Frequency-dependent tensile and compressive effective moduli of elastic solids with distributed penny-shaped microcracks

This paper develops micromechanics models to estimate the tensile and compressive elastic moduli of elastic solids containing randomly distributed penny-shaped microcracks. The crack faces are open under tension and closed under compression. When the crack faces are closed, they may slide against one another following Coulomb’s law of dry friction. The micromechanics models provide analytical expressions of the tensile and compressive moduli for both static and dynamic cases. It is found that the tensile and compressive moduli are different. Further, under dynamic loading, both compressive and tensile moduli are frequency dependent. As a by-product, the micromechanics models also predict wave attenuation in the dynamic case. Numerical simulations using the finite element method are conducted to validate the micromechanics models.