Experimental-analytical and numerical-analytical Halpin-Tsai models for predicting engineering elastic moduli of matrix composites

Based on the Halpin-Tsai analytical model, experimental-analytical and numerical-analytical models of homogenization of elastic moduli of matrix composites have been developed. The calculation results using the analytical model are “fitted” to the results of the experiment or numerical simulation. The fitting parameter of the model is the ratio of the constrained strain of the matrix of the experimental sample or numerical model to the constrained strain of the matrix in the Halpin-Tsai model. Identification of the fitting parameter is performed using one reference point for the basic composition of the composite. A power law relation of the fitting parameter on the volume fraction of inclusions and a logarithmic relation of the power law exponent on the contrast of the elastic moduli of the phases are accepted. For composites with spherical inclusions, the exponent is equal to the decimal logarithm of the contrast. The natural logarithm exponent is used for composites with non-spherical inclusions. A good agreement between the calculation results and experimental and numerical data was obtained for isotropic and transversally isotropic composites with different contents, morphology, and contrast in phase properties.