Introduction to Nonlinear Thermomechanics of Solids

1. Front Matter

   Pages i-viii

   PDF

2. Introduction

   • Michał Kleiber, Piotr Kowalczyk

   Pages 1-4

3. Fundamental Concepts of Mechanics

   • Michał Kleiber, Piotr Kowalczyk

   Pages 5-13

4. Fundamentals of Tensor Algebra and Analysis

   • Michał Kleiber, Piotr Kowalczyk

   Pages 15-79

5. Motion, Deformation and Strain in Material Continuum

   • Michał Kleiber, Piotr Kowalczyk

   Pages 81-113

6. Description of Stress State

   • Michał Kleiber, Piotr Kowalczyk

   Pages 115-141

7. Conservation Laws in Continuum Mechanics

   • Michał Kleiber, Piotr Kowalczyk

   Pages 143-153

8. Constitutive Equations

   • Michał Kleiber, Piotr Kowalczyk

   Pages 155-199

9. Fundamental System of Solid Mechanics Equations

   • Michał Kleiber, Piotr Kowalczyk

   Pages 201-211

10. Fundamentals of Thermomechanics and Heat Conduction Problem

    • Michał Kleiber, Piotr Kowalczyk

    Pages 213-231

11. Variational Formulations in Solid Thermomechanics

    • Michał Kleiber, Piotr Kowalczyk

    Pages 233-264

12. Discrete Formulations in Thermomechanics

    • Michał Kleiber, Piotr Kowalczyk

    Pages 265-286

13. Fundamentals of Finite Element Method

    • Michał Kleiber, Piotr Kowalczyk

    Pages 287-313

14. Solution of FEM Equation Systems

    • Michał Kleiber, Piotr Kowalczyk

    Pages 315-340

15. Back Matter

    Pages 341-345

    PDF

The first part of this textbook presents the mathematical background needed to precisely describe the basic problem of continuum thermomechanics. The book then concentrates on developing governing equations for the problem dealing in turn with the kinematics of material continuum, description of the state of stress, discussion of the fundamental conservation laws of underlying physics, formulation of initial-boundary value problems and presenting weak (variational) formulations. In the final part the crucial issue of developing techniques for solving specific problems of thermomechanics is addressed. To this aim the authors present a discretized formulation of the governing equations, discuss the fundamentals of the finite element method and develop some basic algorithms for solving algebraic and ordinary differential equations typical of problems on hand. Theoretical derivations are followed by carefully prepared computational exercises and solutions.

• computational solid mechanics
• nonlinear thermomechanics of deformable bodies
• tensor algebra and analysis
• variational methods
• finite element method
• CIMNE

“This book introduces thermomechanics mathematically. … The book is a good introduction for beginners who want to do research in solid mechanics and/or thermomechanics. It can be used as a textbook for courses involving solid mechanics/thermomechanics. For computer professionals dealing with engineering problems, this is a good introduction.” (Maulik A. Dave, Computing Reviews, computingreviews.com, October, 2016)

• Inst.of Fund Technik. Research, Polish Academy of Science, Warsaw, Poland

  Michał Kleiber

• Department of Computational Science, Institute of Fundamental Technological R, Warsaw, Poland

  Piotr Kowalczyk

Prof. Michal Kleiber lectured for many years at the Mathematics and Information Science Department of the Warsaw University of Technology. His educational background is thermo-mechanics of solids (M.Sc. in engineering from the Warsaw University of Technology) and applied math and information science (M.Sc. in mathematics from the University of Warsaw). He has done research on modelling and large scale computer simulations in solid and fluid thermo-mechanics, material science, bioengineering and system reliability as well as on numerical methods and software engineering. He has published over 240 articles in leading international journals and authored several world-wide distributed books. He spent over 10 years teaching and doing research at different universities in Stuttgart, Bochum, Hannover and Darmstadt in Germany, Berkeley, CA in the USA and Tokyo in Japan. He has also given lecture courses at many other universities in the USA, Europe, Africa and Asia. Professor Kleiber is an elected member of the Academies of Sciences in Poland and Austria, and has honorary doctor degrees from a number of universities in Poland, Germany and Belgium. He is a member of editorial boards of 15 international research journals and the editor-in-chief of two of them.

In 2001 he received the Foundation for Polish Science Award which is the most prestigious award for research achievements in Poland. Professor Kleiber is currently the president of the European Materials Forum and a member of the Executive Council of the International Association of Computational Mechanics; in 1999-2001 he was a member of the Board of Governors for the EU Joint Research Centre. Professor Kleiber was for some time on leave of absence from his academic duties serving as the Minister of Science and Information Society Technologies in the Polish government. He currently serves as a pro bono scientific adviser to the President of Poland.

Piotr Kowalczyk graduated from Warsaw University of Technology and then received his PhD from the Institute of Fundamental Technological Research (IPPT PAN) in Warsaw in 1993. Currently he is an associate professor at IPPT PAN. In his research he is dealing with computational mechanics with particular applications to biomechanics, plasticity, composite materials, sensitivity analysis and optimization. Since 2003 he has lectured graduate students of informatics on nonlinear computational thermomechanics of solids.   

Policies and ethics