A finite‐element framework for the modelling and simulation of phase transforming magnetic solids using energy relaxation concepts

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.