A novel solution for effective elastic moduli of 2D cracked medium

This paper provides a novel solution for effective elastic moduli of 2D cracked medium. In the solution, the inclined crack is located in the center position of a square plate. The cracked square plate is stretched with a tension p in the y-direction. The elastic responses, or the elongation in y-direction and the shortening in x-direction can be evaluated by using the EEVM (eigenfunction expansion variational method). Therefore, the relevant strains, the Young’s modulus and the Poisson’s ratio can be evaluated accordingly. The effective elastic moduli for the randomly distributed cracks are obtained from an average of many relevant values at different inclined angles of the crack. From computed results, many approximation schemes for the effective elastic moduli are suggested.