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8 results on '"Anza Hafsa, O"'

1. Remarks on homogenization and $3D$-$2D$ dimension reduction of unbounded energies on thin films

Author

Anza Hafsa, Omar and Mandallena, Jean-Philippe

Subjects
Mathematics, QA1-939
Abstract

We study periodic homogenization and $3D$-$2D$ dimension reduction by $\Gamma (\pi )$-con-vergence of heterogeneous thin films whose the stored-energy densities have no polynomial growth. In particular, our results are consistent with one of the basic facts of nonlinear elasticity, namely the necessity of an infinite amount of energy to compress a finite volume of matter into zero volume. However, our results are not consistent with the noninterpenetration of the matter.

Published
2023
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4. Homogenization of periodic nonconvex integral functionals in terms of Young measures

Author

Anza Hafsa, O, Mandallena, J-P, Michaille, G, Anza Hafsa, O, Mandallena, J-P, and Michaille, G

Abstract

Homogenization of periodic functionals, whose integrands possess possibly multi-well structure, is treated in terms of Young measures. More precisely, we characterize the -limit of sequences of such functionals in the set of Young measures, extending the relaxation theorem of Kinderlherer and Pedregal. We also make precise the relationship between our homogenized density and the classical one.

Published
2006

5. Numerical analysis of microstructures: the influence of incompatibility

Author

Chipot, M, Escher, J, Chipot, M ( M ), Escher, J ( J ), Anza Hafsa, O, Chipot, M, Escher, J, Chipot, M ( M ), Escher, J ( J ), and Anza Hafsa, O

Abstract

We are concerned with the appearance of microstructures in some problems of Calculus of Variations experiencing ‘wells’ or minimum of energy. Using piecewise linear finite elements, we give energy estimates and analyze their dependence on the incompatibility of the wells.

Published
2005

7. Homogenization of periodic nonconvex integral functionnals in terms of young measures

Author

Jean-Philippe Mandallena, Gérard Michaille, Omar Anza Hafsa, Laboratoire de Mécanique et Génie Civil (LMGC), Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS), Mathématiques, Informatique, Physique, et Applications / Université de Nîmes (MIPA), Université de Nîmes (UNIMES), University of Zurich, and Anza Hafsa, O

Subjects
2606 Control and Optimization, Control and Optimization, 010102 general mathematics, Mathematical analysis, homogenization, 2207 Control and Systems Engineering, [MATH.MATH-CA]Mathematics [math]/Classical Analysis and ODEs [math.CA], 16. Peace & justice, 01 natural sciences, Homogenization (chemistry), 010101 applied mathematics, 10123 Institute of Mathematics, Computational Mathematics, 510 Mathematics, Control and Systems Engineering, Young measures, 0101 mathematics, 2605 Computational Mathematics, Mathematics
Abstract

Homogenization of periodic functionals, whose integrands possess possibly multi-well structure, is treated in terms of Young measures. More precisely, we characterize the Γ -limit of sequences of such functionals in the set of Young measures, extending the relaxation theorem of Kinderlherer and Pedregal. We also make precise the relationship between our homogenized density and the classical one.

Published
2006
Full Text
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8. Variational formulations on thin elastic plates with constraints

Author

Anza Hafsa, Omar, University of Zurich, Anza Hafsa, O, Laboratoire de Mécanique et Génie Civil (LMGC), and Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS)

Subjects
10123 Institute of Mathematics, 510 Mathematics, [MATH.MATH-CA]Mathematics [math]/Classical Analysis and ODEs [math.CA]
Abstract

We derive variational formulations for thin elastic plates from bulk energies by dimensional reduction. The main feature is to consider a family of problems with internal constraints on normal deformations. Our approach consists of two stages. First we obtain an abstract variational convergence result. Then we study the integral representation of the limit functional.

Published
2005

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