An extension of the present classical elasticity continuum model and its application in the analysis of acoustic wave propagation in elastic media

The purpose of this theoretical analysis has been to develop a comprehensive elastic quasicontinuum model which more accurately describes the behavior of real crystalline solids which possess microstructure, and then to apply this model in the study of acoustic wave propagation. The quasicontinuum mathematical model acknowledges the discrete nature of crystalline materials through the inclusion of scale parameters with dimensions of length which are small relative to both the material body dimensions and the macroscopic length parameters used in the characterization of acoustic waves. The nonlinear properties of anisotropic solids have been included through fourth order in elastic moduli in a second gradient elasticity model. The acoustic wave propagation is then described through boundary conditions and coupled partial differential equations which include both the nonlocal and nonlinear crystalline material properties. This model has been applied in the study of longitudinal and transverse acoustic waves in homogeneous simple cubic crystalline solids. Asymptotic perturbation techniques have been applied to obtain the wavetrain solutions in bulk materials along with the associated dispersion relations. The stability of the wavetrain solutions has been assessed. Bulk solitary waves have been analyzed, and far field differential equations developed in order to investigate transverse bions. Boundary conditions have been developed in unplated and thinly plated materials, and both weakly and strongly coupled shear horizontal surface acoustic wavetrains have been analyzed.