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Mathematical Methods in Continuum Mechanics of Solids

  • Martin Kružík
  • Tomáš Roubíček

Part of the Interaction of Mechanics and Mathematics book series (IMM)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Static Problems

    1. Front Matter
      Pages 1-2
    2. Martin Kružík, Tomáš Roubíček
      Pages 3-23
    3. Martin Kružík, Tomáš Roubíček
      Pages 25-50
    4. Martin Kružík, Tomáš Roubíček
      Pages 51-86
    5. Martin Kružík, Tomáš Roubíček
      Pages 87-159
    6. Martin Kružík, Tomáš Roubíček
      Pages 161-191
  3. Evolution Problems

    1. Front Matter
      Pages 193-194
    2. Martin Kružík, Tomáš Roubíček
      Pages 195-245
    3. Martin Kružík, Tomáš Roubíček
      Pages 247-356
    4. Martin Kružík, Tomáš Roubíček
      Pages 357-408
    5. Martin Kružík, Tomáš Roubíček
      Pages 409-472
  4. Back Matter
    Pages 505-644

About this book

Introduction

This book primarily focuses on rigorous mathematical formulation and treatment of static problems arising in continuum mechanics of solids at large or small strains, as well as their various evolutionary variants, including thermodynamics. As such, the theory of boundary- or initial-boundary-value problems for linear, quasilinear elliptic, parabolic or hyperbolic partial differential equations is the main underlying mathematical tool, along with the calculus of variations. Modern concepts of these disciplines as weak solutions, polyconvexity, quasiconvexity, nonsimple materials, materials with various rheologies or with internal variables are exploited.


This book is accompanied by exercises with solutions, and appendices briefly presenting the basic mathematical concepts and results needed. It serves as an advanced resource and introductory scientific monograph for undergraduate or PhD students in programs such as mathematical modeling, applied mathematics, computational continuum physics and engineering, as well as for professionals working in these fields.


Keywords

Continuum Mechanics of Solids Mathematical Methods in Continuum Mechanics of Solids Thermodynamics Calculus of Variations Elliptic Partial Differential Equations Parabolic Partial Differential Equations Hyperbolic Partial Differential Equations

Authors and affiliations

  • Martin Kružík
    • 1
  • Tomáš Roubíček
    • 2
  1. 1.Institute of Information Theory and AutomationCzech Academy of SciencesPragueCzech Republic
  2. 2.Mathematical Institute, Faculty of Mathematics and PhysicsCharles UniversityPragueCzech Republic

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-030-02065-1
  • Copyright Information Springer Nature Switzerland AG 2019
  • Publisher Name Springer, Cham
  • eBook Packages Engineering
  • Print ISBN 978-3-030-02064-4
  • Online ISBN 978-3-030-02065-1
  • Series Print ISSN 1860-6245
  • Series Online ISSN 1860-6253
  • Buy this book on publisher's site
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