Comparison of the Non-Interaction and Differential Schemes in predicting the Effective Elastic Properties of Fractured Media
Source abstract
Abstract
The non-interaction approximation (NIA) formulated in compliances and the differential effective media (DEM) schemes are believed to be the most accurate theories for predicting the effective elasticity of fractured solids. While their predictions are always plausible, the DEM yields consistently softer effective properties than does the NIA. Here I compare these two theories with the finite element (FE) modeling for arrays of randomly located, parallel, penny-shaped cracks. I perform FE simulations by applying the homogeneous strain and homogeneous stress boundary conditions that establish the upper and lower bounds for the effective stiffness tensor. These numerically derived bounds demonstrate that the NIA is more accurate than the DEM.
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Research context
OpenAlex topics: Rock Mechanics and Modeling · Numerical methods in engineering · Composite Material Mechanics
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