Conclusion

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 8 in Phase Separation Coupled with Damage Processes, 2014, pp 163-165 from Springer

Abstract: Abstract In this work, we have investigated mathematical models describing both phenomena, phase separation and damage processes, in a unifying approach. Phase separation is modeled by elastic Cahn-Hilliard equations, whereas the damage processes are described by a doubly nonlinear differential inclusion. The forces are assumed to be in a quasi-static equilibrium. We have introduced the corresponding PDE model (1.1)-(1.2) in Chapter 3 and we have shown thermodynamic consistency. The main aim has been to prove existence of weak solutions of the coupled system for various types of free energy densities of the form (1.3). The damage dissipation potential is rate-dependent and specified by (1.4).

Date: 2014
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DOI: 10.1007/978-3-658-05252-2_8

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