A Unified Micromechanical Model for the Mechanical Properties of Two Constituent Composite Materials. Part I: Elastic Behavior

Abstract

This series of papers reports a new, general, and unified micromechanical model for estimating the three-dimensional mechanical properties of a composite made from two isotropic constituent materials, i.e., continuous fiber and matrix. The present paper focuses on model development and its application to the prediction of the composite elastic property. The most important feature of this model is that the stresses generated in the constituents in a representative volume element of the composite are correlated with a bridging matrix. Based on this bridging matrix, those required quantities for the composite follow easily. A general routine to determine the bridging matrix elements is presented, and a set of explicit expressions of them for simulating a transversely isotropic composite is given. The bridging matrix depends on the physical as well as the geometrical properties of the fiber and matrix materials. For a fixed geometry, the bridging matrix can depend only on the physical properties of the constituents. This feature makes it easy to extend the present bridging matrix to include any inelastic deformation effect from the constituents and to establish a unified model to simulate, in addition, the plastic, strength, rubber-elastic, and laminate failure behaviors of fibrous composites, which will be addressed subsequently. Only linear elastic properties are considered in the present paper. The model has been applied to estimate the elastic properties of two unidirectional composites and a knitted-fabric-reinforced composite. Good agreement has been found between the predicted and available experimental data.