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MiS Preprint

On the general homogenization and $\Gamma$-closure for the equations of von Kármán plate from $3D$ nonlinear elasticity

Igor Velčić


Starting from $3D$ elasticity equations we derive the model of the homogenized von K\'arm\'an plate by means of $\Gamma$-convergence. This generalizes the recent results, where the material oscillations were assumed to be periodic. We also prove the locality of $\Gamma$-closure i.e. that every energy density obtained in this way by mixing $n$ different materials is at almost every point of domain limit of some sequence of the energy densities obtained by periodic homogenization.

MSC Codes:
35B2, 74Q15, 74K20
elasticity, dimension reduction, homogenization, von K\'arm\'an plate model

Related publications

2017 Repository Open Access
Igor Velčić

On the general homogenization of von Kármán plate equations from three-dimensional nonlinear elasticity

In: Analysis and applications, 15 (2017) 1, pp. 1-49