THE RATIONAL SPIRIT IN MODERN CONTINUUM MECHANICS

By JESSICA LOPEZ

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 TRUESDELL’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 CONTENTS 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