Published Paper

Inserted: 24 jan 2015
Last Updated: 29 mar 2016

Journal: SIAM J. Math. Anal.
Volume: 48
Pages: 1178-1209
Year: 2016

Abstract:

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

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