Advertisement
Published in:
2017 | OriginalPaper | Chapter
A Phase Transition Model Describing Auxetic Materials
Authors : Elena Bonetti, Mauro Fabrizio, Michel Frémond
Published in: Solvability, Regularity, and Optimal Control of Boundary Value Problems for PDEs
Publisher: Springer International Publishing
Activate our intelligent search to find suitable subject content or patents.
Select sections of text to find matching patents with Artificial Intelligence. powered by
Select sections of text to find additional relevant content using AI-assisted search. powered by
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.