scholarly journals A REBO-Potential-Based Model for Graphene Bending by $${{\Gamma}}$$ Γ -Convergence

2018 ◽  
Vol 229 (3) ◽  
pp. 1153-1195 ◽  
Author(s):  
Cesare Davini ◽  
Antonino Favata ◽  
Roberto Paroni
Keyword(s):  
Rebo Potential ◽  
Γ Convergence

scholarly journals From nonlinear to linearized elasticity via Γ-convergence: The case of multiwell energies satisfying weak coercivity conditions

2014 ◽  
Vol 25 (01) ◽  
pp. 1-38 ◽  
Author(s):  
V. Agostiniani ◽  
T. Blass ◽  
K. Koumatos
Keyword(s):  
Coercivity Conditions ◽  
Coercivity Condition ◽  
Nematic Elastomers ◽  
Linearized Elasticity ◽  
Γ Convergence

Linearized elasticity models are derived, via Γ-convergence, from suitably rescaled nonlinear energies when the corresponding energy densities have a multiwell structure and satisfy a weak coercivity condition, in the sense that the typical quadratic bound from below is replaced by a weaker p bound, 1 < p < 2, away from the wells. This study is motivated by, and our results are applied to, energies arising in the modeling of nematic elastomers.

FRACTURE MECHANICS IN PERFORATED DOMAINS: A VARIATIONAL MODEL FOR BRITTLE POROUS MEDIA

2009 ◽  
Vol 19 (11) ◽  
pp. 2065-2100 ◽  
Author(s):  
MATTEO FOCARDI ◽  
M. S. GELLI ◽  
M. PONSIGLIONE
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Fracture Mechanics ◽  
Special Functions ◽  
Variational Model ◽  
Perforated Domain ◽  
Functions Of Bounded Variation ◽  
Perforated Domains ◽  
Γ Convergence ◽  
Internal Scale

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.

ON A NONLOCAL FUNCTIONAL ARISING IN THE STUDY OF THIN-FILM BLISTERING

2010 ◽  
Vol 08 (02) ◽  
pp. 109-123
Author(s):  
N. ANSINI ◽  
V. VALENTE
Keyword(s):  
Thin Film ◽  
Asymptotic Analysis ◽  
Circular Plate ◽  
One Dimensional ◽  
Von Karman ◽  
Nonlocal Functional ◽  
Γ Convergence ◽  
Von Kármán

The energy of a Von Kármán circular plate is described by a nonlocal nonconvex one-dimensional functional depending on the thickness ε. Here we perform the asymptotic analysis via Γ-convergence as the parameter ε goes to zero.

A note on configurational anisotropy

2010 ◽  
Vol 466 (2123) ◽  
pp. 3167-3179 ◽  
Author(s):  
Valeriy V. Slastikov
Keyword(s):  
Variational Principle ◽  
Finite Number ◽  
Ferromagnetic Nanoparticles ◽  
Soft Ferromagnetic ◽  
Γ Convergence

We investigate an effect of configurational anisotropy in highly symmetric soft ferromagnetic nanoparticles. Using the micromagnetic variational principle and methods of Γ-convergence, we show that in ferromagnetic generalized right prisms with symmetry , 1 there is a finite number of preferred magnetization directions and that these directions are independent of the shape of the magnet. This result provides a rigorous justification of work by Cowburn and Welland.

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