Multiscale Modeling of a Magnetostrictive Sound Detector

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Problem description

Multi-scale modeling of a Magnetostrictive Sound Detector.

This paper studies the implementation of the ICME as a design tool for innovative magnetostrictive cantilever sound resonator. The sensor exploits the inverse Joule effect – when subjected to a sound wave with close to its resonance frequency, it begins to oscillate and produces magnetic field (which is captured and measured by a magnetic coil). A multitude of such cantilever resonators forms a sound sensor platform, capable of detecting a broad range of sound frequencies. This type of sensor application has the advantages of simple structure, fast response, wireless non-contact measurement and overall reduced cost.

Even in this simple case, calculating the resonant frequencies and resulting magnetic field of the magnetostrictive resonator is non-trivial due to the nonlinear magnetization and stress distribution in the material, hysteresis effects, second order magnetic strains. In this paper a five-scale ICME approach is proposed to describe and predict the complex nonlinear and hysteretic behavior of the sensor - calculations and simulations is performed on five length-scales (from electronic through atomistic, micro and meso-scales to the macroscale continuum). The model is calibrated and validated with experiments; its findings are implemented into FEA for resonator design and optimization.

From scientific point of view, this problem provides an excellent opportunity to implement magneto-mechanic relations into ICME framework and to test the framework’s capabilities. Starting simulations on magneto-elacticity from electronic level all the way to continuum level is an innovative approach in describing magnetostrictive materials behavior.

Design Requirements

Engineering design of the magnetostrictive sound detector requires:

• material constants (density) – obtained from product documentation (or measured through experiments);

• elastic constants (modulus of elasticity and poisons ratio) – obtained from product documentation (or measured through experiments), downscaled to electronic and atomistic levels for calibration and validation purposes;

• strain - magnetic field relation (inverse Joule Effect) – downscaled to meso-scale simulations;

Electronic scale

On electronic scale, interfacial energy, elastic moduli and magnetic dipole moments for iron (Fe) and nickel (Ni) are obtained using density functional theory (DFT) methodology.

Atomistic scale

On atomistic scale, the magnetic domain formation and inter-domain interactions are studied. Ni-Fe alloy’s magnetic permeability and elastic moduli are calculated and upscaled to macro-scale for validation and calibration purposes.


On micro-scale, domain switching mechanism under applied strain is studied for upscaling to meso-scale and validation/ calibration with macro-scale data.


On meso-scale, magnetic domain interaction and domain wall motion under mechanical strain is researched. The resulting strain - magnetic field relation (inversed Joule Effect) is upscaled to macro-scale level for further implementation into Fine Element Analysis (FEA) and design optimization. The stress – magnetization relation (Villari effect) can be used on macroscale level for validation and model calibration purposes.


[1] Aboudi J., Zheng X., Jin K., 2014. Micromechanics of magnetostrictive composites. International Journal of Engineering Science 81 (2014) 82–99.

[2] Buiron N., He S., Hirsinger L., Depeyre S., Bernadou M., Billardon R., 2001. From micromagnetic to multiscale modeling of the coupled magnetoelastic behavior of ferromagnetic materials. Physica B 306 (2001) 33–37.

[3] Daniel L., Hubert O., Buiron N., Billardon R., 2008. Reversible magneto-elastic behavior: A multiscale approach. Journal of the Mech.and Physics of Solids 56 (2008) 1018–1042.

[4] Davino D., Natale C., Pirozzi S., Visone C., 2004. Phenomenological dynamic model of a magnetostrictive actuator. Physica B 343 (2004) 112–116.

[5] Olabi, A.G., Grunwald A., 2008. Design and application of magnetostrictive materials. Materials and Design 29 (2008) 469–483.

[6] Zhang K., Zhang L., Fu L., Li S., Chen H., Cheng Z.Y., 2013. Magnetostrictive resonators as sensors and actuators. Sensors and Actuators A 200 (2013) 2– 10.

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