Microstructural Randomness and Scaling in Mechanics of Materials

摘要: PREFACE BASIC RANDOM MEDIA MODELS Probability Measure of Geometric Objects Basic Point Fields Directional Data Random Fibers, Line Fields, Tessellations Concepts and Definitions Microstructures PROCESSES AND FIELDS Elements One-Dimensional Mechanics Problems on Two- Three-Dimensional Ergodicity The Maximum Entropy Method PLANAR LATTICE MODELS: PERIODIC TOPOLOGIES ELASTOSTATICS Lattices Planar Lattices: Classical Continua Applications in Composites Nonclassical Extension-Twist Coupling a Helix RIGIDITY, RANDOMNESS, DYNAMICS, OPTIMALITY Rigidity Networks Spring Network Models for Disordered Topologies Particle Michell Trusses: Optimal Use Material TWO- VERSUS THREE-DIMENSIONAL CLASSICAL ELASTICITY Relations CLM Result Stress Invariance Poroelasticity MICROPOLAR Micropolar Elastic vis-a-vis (Elasticity) Cosserat Elasticity Effective Moduli Characteristic Lengths MESOSCALE BOUNDS FOR LINEAR ELASTIC MICROSTRUCTURES Micro-, Meso-, Macroscales Volume Averaging Spatial Randomness Hierarchies Mesoscale Bounds Examples Trabecular Bone FIELD STOCHASTIC FINITE ELEMENTS Second-Order Properties Does There Exist Locally Isotropic, Smooth Material? Stochastic Finite Media Slip-Lines Inhomogeneous Plastic Trusses the Presence Microstructure HIERARCHIES OF NONLINEAR INELASTIC Physically Nonlinear Elastic-Plastic Rigid-Perfectly Viscoelastic Stokes Flow Porous Thermoelastic Scaling Evolution Damage Phenomena Comparison Trends RESPONSE IN THERMOMECHANICS From Statistical to Continuum Thermodynamics Extensions Hill Condition Legendre Transformations (Thermo)Elasticity Thermodynamic Orthogonality Complex versus Compound Processes: Viewpoint Toward Fractal WAVES WAVEFRONTS Methods Wave Propagation Spectral Waves 1D Transient Heterogeneous Acceleration Wavefronts BIBLIOGRAPHY INDEX