A Phase Transition Model Describing Auxetic Materials
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.
KeywordsAuxetic materials Nonlinear PDE system Phase transitions Second gradient theory
AMS (MOS) Subject Classification35K87 74N25
This paper is dedicated to Gianni Gilardi, with friendship and gratitude.
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