EFFECTIVE ELASTIC-MODULI OF 2-DIMENSIONAL BRITTLE SOLIDS WITH INTERACTING MICROCRACKS .1. BASIC FORMULATIONS

Statistical micromechanical formulations are presented to investigate effective elastic moduli of two-dimensional brittle solids with intera cting slit microcracks. The macroscopic stress-strain relations of ela stic solids with interacting microcracks are micromechanically derived by taking the ensemble average over all possible realizations which f eature the same material microstructural geometry, characteristics, an d loading conditions. Approximate analytical solutions of a two-microc rack interaction problem are introduced to account for microcrack inte raction among many randomly oriented and located microcracks. The over all elastic-damage compliances of microcrack-weakened brittle solids u nder uniaxial and biaxial loads are also derived. Therefore, stationar y statistical micromechanical formulation is completed. Moreover, some special cases are investigated by using the proposed framework. At va riance with existing phenomenological continuum damage models, the pro posed framework does not employ any fitted ''material parameters.'' '' Cleavage 1'' microcrack growth and ''evolutionary damage models'' with in the proposed context will be presented in Part II of this series. I t is emphasized that microstructural statistical informations are alre ady embedded in the proposed ensemble-averaged equations and, therefor e, no Monte Carlo simulations are needed.