MIXTURE THEORY FOR ELASTIC LAMINATED COMPOSITES

A theory is developed which governs the dynamic response of a homogeneous, elastic, dispersive material. The material is used as a model of a two phase layered material in which each of the layers is isotropically elastic. The theory is derived from a general theory for all two phase periodic materials which was developed earlier [1]. The general theory was derived using the theory of mixtures. Dispersion is accommodated through the use of elastodynamic operators and for the layered material a micro model is used to establish the forms of the operators appropriate to the material. These specific operators are simplified by replacing them with truncated power series before introducing them into the equations of linear momentum. The theory for layered materials contains nineteen model constants and equations are developed from which these constants can be derived from the layer constants. The equations are derived partly using micro model analysis and partly by matching specific dynamic behaviors of the model and prototype. The ability with which the model predicts the dynamic response of the layered material is assessed in two ways. Both compare spectra reflecting the behavior of infinite trains of the principal kinds of waves. The first compares spectral lines from the model with those derived from the exact theory for layered materials. The second compares lines from the model with those obtained from experiments. Predictions from the model prove to be quite accurate. © 1979.