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Mathematical Methods in Continuum Mechanics of Solids

  • Textbook
  • © 2019


  • Serves as an advanced textbook for graduate students, as well as a monograph for theoretically oriented researchers
  • Merges rational continuum mechanics with mathematical analysis. Focuses on rigorous mathematical formulation and treatment of static and evolutionary problems arising in mechanics of solids
  • Includes exercises, and also appendices that briefly present the basic mathematical concepts and results needed

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

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About this book

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 or 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.


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Table of contents (9 chapters)

  1. Static Problems

  2. Evolution Problems


“Advanced mathematical concepts are presented in a logical and clear manner, making the book accessible to graduate students as well as non-mathematicians working on problems in continuum mechanics of solids. … The book is very well organized and well written. The mathematical results are clearly presented.” (Corina- Stefania Drapaca, Mathematical Reviews, November, 2019)

Authors and Affiliations

  • Institute of Information Theory and Automation, Czech Academy of Sciences, Prague, Czech Republic

    Martin Kružík

  • Mathematical Institute, Faculty of Mathematics and Physics, Charles University, Prague, Czech Republic

    Tomáš Roubíček

About the authors

Martin Kružík is a Senior Researcher at the Institute of Information Theory and Automation of the Czech Academy of Sciences and an Associate Professor at Charles University and at the Czech Technical University in Prague, having received his habilitation from the Technical University Munich. His research interests range from calculus of variations and applied mathematical analysis to mathematical problems of continuum physics.

Tomáš Roubíček is a Professor at Charles University in Prague, as well as a Researcher at the Institutes of Thermomechanics and of Information Theory and Automation of the Czech Academy of Sciences. With an engineering background, his professional activity has evolved from computer simulations of systems of nonlinear partial differential equations, numerical mathematics and optimization theory to applied mathematical analysis focused on mathematical modeling in engineering and physics.

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