Adaptive modeling of wave propagation in heterogeneous elastic solids

This manuscript presents the results of a detailed research investigation on a fundamental problem in wave mechanics: the propagation of stress waves in heterogeneous elastic solids. The theory and methodologies of hierarchical modeling of heterogeneous materials [J. Comput. Phys. 164 (2000) 22; Int. J. Comp. Civil Str. Engrg. 1 (2000) 1; Goal-oriented Adaptive Modeling of Heterogeneous Elastic Solids, Ph.D. thesis, The University of Texas at Austin, 2000; Comput. Methods Appl. Mech. Engrg. 190 (2001) 6089] are extended to elastodynamic cases to make possible the control of the modeling error in the local average stress. One-dimensional numerical applications are given.

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