The Universality of Nonclassical Nonlinearity -- Nonlinear Dynamical Systems in Economics -- Towards a Top-Down Approach in Materials Science -- Nonlinearity and Complexity in Elastic Wave Motion -- Hierarchies of Waves in Nonclassical Materials -- Nonequilibrium Nonlinear Dynamics in Solids: State of the Art -- Nonlinear Rock Mechanics -- Universality in Nonlinear Structural Dynamics -- The Evolutionary Advantage of Being Conservative: The Role of Hysteresis -- Cancer Growth: A Nonclassical Nonlinear Phenomenon? -- Seasonality and Harvesting, Revisited -- Applications to NDE and Ultrasonics: Models and Numerical Simulations -- Micropotential Model for Stress–Strain Hysteresis and PM Space -- Multiscale Approach and Simulations of Wave Propagation and Resonance in Media with Localized Microdamage: 1-D and 2-D Cases -- Modeling and Numerical Simulation of Nonclassical Effects of Waves, Including Phase Transition Front -- The Spectral Analysis of a PM Space Unit in the Context of the Classification of Nonlinear Phenomena in Ultrasonic Wave Propagation -- Nonlinear Ultrasonic Transmission Through Thin Bonded Interface: Theoretical Background and Numerical Simulations -- A LISA Model of the Nonlinear and Hysteretic Response of Interstitial Regions to Applied Stresses -- Numerical Analysis of the Anomalous Elastic Behavior of Hysteretic Media: Quasistatic, Dynamic, and Relaxation Experiments -- A 2-D Spring Model for the Simulation of Nonlinear Hysteretic Elasticity -- Nonclassical Nonlinear Dynamics of Solid Surfaces in Partial Contact for NDE Applications -- Nonlinear Dynamics in Granular Materials -- Thermally Induced Rate-Dependence of Hysteresis in Nonclassical Nonlinear Acoustics -- Inverse Problems and Genetic Algorithms -- Experimental Results and Applications -- Characterization and Imaging of Microdamage Using Nonlinear Resonance Ultrasound Spectroscopy (NRUS): An Analytical Model -- Laboratory Experiments using Nonlinear Elastic Wave Spectroscopy (NEWS): a Precursor to Health Monitoring Applications in Aeronautics, Cultural Heritage, and Civil Engineering -- Nonlinear Elastic Wave Experiments: Learning About the Behaviour of Rocks and Geomaterials -- Intrinsic Nonlinearity in Geomaterials: Elastic Properties of Rocks at Low Strain -- Nonlinear Acoustic Techniques for NDE of Materials with Variable Properties -- Nonlinear Elastic Behavior and Ultrasonic Fatigue of Metals -- Nonlinear Acoustic NDE: Inherent Potential of Complete Nonclassical Spectra -- Generation Threshold of Subharmonic Modes in Piezoelectric Resonator -- An Overview of Failure Modes and Linear Elastic Wave Propagation Damage Detection Methods in Aircraft Structures -- Inverse Problem Solution in Acoustic Emission Source Analysis: Classical and Artificial Neural Network Approaches.

This book comes as a result of the research work developed in the framework of two international projects: the European Science Foundation supported program NATEMIS (Nonlinear Acoustic Techniques for Micro-Scale Damage Diagnostics) and a Los Alamos-based international network. The main topics of both the programs and the book cover the phenomenology, theory and applications of Nonclassical Nonlinearity (NCNL). NCNL techniques have been found in recent years to be extremely powerful (up to 1000 times more than the corresponding linear techniques) in a wide range of applications, including Material Characterization, Ultrasonics, Geophysics and Maintenance and Restoration of artifacts. These techniques are being adopted as the main inspection and research tool in another European program: AERONEWS (Health monitoring of aircraft by nonlinear elastic wave propagation). In the future, the proposed Universality of NCNL is expected to extend the range of applications to numerous other fields and scientific disciplines outside acoustics and NDE.