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Degenerating Cahn-Hilliard systems coupled with mechanical effects and complete damage processes

Christian Heinemann, Christiane Kraus (2014)

Mathematica Bohemica

This paper addresses analytical investigations of degenerating PDE systems for phase separation and damage processes considered on nonsmooth time-dependent domains with mixed boundary conditions for the displacement field. The evolution of the system is described by a degenerating Cahn-Hilliard equation for the concentration, a doubly nonlinear differential inclusion for the damage variable and a quasi-static balance equation for the displacement field. The analysis is performed on a time-dependent...

Design-dependent loads in topology optimization

Blaise Bourdin, Antonin Chambolle (2003)

ESAIM: Control, Optimisation and Calculus of Variations

We present, analyze, and implement a new method for the design of the stiffest structure subject to a pressure load or a given field of internal forces. Our structure is represented as a subset S of a reference domain, and the complement of S is made of two other “phases”, the “void” and a fictitious “liquid” that exerts a pressure force on its interface with the solid structure. The problem we consider is to minimize the compliance of the structure S , which is the total work of the pressure and...

Design-dependent loads in topology optimization

Blaise Bourdin, Antonin Chambolle (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We present, analyze, and implement a new method for the design of the stiffest structure subject to a pressure load or a given field of internal forces. Our structure is represented as a subset S of a reference domain, and the complement of S is made of two other “phases”, the “void” and a fictitious “liquid” that exerts a pressure force on its interface with the solid structure. The problem we consider is to minimize the compliance of the structure S, which is the total work of the pressure...

Dissipatività e unicità per il problema dinamico unidimensionale della viscoelasticità lineare

Giorgio Vergara Caffarelli (1988)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Fissato lo spazio di Sobolev H 1 , 2 come ambiente del problema dinamico per un corpo viscoelastico unidimensionale si dimostra un teorema di unicità per la classe delle funzioni di rilassamento convesse. Si fa inoltre vedere come tale unicità sia strettamente legata allo spazio ambiente considerato.

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