Field singularities and wave analysis in continuum mechanics. Transl. from the Polish ed. by R. W. Ogden, rev. and enlarged. (English) Zbl 0622.73032

Ellis Horwood Series Mathematics and its Applications. Chichester: Ellis Horwood Limited; New York etc.: Halsted Press: a division of John Wiley & Sons; Warsaw: PWN - Polish Scientific Publishers. 251 p. £30.00 (1986).
The book is essentially devoted to the study of discontinuity surfaces (shock waves and acceleration waves) in a three-dimensional continuous medium. Phenomena discussed are, in the main, mechanical, though in some paragraphs thermomechanical effects are considered and the basic axioms are those of rational thermomechanics.
The content is well summarized by the titles of chapters: 1. Moving surfaces in a continuum; 2. Functions with surface singularities; 3. General balance laws; 4. The laws of dynamics and thermodynamics for deformable bodies; 5. Singular surfaces of the motion; 6. Kinematic theory of acceleration waves. The examples of Chapter 7 comprise acoustic and shock waves in a barotropic medium and (slightly out of context) Love surface waves in a linearly elastic half space. The final paragraph of Chapter 7 gives a short review of thermomechanical waves in materials with internal state variables (matters of principle as well as complexity of models would have recommended here an ampler, less cavalier approach or, at least, some words of caution reflecting the unsettled state of the topic). The final Chapter 8 deals with one-dimensional waves.
Thus the book is quite a useful addition to the literature. It can be proposed for a graduate course; besides those involved in research will find it convenient reference to results in the field. A systematic exposition of matters currently under development suggest, and sometimes impose, original additions (and the Author points out such additions here and there). Essential contributions and related papers are quoted with ecumenical grace, so that the reader is left to find out which are really of import by himself.
Reviewer: G.Capriz


74J99 Waves in solid mechanics
74M20 Impact in solid mechanics
74-02 Research exposition (monographs, survey articles) pertaining to mechanics of deformable solids
74A20 Theory of constitutive functions in solid mechanics
76L05 Shock waves and blast waves in fluid mechanics
74J10 Bulk waves in solid mechanics
74J20 Wave scattering in solid mechanics
74H45 Vibrations in dynamical problems in solid mechanics