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A finite‐element framework for the modelling and simulation of phase transforming magnetic solids using energy relaxation concepts
Author(s) -
Bartel Thorsten,
Kiefer Bjoern,
Buckmann Karsten,
Menzel Andreas
Publication year - 2018
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201800415
Subject(s) - finite element method , magnetic field , dissipative system , relaxation (psychology) , statistical physics , physics , microstructure , scalar (mathematics) , classical mechanics , mechanics , computer science , materials science , mathematics , geometry , thermodynamics , quantum mechanics , psychology , social psychology , metallurgy
Abstract In this contribution we present a variational framework suitable for the finite element implementation of energy relaxation‐based dissipative magnetostriction and magnetic shape memory alloy models. Inspired by the non‐local nature of the magnetostatic energy stored in the self‐field associated with magnetised solids, three global fields are considered: the displacement field, the scalar magnetic potential, and additional state variable fields that parameterise the microstructure. This global variational three‐field problem is enhanced by the consideration of Karush‐Kuhn‐Tucker parameters—stemming from restrictions w.r.t. the microstructural variable evolution—at each node of the finite element mesh. This approach allows the simulation of magnetomechanically fully‐coupled, microstructure evolution‐driven responses in arbitrarily shaped domains.