the Springer Monographs in Mathematics book series (SMM)

Table of contents

  1. Front Matter
    Pages I-IX
  2. Jaan Janno, Jüri Engelbrecht
    Pages 1-3
  3. Jaan Janno, Jüri Engelbrecht
    Pages 5-9
  4. Jaan Janno, Jüri Engelbrecht
    Pages 11-19
  5. Jaan Janno, Jüri Engelbrecht
    Pages 21-35
  6. Jaan Janno, Jüri Engelbrecht
    Pages 37-59
  7. Jaan Janno, Jüri Engelbrecht
    Pages 61-101
  8. Jaan Janno, Jüri Engelbrecht
    Pages 103-145
  9. Jaan Janno, Jüri Engelbrecht
    Pages 147-154
  10. Back Matter
    Pages 155-160

About this book

Introduction

Complex, microstructured materials are widely used in industry and technology and include alloys, ceramics and composites. Focusing on non-destructive evaluation (NDE), this book explores in detail the mathematical modeling and inverse problems encountered when using ultrasound to investigate heterogeneous microstructured materials. The outstanding features of the text are firstly, a clear description of both linear and nonlinear mathematical models derived for modelling the propagation of ultrasonic deformation waves, and secondly, the provision of solutions to the corresponding inverse problems that determine the physical parameters of the models. The data are related to nonlinearities at both a macro- and micro- level, as well as to dispersion. 

The authors’ goal has been to construct algorithms that allow us to determine the parameters within which we are required to characterize microstructure. To achieve this, the authors not only use conventional harmonic waves, but also propose a novel methodology based on using solitary waves in NDE. The book analyzes the uniqueness and stability of the solutions, in addition to providing numerical examples.

Keywords

deformation waves inverse problems microstructured solids nonlinearity

Authors and affiliations

  • Jaan Janno
    • 1
  • Jüri Engelbrecht
    • 2
  1. 1.Institute of CyberneticsTallinn University of TechnologyTallinnEstonia
  2. 2.Institute of CyberneticsTallinn University of TechnologyTallinnEstonia

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-21584-1
  • Copyright Information Springer-Verlag Berlin Heidelberg 2011
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-642-21583-4
  • Online ISBN 978-3-642-21584-1
  • Series Print ISSN 1439-7382
  • Buy this book on publisher's site