In the thesis we describe the new notion of Visco-Energetic solutions to rate-independent systems (X, E, d) driven by a time dependent energy E and a dissipation quasi-distance d in a general metric-topological space X. As for the classic Energetic approach, solutions can be obtained by solving a modified time Incremental Minimization Scheme, where at each step the dissipation (quasi-)distance d is incremented by a viscous correction (e.g. proportional to the square of the distance d), which penalizes far distance jumps by inducing a localized version of the stability condition. We prove a general convergence result and a typical characterization by Stability and Energy Balance in a setting comparable to the standard energetic one, thus capable to cover a wide range of applications. Some of these applications, such as the evolution of Allen-Cahn energies and of some elastic material driven by noncovex energies, are included in the thesis and are explained in full details.

SOLUZIONI VISCO-ENERGETICHE PER PROBLEMI DI EVOLUZIONE RATE-INDEPENDENT

MINOTTI, LUCA
2017-03-22

Abstract

In the thesis we describe the new notion of Visco-Energetic solutions to rate-independent systems (X, E, d) driven by a time dependent energy E and a dissipation quasi-distance d in a general metric-topological space X. As for the classic Energetic approach, solutions can be obtained by solving a modified time Incremental Minimization Scheme, where at each step the dissipation (quasi-)distance d is incremented by a viscous correction (e.g. proportional to the square of the distance d), which penalizes far distance jumps by inducing a localized version of the stability condition. We prove a general convergence result and a typical characterization by Stability and Energy Balance in a setting comparable to the standard energetic one, thus capable to cover a wide range of applications. Some of these applications, such as the evolution of Allen-Cahn energies and of some elastic material driven by noncovex energies, are included in the thesis and are explained in full details.
File in questo prodotto:
File Dimensione Formato  
tesi_minotti.pdf

accesso aperto

Descrizione: tesi di dottorato
Dimensione 1.56 MB
Formato Adobe PDF
1.56 MB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11571/1215980
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus ND
  • ???jsp.display-item.citation.isi??? ND
social impact