A Mixture Theory for Wave Propagation in Angle-Ply Laminates, Part 1: Theory

Abstract

In an effort to construct a continuum model with microstructure for elastic angle-ply laminates, an asymptotic mixture theory with multiple scales is presented in this two-part paper. The theory, which is in the form of a binary mixture, can simulate wave propagation in linearly elastic laminated composites with orthotropic lamina. Reissner’s new variational principle has been adopted to avoid the numerous solution procedures of microstructure boundary value problems (MBVP’s), which are required to find mixture properties in terms of the geometrical and material properties of the two constituents of the composite. For the special case of isotropic lamina the variational approach yields the same results as those derived by the asymptotic mixture theory with multiple scales [10] which requires the solution of the MBVP’s. The advantage of the variational approach over the alternative is that it makes the application of the technique feasible to wave propagation in fiber-reinforced and particulate composites. The application of the mixture model to angle-ply laminates is deferred to the second part of the paper, which also contains a study of dispersion of time harmonic waves in angle-ply laminates.