FRACTURE MECHANICS IN PERFORATED DOMAINS: A VARIATIONAL MODEL FOR BRITTLE POROUS MEDIA
Copyright policy )FRACTURE MECHANICS IN PERFORATED DOMAINS: A VARIATIONAL MODEL FOR BRITTLE POROUS MEDIA
This paper deals with fracture mechanics in periodically perforated domains. Our aim is to provide a variational model for brittle porous media in the case of anti-planar elasticity. Given the perforated domain Ωε ⊂ ℝN (ε being an internal scale representing the size of the periodically distributed perforations), we will consider a total energy of the type [Formula: see text] Here u is in SBV(Ωε) (the space of special functions of bounded variation), Su is the set of discontinuities of u, which is identified with a macroscopic crack in the porous medium Ωε, and [Formula: see text] stands for the (N - 1)-Hausdorff measure of the crack Su. We study the asymptotic behavior of the functionals [Formula: see text] in terms of Γ-convergence as ε → 0. As a first (nontrivial) step we show that the domain of any limit functional is SBV(Ω) despite the degeneracies introduced by the perforations. Then we provide explicit formula for the bulk and surface energy densities of the Γ-limit, representing in our model the effective elastic and brittle properties of the porous medium, respectively.
- Roma Tre University Italy
- University of Pisa Italy
- New York University Italy
- Sapienza University of Rome Italy
- University of Florence Italy
special functions of bounded variation, PDEs with low regular coefficients and/or low regular data, cavities, Functions of bounded variation, generalizations, homogenization, variational methods, brittle fracture; cavities; composite and mixture properties; homogenization; perforated domains; special functions of bounded variation; variational methods, Other numerical methods in solid mechanics, Effective constitutive equations in solid mechanics, Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.), brittle fracture, composite and mixture properties, Brittle fracture, Neumann problems; fracture mechanics; porous media, Brittle fracture; Homogenization; Perforated domains; Composite and mixture properties; Cavities; Variational methods; Special functions of bounded variation., Composite and mixture properties, perforated domains
special functions of bounded variation, PDEs with low regular coefficients and/or low regular data, cavities, Functions of bounded variation, generalizations, homogenization, variational methods, brittle fracture; cavities; composite and mixture properties; homogenization; perforated domains; special functions of bounded variation; variational methods, Other numerical methods in solid mechanics, Effective constitutive equations in solid mechanics, Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.), brittle fracture, composite and mixture properties, Brittle fracture, Neumann problems; fracture mechanics; porous media, Brittle fracture; Homogenization; Perforated domains; Composite and mixture properties; Cavities; Variational methods; Special functions of bounded variation., Composite and mixture properties, perforated domains
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