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math.AP2020
Microscopical justification of Solid-State Wetting and Dewetting
Paolo Piovano, Igor Velčić
The continuum model related to the Winterbottom problem, i.e., the problem of determining the equilibrium shape of crystalline drops resting on a substrate, is derived in dimension…
math.AP2012
Derivation of a homogenized von-Karman shell theory from 3D elasticity
Peter Hornung, Igor Velcic
We derive the model of homogenized von Kármán shell theory, starting from three dimensional nonlinear elasticity. The original three dimensional model contains two small parameters…
math.AP2012
Derivation of a homogenized nonlinear plate theory from 3d elasticity
Peter Hornung, Stefan Neukamm, Igor Velcic
We derive, via simultaneous homogenization and dimension reduction, the Gamma-limit for thin elastic plates whose energy density oscillates on a scale that is either comparable to,…