Effective elastic properties of fractured materials by means of a homogenization approach

Resumo

A main characteristic of many engineering materials is the presence of natural fractures at different
scales. The effective mechanical behavior of these materials is strongly affected by that of the fractures, which can

be viewed as discontinuities able to transfer stresses. The contribution of the present work relies upon microme-
chanics for assessing the effective stiffness through homogenization upscaling of elastic materials with embedded

microfractures. In the context of Eshelby equivalent inclusion theory, the approach makes use of the Mori-Tanaka

scheme to formulate estimates for the homogenized elastic moduli. For this purpose, the fractures are geometri-
cally modeled as oblate spheroids endowed with appropriate elastic properties. Particular emphasis is dedicated to

addressing the configurations of a single family or two families of parallel fractures, as well as the configuration
of randomly oriented fractures.