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Complete damage processes

In: Phase Separation Coupled with Damage Processes

Author

Listed:
  • Christian Heinemann

    (Weierstrass Institute for Applied Analysis and Stochastics)

  • Christiane Kraus

    (Weierstrass Institute for Applied Analysis and Stochastics)

Abstract

In the preceding chapters, Cahn-Hilliard equations have been coupled with incomplete damage processes. The uniform convexity assumptions in (4.2a) as well as in (5.2a), respectively, prevents the PDE system (3.27) from degeneration (in the elastic energy). However, for a more precise description of damage phenomena, the elastic energy should be allowed to degenerate on maximally damaged regions. Studying this case requires further mathematical tools such as Γ -convergence of regularized free energies, representation of shrinking sets with Lipschitz domains and space-time local Sobolev spaces.

Suggested Citation

  • Christian Heinemann & Christiane Kraus, 2014. "Complete damage processes," Springer Books, in: Phase Separation Coupled with Damage Processes, edition 127, chapter 6, pages 119-143, Springer.
    • Handle: RePEc:spr:sprchp:978-3-658-05252-2_6
    DOI: 10.1007/978-3-658-05252-2_6
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