CONTINUUM MECHANICS (Lecture Notes) Zdenekˇ Martinec Department of Geophysics Faculty of Mathematics and Physics Charles University in Prague V Holeˇsoviˇck´ach 2, 180 00 Prague 8 Czech Republic e-mail:
[email protected]ff.cuni.cz Original: May 9, 2003 Updated: January 11, 2011 Preface This text is suitable for a two-semester course on Continuum Mechanics. It is based on notes from undergraduate courses that I have taught over the last decade. The material is intended for use by undergraduate students of physics with a year or more of college calculus behind them. I would like to thank Erik Grafarend, Ctirad Matyska, Detlef Wolf and Jiˇr´ıZahradn´ık,whose interest encouraged me to write this text. I would also like to thank my oldest son Zdenˇekwho plotted most of figures embedded in the text. I am grateful to many students for helping me to reveal typing misprints. I would like to acknowledge my indebtedness to Kevin Fleming, whose through proofreading of the entire text is very much appreciated. Readers of this text are encouraged to contact me with their comments, suggestions, and questions. I would be very happy to hear what you think I did well and I could do better. My e-mail address is
[email protected]ff.cuni.cz and a full mailing address is found on the title page. ZdenˇekMartinec ii Contents (page numbering not completed yet) Preface Notation 1. GEOMETRY OF DEFORMATION 1.1 Body, configurations, and motion 1.2 Description of motion 1.3 Lagrangian and Eulerian coordinates 1.4 Lagrangian and Eulerian variables 1.5 Deformation gradient 1.6 Polar decomposition of the deformation gradient 1.7 Measures of deformation 1.8 Length and angle changes 1.9 Surface and volume changes 1.10 Strain invariants, principal strains 1.11 Displacement vector 1.12 Geometrical linearization 1.12.1 Linearized analysis of deformation 1.12.2 Length and angle changes 1.12.3 Surface and volume changes 2.