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A modelling framework for finite strain magnetoviscoelasticity. (English) Zbl 1446.74121

Summary: The main objective of this contribution is the theoretical modelling of magnetizable materials that exhibit viscoelastic properties. The current state of the art in the mathematical modelling of non-linear magnetomechanics in deformable media can be easily integrated within the unified framework of continuum thermodynamics, which is crucial in setting the convenient forms for the constitutive laws and evolution equations. Owing to the soft nature of the materials we have in mind, the finite strain range is adopted a priori and, in this first approach, only isotropic materials are considered. We adopt the currently well-accepted multiplicative split of the deformation gradient, which, moreover, gives rise to an intermediate configuration. Herein, the novelty resides in the fact that the magnetic field vectors are transported onto the aforementioned intermediate configuration and, therefore, can be implicitly decomposed. The proposed formulation is based on the magnetic induction as the main independent variable for the magnetic part of the problem. An alternative formulation based on the magnetic field as main independent variable can easily be deduced, but this latter will not be considered in this paper for the sake of clarity. A very simple model example that agrees with the laws of thermodynamics is proposed for the purpose of demonstration to study some phenomena qualitatively.

MSC:

74F15 Electromagnetic effects in solid mechanics
74D10 Nonlinear constitutive equations for materials with memory
74A15 Thermodynamics in solid mechanics
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