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Flexomagneticity in Functionally Graded Nanostructures

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Advanced Materials Modelling for Mechanical, Medical and Biological Applications

Part of the book series: Advanced Structured Materials ((STRUCTMAT,volume 155))

Abstract

Functionally graded structures have shown the perspective of materials in a higher efficient and consistent manner. This study reports a short investigation by concentrating on the flexomagnetic response of a functionally graded piezomagnetic nano-actuator, kee** in mind that the converse magnetic effect is only taken into evaluation. The rule of mixture assuming exponential composition of properties along with the thickness is developed for the ferromagnetic bulk. Nonlocal effects are assigned to the model, respecting Eringen’s hypothesis. The derived equations deserve to be analytically solved. Therefore, numerical results are generated for fully fixed ends. It is denoted that the functionality grading feature of a magnetic nanobeam can magnify the flexomagnetic effect leading to high-performance nanosensors/actuators.

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Abbreviations

\(\sigma_{xx}\) :

Stress component

\(\tau_{xz}^{{}}\) :

Shear stress

\(\xi_{xxz}\) :

Hyperstress

\(\eta_{xxz}\) :

Hyperstrain

\(\varepsilon_{xx}\) :

Strain component

\(\gamma_{xz}\) :

Shear strain

\(E\) :

Elasticity modulus

\(G\) :

Shear modulus

\(u_{1}\) :

Displacement along x

\(u_{3}\) :

Displacement along z

\(\nu\) :

Poisson's ratio

\(L\) :

Length of the beam

\(b\) :

Width of the beam

\(z\) :

Thickness coordinate

\(h\) :

Thickness of the beam

\(k_{{\text{s}}}\) :

Shear correction factor

\(k\) :

Material property variation

\(I_{z}\) :

Area moment of inertia

\(u\) :

Axial displacement of the mid-plane

\(w\) :

Transverse displacement of the mid-plane

\(\phi\) :

Rotation of beam nodes around the y-axis

\(q_{31}\) :

Component of the third-order piezomagnetic tensor

\(g_{31}\) :

Component of the sixth-order gradient elasticity tensor

\(f_{31}\) :

Component of fourth-order flexomagnetic tensor

\(a_{33}\) :

Component of the second-order magnetic permeability tensor

\(A\) :

Area of the cross section of the beam

\(N_{x}^{{}}\) :

Axial stress resultant

\(M_{x}^{{}}\) :

Moment stress resultant

\(Q_{x}^{{}}\) :

Shear stress resultant

\(T_{xxz}\) :

Hyperstress resultant

\(\psi\) :

Magnetic potential.

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Acknowledgements

V. A. Eremeyev acknowledges the support of the Government of the Russian Federation (contract No. 14.Z50.31.0046).

Author information

Authors and Affiliations

  1. Department of Mechanics of Materials and Structures, Faculty of Civil and Environmental Engineering, Gdansk University of Technology, 80-233, Gdansk, Poland

    Mohammad Malikan, Tomasz Wiczenbach & Victor A. Eremeyev

  2. Don State Technical University, Gagarina sq., 1, Rostov on Don, 344000, Russia

    Victor A. Eremeyev

  3. DICAAR, Università degli Studi di Cagliari, Via Marengo, 2, 09123, Cagliari, Italy

    Victor A. Eremeyev

Authors
  1. Mohammad Malikan
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  2. Tomasz Wiczenbach
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  3. Victor A. Eremeyev
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Corresponding author

Correspondence to Victor A. Eremeyev .

Editor information

Editors and Affiliations

  1. Institut für Mechanik, Fakultät für Maschinenbau, Otto-von-Guericke-Universität Magdeburg, Magdeburg, Germany

    Holm Altenbach

  2. DICAAR, Università degli Studi di Cagliari, Cagliari, Italy

    Victor A. Eremeyev

  3. Schmidt Institute of Physics of the Earth, Moscow, Russia

    Alexander Galybin

  4. Don State Technical University, Rostov-on-Don, Russia

    Andrey Vasiliev

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Malikan, M., Wiczenbach, T., Eremeyev, V.A. (2022). Flexomagneticity in Functionally Graded Nanostructures. In: Altenbach, H., Eremeyev, V.A., Galybin, A., Vasiliev, A. (eds) Advanced Materials Modelling for Mechanical, Medical and Biological Applications. Advanced Structured Materials, vol 155. Springer, Cham. https://doi.org/10.1007/978-3-030-81705-3_17

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