Stress wave propagation is of fundamental importance in modern technology because it provides the primary means for the nondestructive examination of defects and in-homogeneities in opaque materials and the only means for studying the response of materials under the dynamic loading conditions associated with impact and explosions. Advances in such diverse technologies as nuclear reactor safety, integrated circuit inspection, and armor penetration depend strongly on advances in the modeling of the propagation of stress waves and in the improved characterization of the dynamic response of materials. Stress waves play a central role in a wide range of geotechnical and geophysical applications including reservoir exploration, earthquake monitoring, and the prediction of ground motion due to earthquakes and blast loading. Because of the inherent complexity of stress waves in solids (i.e., three wave speeds, anisotropy, and inhomogeneity), as well as the importance of nonlinearity in applications involving intense loading, progress in the modeling of stress wave phenomena depends critically on large scale computations. Increased availability of supercomputers provides an excellent opportunity for advances in the modeling of three dimensional phenomena, including such complicating features as anisotropy, inhomogeneity, defects, nonlinearity, and sliding interfaces. Research is needed on accurate and efficient algorithms for these calculations and for acoustic imaging which requires algorithms for inverse problems in which the size and shape of defects, as well as variations in density and in elastic moduli, are to be obtained by probing the region of interest with ultrasonic waves. Improved characterization of the sources and receivers of ultrasound is essential for reliable determination of the required geometrical features and material properties. Improved understanding of the dynamic inelastic response of materials is crucial to realizing the full benefits of the emerging computational power. Strain rate sensitivity, shear strain localization, crack propagation, twinning, and phase transformations are all aspects of mechanical response that need to be modeled in many dynamic loading applications. Basic experiments on these aspects of material behavior combined with computer simulation of the experiments should lead to significant progress in understanding the underlying mechanisms and, thereby, to improved models for use in computations.

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