Stress-Wave Propagation and Dynamic Effects in Shells (SPADES). Micromechanical Stress-Wave Response of 3-D Quartz Phenolic. Book 1: Development of Bloch-Fourier Analysis.

Abstract : This report describes the mathematical development and computer-code implementation of an analysis designed to calculate the micromechanical stress-wave response of composite materials. The analysis utilizes the Bloch sinusoidal-wave modes, which are found using a single unit cell of the composite, and superposes them by Fourier series in time to calculate the transient response of slabs to surface loads. Two computer codes are used: the BLOCH code, which determines the modes by a finite- element technique, and the FOURIER code, which superposes the modes and determines the transient response. The codes are set up to handle two-dimensional rectangular geometries. The prime advantage of the Bloch-Fourier analysis over two-dimensional direct-integration codes is that it can solve problems with large numbers of repeating fiber cells in the propagation direction. Such solutions would be prohibitively expensive or completely unfeasible with direct integration codes. A variety of check cases have been solved with the codes. (Author, modified-PL)