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

摘要

The report describes the mathematical development and computer-code implementation of an analysis designed to calculate the micromechanical stress-wave response of composite materials. Such information is essential to understand and minimize gross fracture and mechanical property degradation in 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: (1) the BLOCH code, which determines the modes by a finite-element technique; and (2) 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)