Non-SmoothThermomechanics

9R57. Non-Smooth Thermomechanics. - M Fremond (Laboratoire Lagrange, LCPC, 58 Blvd Lefebve, Paris Cedex 15, 75732, France). Springer-Verlag, Berlin. 2002. 480 pp. ISBN 3-540-66500-5. $89.95.Reviewed by MV Shitikova (Dept of Struct Mech, Voronezh State Univ of Architec and Civil Eng, ul Kirova 3-75, Voronezh, 394018, Russia).Non-smooth thermomechanical processes occurring in different solids are considered in this book consisting of 14 chapters, an appendix, list of 256 references, and a subject index. A finite number of the quantities that characterize the state of a material or of a structure, ie, the state quantities, are introduced in Chapter 1. The author deals not only with the discontinuous state quantities and their time-derivatives, but also includes into consideration different constraints and limitations imposed on the state quantities due to physical and/or geometrical properties of each particular problem. The account for these two aspects results in non-smooth equations with the corresponding non-smooth solutions. The basic mechanical relationships and constitutive laws involving the properties induced by the constraints and limitations are derived in Chapters 3–5 using the principle of virtue power, which is formulated in Chapter 2, either from the free energy or from the pseudopotential of dissipation that define a material. Deformable solids with and without interaction at a distance are considered in Chapters 6 and 7, respectively. Collision of rigid bodies is analyzed using the proposed technique in Chapter 8 and is illustrated by the problem of the collisions of three aligned balls. Evolution of two colliding deformable solids is described in Chapter 9 starting from the principle of virtue work. Chapter 10 presents the evaluation of the evolution of fibre reinforced materials under traction. Chapter 11, one of the most interesting in the opinion of this reviewer, is devoted to the analysis of solid-liquid phase change using classical ice-water phase change, the supercooling phenomena, and phase changes in porous media during soil freezing as the examples. Such problems can be of interest to engineers dealing with fall and winter maintenance and control of highways in countries with rather a long, cold season and frequent changes in temperatures, resulting in generation of so called black ice on a road surface. The damage theory founded on the principle of virtual power is formulated in Chapter 12, in so doing numerical examples related to simple concrete beams are given, which are useful for evaluating the damage state of civil engineering structures. The evolution of structures made of shape memory alloys is considered in Chapter 13 at the macroscopic level involving internal quantities describing the mixture of martensites and austenite, which can transform into one another. Such problems are also very important due to wide application of such materials in modern civil engineering structures. The last chapter, 14 presents contact problem with and without adhesion. But a reader cannot find well-defined boundaries for applicability of the approach proposed in this book. The circle of problems, wherein it works effectively, is not sharply outlined. Having read the book, this reviewer is under impression that the procedure developed is well suited to static and quasi-static problems, but needs some correction for application in boundary-value dynamic problems. By the way, dynamic problems are the least presented. One cannot find the boundary-value problems, resulting in the shock wave propagation in solids, but it is precisely these problems of non-smooth thermomechanics that are of prime interest, since they lead to non-equilibrium thermomechanics. Therefore, some doubts are cast upon the applicability of the author’s approach for solving such problems. The question arises as to whether it can be useful for determining the location of the shock wave front, its velocity, polarization, phase transitions which may occur on the wave front, the smearing of the wave front, and so on. It is not evident how to choose the optimal number of internal variables, which can help to solve successfully the problems that challenge engineers today. Since there are no general-purpose recipes for choosing the internal values, then it seems likely that the optimal choosing of the internal quantities is sort of a special skill, but one that an ordinary engineer without special training will probably not possess. This reviewer thinks that Non-Smooth Thermomechanics can be useful for individuals and students of mechanical engineering or civil engineering departments who want to improve mathematical knowledge in non-smooth thermomechanics, as well as for those who are interested in problems of heat and mass transfer.