View source for Multiscale Modeling of a Magnetostrictive Sound Detector

====Problem description====
[[Image:Slide_MCM_sond detector.png|right|thumb|800px|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.

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

===Meso-scale===
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.

===References===
[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.

[[Category:Microscale]][[Category:Nanoscale]][[Category:Nanoscale]][[Category:Mesoscale]][[Category:Metals]]