Data di Pubblicazione:
2017
Citazione:
A phase transition model describing auxetic materials / E. Bonetti, M. Fabrizio, M. Fremond (SPRINGER INDAM SERIES). - In: Solvability, Regularity, and Optimal Control of Boundary Value Problems for PDEs : in Honour of Prof. Gianni Gilardi / [a cura di] P. Colli; A. Favini; E. Rocca; G. Schimperna; J. Sprekels. - [s.l] : Springer, 2017. - ISBN 9783319644882. - pp. 75-95 (( convegno INdAM tenutosi a Cortona nel 2016 [10.1007/978-3-319-64489-9_4].
Abstract:
In this paper we introduce a new model describing the behavior of auxetic materials in terms of a phase-field PDE system. More precisely, the evolution equations are recovered by a generalization of the principle of virtual power in which microscopic motions and forces, responsible for the phase transitions, are included. The momentum balance is written in the setting of a second gradient theory, and it presents nonlinear contributions depending on the phases. The evolution of the phases is governed by variational inclusions with non-linear coupling terms. By use of a fixed point theorem and monotonicity arguments, we are able to show that the resulting initial and boundary value problem admits a weak solution.
Tipologia IRIS:
03 - Contributo in volume
Keywords:
auxetic materials; nonlinear PDE; phase transitions
Elenco autori:
E. Bonetti, M. Fabrizio, M. Fremond
Link alla scheda completa:
Titolo del libro:
Solvability, Regularity, and Optimal Control of Boundary Value Problems for PDEs : in Honour of Prof. Gianni Gilardi