Inserted: 24 jan 2015
Last Updated: 29 mar 2016
Journal: SIAM J. Math. Anal.
We provide a homogenisation result for the energy-functional associated with a purely brittle composite whose microstructure is characterised by soft periodic inclusions embedded in a stiffer matrix. We show that the two constituents as above can be suitably arranged on a microscopic scale $\varepsilon$ to obtain, in the limit as $\varepsilon$ tends to zero, a homogeneous macroscopic energy-functional explicitly depending on the opening of the crack.
Keywords: $\Gamma$-convergence, Free-discontinuity problems, fracture mechanics, multiscale analysis, homogenisation