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Hier Partnerlogo einfügen An linker oberer Ecke dieses Rechtecks ausrichten,

Homogenization via unfolding in periodic elasticity with contact on closed and open cracks Alain Damlamian, Doina Cioranescu, Julia Orlik. Udine 2012. Hier Partnerlogo einfügen An linker oberer Ecke dieses Rechtecks ausrichten, Rechteck anschließend löschen.

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Hier Partnerlogo einfügen An linker oberer Ecke dieses Rechtecks ausrichten,

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  1. Homogenization via unfolding in periodic elasticity with contact on closed and open cracksAlain Damlamian, Doina Cioranescu, Julia Orlik Udine 2012 Hier Partnerlogo einfügen An linker oberer Ecke dieses Rechtecks ausrichten, Rechteck anschließend löschen. Wenn kein Partnerlogo verwendet wird, Rechteck und Gliederungslinie löschen.

  2. Content • Auxiliary inequalities • Statement of periodic contact problem • Boundedness, compactness estimates • Convergences • Homogenized and auxiliary contact problems

  3. Strong formulation of the contact problem • Elasticity: • Signorini with friction: • Boundary conditions:

  4. Weak formulation of the - contact problem

  5. Unfolding

  6. Some auxiliary results related to unfolding

  7. Further properties of the unfolding Unfolding provides the equivalent formulation of the problem with a strong advantage that sequences of functions defined on varying domains are transformed to sequences on fixed domains.

  8. Reverse Hölder inequality

  9. An inequality the matrix domain For open cracks, we refer to [Attouch, Murat, 1985] and Chapter 3 [Lewinski, Telega, 1999 ]. In [Cioranescu, D., Saint Jean Paulin, J., 1999] both, cracks and perforated by holes domain are staddied. The traces on the cracks are controlled by the -norm.

  10. Inequalities for the inclusions

  11. Korn‘s inequality for non-locked -periodic inclusions

  12. Modification of Korn‘s inequality for inclusions Proof: For the tangential part of the jump we used the same argument + reverse Hölder‘s inequality.

  13. Compactness of the solution.

  14. Homogenization. Assumptions

  15. Weak convergences for functions on

  16. Weak convergences for functions on

  17. Weak convergences for functions on

  18. Weak convergence of jumps

  19. Convergence of the frictional functional

  20. Main homogenization result

  21. The problem for corrector

  22. Strong formulation for open cracks with Treska friction Homogenized problem Contact problem for the corrector on the unit cell

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