9R1. Mesomechanical Constitutive Modeling. Advances in Mathematics for Applied Sciences Series, Vol 55. - V Kafka (Inst of Theor and Appl Mech, Acad of Sci, Czech Republic). World Sci Publ, Singapore. 2001. 225 pp. ISBN 981-02-4485-1. $58.00.
Reviewed by K Hutter (Dept of Mech, Darmstadt Univ of Tech, Hochschulstr 1, Darmstadt, D-64289, Germany).
This book—a reference source book of the author’s and his associates’ work on homogenization procedures in heterogeneous media—summarizes the author’s research work on the mentioned topic performed during the last 30 years, with emphasis on the more recent work performed in the last 15 years.
After a brief introduction and presentation of notation, Chapter I presents the general mesomechanical model of heterogeneous, statistically homogeneous materials. Basic is Hills 1963-equation stating that the averaged work of the stresses on the strains equals the corresponding work of the averaged stresses and averaged strains from which the Voigt and Reuss approximations can be deduced. Chapter II then treats ma-terials with statistically isotropic structure, thereby emphasising two-phase materials. Static behavior of polycrystalline metals under plastic deformations is dealt with in Chapter III. Yield point jog, cyclic loading, necking, and damage are all touched upon. Chapters IV and V are devoted to time-dependent deformations and fracturing, featuring creep of concrete and its application in structural mechanics. Chapter VI brings homogenization procedures in shape memory alloys and is dealing with pseudoelasticity and one- as well as two-way shape memory effects. Chapter VIII finally brings an analysis of homogenization in transversely isotropic materials. Appendices, collected in Chapter VIII, bring complementary proofs and material not dealt with in greater detail in the main text.
The intention of writing a book on one’s own research is to summarize, at one place and in a consistent form, earlier work that may be scattered in various periodicals and perhaps written with different notation and emphasis. A second purpose is to write the subject more carefully and perhaps more extensively to reach a broader readership. In this book, the first goal has likely been achieved, the second has not. The text is very brief, not explicatory and not an improvement over the original papers. Cross-references are seldom or missing altogether, and the verbalization of the ideas is unimaginative. This reviewer can dispense with this book on his shelf, and would not recommend it to individuals and only reluctantly to libraries.