A simple model for phase transitions: from the discrete to the continuum problem-Reference-Cited by-同舟云学术

A simple model for phase transitions: from the discrete to the continuum problem

Published:2003 Issue:1 Volume:61 Page:89-109
ISSN:0033-569X
Container-title:Quarterly of Applied Mathematics
language:en
Short-container-title:Quart. Appl. Math.

Author:

Pagano S.,Paroni R.

Abstract

In this paper we study a one-dimensional model simulating the shear in a two-dimensional body. We analyse the discrete system and we deduce the continuum limit of the lattice model as the lattice parameter goes to zero. Different energies are introduced and linked together.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics

Link

http://www.ams.org/qam/2003-61-01/S0033-569X-2003-1955225-9/S0033-569X-2003-1955225-9.pdf

Reference22 articles.

1. Fine phase mixtures as minimizers of energy;Ball, J. M.;Arch. Rational Mech. Anal.,1987

2. J. M. Ball and R. D. James, Proposed experimental tests of a theory of fine microstructure and the two-well problem, Phil. Tran. R. Soc. Lond. A 338, 389–450 (1992)

3. Variational formulation of softening phenomena in fracture mechanics: the one-dimensional case;Braides, Andrea;Arch. Ration. Mech. Anal.,1999

4. Continuum limits of discrete systems without convexity hypotheses;Braides, Andrea;Math. Mech. Solids,2002

5. Limits of discrete systems with long-range interactions;Braides, Andrea;J. Convex Anal.,2002

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