Development of a nonlinear continuum model for wave propagation in joined media: theory for single joint set

Abstract A method for constructing dispersive, nonlinear continuum models of jointed media is described herein and exemplified for the case of a single regular joint set. System nonlinearities in the example treated result from nonlinear joint properties. 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 constitutive relations. For linear response, the derived model is validated by comparing the predicted phase velocity spectra with the exact spectra. For nonlinear response, model validation is accomplished by comparing predicted results for several transient wave propagation problems with “exact” data obtained by use of detailed FEM analyses wherein the microstructure of the joined media is modeled explicitly. The validation studies reveal that the derived continuum model provides good simulation of complex wave phenomena and furnishes an economical alternative to detailed, explicit FEM models. The studies performed reveal the importance of wave dispersion effects for nonlinear as well as linear joint responses. The research presented is in response to a need for an advanced computation model to be used in conjunction with explosive source identification.