Development of a mixture model for nonlinear wave propagation in fiber-reinforced composites

Abstract

A method for constructing dispersive, nonlinear mixture models for unidirectionally fiber-reinforced composites is described. System nonlinearities in the treated example result from nonlinear material properties of the constituents. The proposed model is a nonlinear generalization of the linear model developed by Murakami and Hegemier [Journal of Applied Mechanics. Vol. 53, pp. 765–773 (1986)] for elastic constituents. Model construction is based upon a homogenization technique which employs multivariable asymptotic expansions in conjunction with certain weighted residual procedures. The methodology furnishes the equations of motion, the appropriate initial and boundary conditions, and a set of consistent rate constitutive relations. Model validation for linear and nonlinear dynamic responses is accomplished by comparing predicted results for wave-guide and wave-reflect problems with available experimental data or data obtained by use of a detailed finite element (FE) analysis. The validation studies reveal that the derived continuum model provides good simulations of complex wave phenomena and furnishes an economical alternative to detailed, explicit FE, models. The studies performed reveal the importance of wave dispersion and attenuation phenomena in nonlinear as well as linear wave propagation in the composites.