The Rational Spirit in Modern Continuum Mechanics Essays and Papers Dedicated to the Memory of Clifford Ambrose Truesdell III

Through his voluminous and in?uential writings, editorial activities, organi- tional leadership, intellectual acumen, and strong sense of history, Clifford - brose Truesdell III (1919–2000) 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.

Memories of Clifford Truesdell.- Clifford Truesdell (1919–2000), 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 (1906–1962): 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 Nonlinear Elasticity 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.