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Analytic investigation of stress coupling effects of spherically anisotropic functionally graded piezoelectric hollow spheres

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Abstract

We investigate the stress coupling effects of spherically anisotropic piezoelectric hollow spheres with functional gradients (represented by radial power law functions) under external uniform radial traction. By means of submatrix operations, we derive a dimensionless expression that signifies not only the characteristic (amplification/shielding) of the stress coupling, but also the magnitude of the effect. This should be very beneficial for structural design. When bounded strain energy conditions are assumed, the study extends to solid spheres under uniform radial traction on the surface. As in the case of pure elasticity, infinite stresses can occur at the center of the sphere regardless of the magnitude of the applied stress, but all have weaker stress singularities.

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Abbreviations

u i :

Displacement components

ϕ :

Electrostatic potential

ε ij :

Components of the infinitesimal strain

E i :

Electric field components

σ ij :

Elastic stress components

D i :

Components of the electric displacement

C ijkm :

Elastic stiffnesses

e mij :

Piezoelectric stress constants

ω im :

Dielectric permittivity constants

\({{\bf{\hat \sigma }}}\) :

Generalized stress vector

Ĉ(r):

Generalized elastic stiffnesses matric

\({{\bf{\hat \varepsilon }}}\) :

Generalized strain vector

δ :

Stress singularity

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Authors and Affiliations

  1. Department of Civil Engineering, School of Chemistry and Civil Engineering, Shaoguan University, Shaoguan, Guangdong, 512005, P. R. China

    M. Y. Chung & C. T. Lu

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  1. M. Y. Chung
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  2. C. T. Lu
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Correspondence to C. T. Lu.

Additional information

Ming-Yan Chung is an Associate Professor of the School of Chemistry and Civil Engineering, Shaoguan University, Guangdong, China. He received his Ph.D. in Engineering Mechanics from University of Illinois at Chicago. His research interests include anisotropic elasticity and piezoelectricity.

Cheng-Tsung Lu is an Associate Professor of the School of Chemistry and Civil Engineering, Shaoguan University, Guangdong, China. He received his Ph.D. from National Taiwan University of Science and Technology. His current research focuses on civil engineering materials.

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Chung, M.Y., Lu, C.T. Analytic investigation of stress coupling effects of spherically anisotropic functionally graded piezoelectric hollow spheres. J Mech Sci Technol 38, 2375–2383 (2024). https://doi.org/10.1007/s12206-023-0615-2

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  • DOI: https://doi.org/10.1007/s12206-023-0615-2

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