• Coupled systems mechanics
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• v.7 no.1
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• pp.5-25
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• 2018

A fully-coupled thermodynamic-based transient finite element formulation is proposed in this article for electric, magnetic, thermal and mechanic fields interactions limited to the linear case. The governing equations are obtained from conservation principles for both electric and magnetic flux, momentum and energy. A full-interaction among different fields is defined through Helmholtz free-energy potential, which provides that the constitutive equations for corresponding dual variables can be derived consistently. Although the behavior of the material is linear, the coupled interactions with the other fields are not considered limited to the linear case. The implementation is carried out in a research version of the research computer code FEAP by using 8-node isoparametric 3D solid elements. A range of numerical examples are run with the proposed element, from the relatively simple cases of piezoelectric, piezomagnetic, thermoelastic to more complicated combined coupled cases such as piezo-pyro-electric, or piezo-electro-magnetic. In this paper, some of those interactions are illustrated and discussed for a simple geometry.