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A Phase Transition Model Describing Auxetic Materials

  • Elena BonettiEmail author
  • Mauro Fabrizio
  • Michel Frémond
Chapter
Part of the Springer INdAM Series book series (SINDAMS, volume 22)

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.

Keywords

Auxetic materials Nonlinear PDE system Phase transitions Second gradient theory 

AMS (MOS) Subject Classification

35K87 74N25 

Notes

Acknowledgement

This paper is dedicated to Gianni Gilardi, with friendship and gratitude.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Elena Bonetti
    • 1
    • 2
    Email author
  • Mauro Fabrizio
    • 3
  • Michel Frémond
    • 4
  1. 1.Dipartimento di Matematica F. EnriquesUniversità di MilanoMilanoItaly
  2. 2.IMATI-CNRPaviaItaly
  3. 3.Università di BolognaScuola di Ingegneria e ArchitetturaBolognaItaly
  4. 4.Dipartimento di Ingegneria Civile e InformaticaUniversità di Roma Tor VergataRomaItaly

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