The Rational Spirit in Modern Continuum Mechanics

Through his voluminous and in?uential writings, editorial activities, organi- tional leadership, intellectual acumen, and strong sense of history, Clifford - brose Truesdell III (19192000) was the main architect for the renaissance of - tional continuum mechanics since the middle of the twentieth century. The present collection of 42 essays and research papers pays tribute to this man of mathematics, science, and natural philosophy as well as to his legacy. The ?rst ?ve essays by B. D. Coleman, E. Giusti, W. Noll, J. Serrin, and D. Speiser were texts of addresses given by their authors at the Meeting in memory of Clifford Truesdell, which was held in Pisa in November 2000. In these essays the reader will ?nd personal reminiscences of Clifford Truesdell the man and of some of his activities as scientist, author, editor, historian of exact sciences, and principal founding member of the Society for Natural Philosophy. The bulk of the collection comprises 37 research papers which bear witness to the Truesdellian legacy. These papers cover a wide range of topics; what ties them together is the rational spirit. Clifford Truesdell, in his address upon receipt of a Birkhoff Prize in 1978, put the essence of modern continuum mechanics succinctly as conceptual analysis, analysis not in the sense of the technical term but in the root meaning: logical criticism, dissection, and creative scrutiny.

Chi-Sing Man, Fosdick, R. L.:
The Rational Spirit in Modern Continuum Mechanics
Kluwer Acad. Pub. I Springer Netherlands, 2004, 1. Auflage, 8O8p., Hardcover
ISBN-1O: 1-4020-1828-2, ISBN-13: 978-1-4020-1828-2, 180,- , 198.- $
On January 14, 2000 Clifford A. Truesdell passed away. He can be considered as the "main architect for the renaissance of rational continuum mechanics since the middle of the twentieth century" (R. Fosdick). The essays and articles of the present book are dedicated to this important and remarkable person. They have been previously published in the Journal ofElasticity Vols. 70, 71, 72 (2003).
The book starts with a reproduction of a painting of Truesdell by J. Sheppard. In the sequel, some more pictures of Truesdell can be found. After a brief foreword by R. Fosdick, a list of Truesdell's published works is given, which contains more than 270 titles. The last one is the third editions of The Non-Linear Field Theories of Mechanics, co-authored by W. Noll.
The following articles by B. D. Coleman, E. Giusti, W. Noll, J. Serrin and D. Speiser contain considerations of Truesdell's life, work, and academic activities.
The rest of this voluminous book contains almost 40 scientific papers on various aspects of continuum mechanics, thermodynamics, mathematics, and related fields. The list of the authors reads like the Who is Who of modem continuum mechanics. Some of these papers also contain small dedications and references to Truesdell's life, work, and personality. In fact, many of these authors can be considered as scholars of Truesdell, which demonstrates the huge range of his influence upon natural science. Apart from the American school, there is also a significant amount of Italian contributions, among many others worldwide.
This brief review is not the right place to consider all these papers individually, although many of them are rather remarkable. Most of them show the high mathematical standard ofrational mechanics, which is also due to Truesdell's intentions. The book may serve as an overview on the state of art of modem natural science, and gives some insight into particular fields of current research activities as well. Consequently, it is not only interesting for historical reasons, but also for those who want to know more about modem mechanics and applied mathematics.

Contenu
Memories of Clifford Truesdell.- Clifford Truesdell (19192000), Historian of Mathematics.- The Genesis of Truesdell's Nonlinear Field Theories of Mechanics.- An Appreciation of Clifford Truesdell.- Clifford A. Truesdel?s Contributions to the Euler and the Bernoulli Edition.- Invariant Dissipative Mechanisms for the Spatial Motion of Rods Suggested by Artificial Viscosity.- An Average-Stretch Full-Network Model for Rubber Elasticity.- From 3-D Nonlinear Elasticity Theory to 1-D Bars with Nonconvex Energy.- Eshelby Tensor as a Tensor of Free Enthalpy.- E. Frola (19061962): an Attempt Towards an Axiomatic Theory of Elasticity.- Symmetries and Hamiltonian Formalism for Complex Materials.- Geometrically-based Consequences of Internal Constraints.- Second Variation Condition and Quadratic Integral Inequalities with Higher Order Derivatives.- Principal Compliance and Robust Optimal Design.- Rivlin's Representation Formula is Ill-Conceived for the Determination of Response Functions via Biaxial Testing.- Generalized Hessian and External Approximations in Variational Problems of Second Order.- Static Deformations of a Linear Elastic Porous Body Filled with an Inviscid Fluid.- A Class of Fit Regions and a Universe of Shapes for Continuum Mechanics.- Toward a Field Theory for Elastic Bodies Undergoing Disarrangements.- Continuous Distributions of Dislocations in Bodies with Microstructure.- A Model of the Evolution of a Two-dimensional Defective Structure.- On the Theory of Rotation Twins in Crystal Multilattices.- Minimum Free Energies for Materials with Finite Memory.- About Clapeyron's Theorem in Linear Elasticity.- The Lavrentiev Phenomenon in Nonlinear Elasticity.- Steady Flow of a Navier-Stokes Fluid around a Rotating Obstacle.- Global Bifurcation in NonlinearElasticity with an Application to Barrelling States of Cylindrical Columns.- Constitutive Relation of Elastic Polycrystal with Quadratic Texture Dependence.- Reconstruction Formula for Identifying Cracks.- An Approximate Treatment of Blunt Body Impact.- On the Transformation Property of the Deformation Gradient under a Change of Frame.- Some New Advances in the Theory of Dynamic Materials.- Pseudo-plasticity and Pseudo-inhomogeneity Effects in Materials Mechanics.- On the Microscopic Interpretation of Stress and Couple Stress.- The Hanging Rope of Minimum Elongation for a Nonlinear Stress-Strain Relation.- On Certain Weak Phase Transformations in Multilattices.- A New Quasilinear Model for Plate Buckling.- Cauchy's Flux Theorem in Light of Geometric Integration Theory.- A Comparison of the Response of Isotropic Inhomogeneous Elastic Cylindrical and Spherical Shells and Their Homogenized Counterparts.- On SO(n)-Invariant Rank 1 Convex Functions.- On Thermodynamics of Nonlinear Poroelastic Materials.- Anisotropic Elasticity and Multi-Material Singularities.