Phase field modeling of nonlinear material behavior

Details Phase field modeling of nonlinear material behavior Phase field modeling of nonlinear material behavior

2009-05-28

arxiv.org/abs/0905.4617v2

In K. Hackl (ed.), IUTAM Symposium on Variational Concepts with Applications to the Mechanics of Materials, IUTAM Bookseries 2

Physics

Condensed Matter

Materials Science

12 pages, 4 figures. v1: as submitted. v2: as published (conclusion added, unessential part of appendix removed, minor typeset

Scientific paper

10.1007/978-90-481-9195-6_16

Materials that undergo internal transformations are usually described in solid mechanics by multi-well energy functions that account for both elastic and transformational behavior. In order to separate the two effects, physicists use instead phase-field-type theories where conventional linear elastic strain is quadratically coupled to an additional field that describes the evolution of the reference state and solely accounts for nonlinearity. In this paper we propose a systematic method allowing one to split the non-convex energy into harmonic and nonharmonic parts and to convert a nonconvex mechanical problem into a partially linearized phase-field problem. The main ideas are illustrated using the simplest framework of the Peierls-Nabarro dislocation model.

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