The object of mechanics is to investigate the motions of material bodies under the influence of forces. Mechanics is a branch of science generally aiming to understand the processes of motion and present them in accordance with the general laws of nature governing their origins. From a mechanical point of view, all motions result from the effects of forces. This general concept also includes the special state of immobility, i.e. statics. Scientific comprehension thrives on the accumulated wealth of experience, the abstractions derived from it and on mathematical argumentation.
KeywordsConstitutive Equation Material Behaviour Kinematic Constraint Constitutive Theory Material Body
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- 1.We employ vector and tensor calculus throughout this book. An introduction to this basic mathematical tool is to be found in De Boer ; Betten ; Klingbeil ; Lippmann ; Bowen & Wang ; Marsden & Hoffman ; Marsden & Tromba . See also Leigh  and Giesekus .Google Scholar
- 2.There are numerous textbooks dealing with continuum mechanics; since they differ considerably in layout and order of priorities, it is impossible to make an objective choice from the wide selection available. For those confronting this field for the very first time, the introductory works by Malvern ; Fung ; Bowen ; Becker & Bürger ; Ziegler  might be recommended. Further interpretations of modern nonlinear continuum mechanics are to be found in Altenbach & Altenbach ; Jaunzemis ; Eringen ; Eringen ; Leigh ; Wang & Truesdell ; Chadwick ; Gurtin ; Ogden ; Marsden & Hughes ; Bertram  and Giesekus . For beginners and experts alike, the monography by Truesdell & Noll  still retains its hitherto unrivalled position as absolutely essential reading-matter, which, in conjunction with Truesdell & Toupin  provides a comprehensive representation of continuum mechanics with an abundance of quotations from literature, upon which the authors comment with refined diligence. The stimulating essay by Truesdell , written in his own inimitable style, which pertinently captures the spirit of rational continuum mechanics, also makes excellent reading. Initial-boundary-value problems are studied from the mathematical point of view in Alber .Google Scholar
- 3.Truesdell & Noll , Sect. 1.Google Scholar
- 4.Truesdell & Noll , Sect. 16.Google Scholar
- 5.Truesdell & Noll , Sect. 26.Google Scholar
- 6.Truesdell & Noll , Sect. 31.Google Scholar
- 7.Truesdell & Noll , Sect. 30.Google Scholar
- 8.Truesdell & Noll , Sect. 41.Google Scholar
- 9.In literature dealing with continuum mechanics, it is not uncommon to find the principles of thermodynamics treated as well, although usually very briefly. Introductions to thermodynamics in its own right are given by Baehr ; Müller ; Müller  and Lavenda . Owen ; Day  and, in particular, Truesdell [1984a, 1984b] allow a certain insight into the school of Rational Thermodynamics. The comprehensive article by Hutter  is very readable and informative.Google Scholar
- 10.The concept of this idea was clearly formulated by Coleman & Noll  and often applied thereafter with great success. It is also intended to form the basis of the thermomechanical theory of materials in this treatise.Google Scholar