Complete damage processes

Christian Heinemann () and Christiane Kraus ()
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Christian Heinemann: Weierstrass Institute for Applied Analysis and Stochastics
Christiane Kraus: Weierstrass Institute for Applied Analysis and Stochastics

Chapter 6 in Phase Separation Coupled with Damage Processes, 2014, pp 119-143 from Springer

Abstract: 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.

Keywords: Weak Solution; Variational Inequality; Lipschitz Domain; Jump Condition; Energy Inequality (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/978-3-658-05252-2_6

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