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10.3390/ma18092136
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Article

Analytical and Finite Element Solution for Functionally Graded Pressure Vessels Subjected to Finite Strain Coupled Axial and Torsional Deformations

by
Mohammad Shojaeifard
1,
Arash Valiollahi
2,
Davood Rahmatabadi
1,
Ali Taheri
3,
Eunsoo Choi
4,
Alireza Ostadrahimi
4 and
Mostafa Baghani
1,*
1
School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran 1417466191, Iran
2
Mechanical and Aerospace Engineering Department, University of Texas at Arlington, Arlington, TX 76019, USA
3
Department of Mechanical Engineering, Faculty of Engineering, University of Larestan, Larestan 7431813115, Iran
4
Department of Civil Engineering, Hongik University, Seoul 04066, Republic of Korea
*
Author to whom correspondence should be addressed.
Materials 2025, 18(9), 2136; https://doi.org/10.3390/ma18092136
Submission received: 21 March 2025 / Revised: 25 April 2025 / Accepted: 28 April 2025 / Published: 6 May 2025
(This article belongs to the Special Issue Modelling of Deformation Characteristics of Materials or Structures)
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Abstract

This study presents an analytical solution to examine the mechanical behavior of an incompressible, functionally graded hyperelastic cylinder under combined extension and torsion. The exp-exp strain energy density function characterizes the hyperelastic material, with parameters varying exponentially along the radial direction. To validate the solution, finite element simulations using a custom UHYPER in ABAQUS are performed. The analytical and numerical results show strong agreement across different stretch and twist levels. The stress distribution and maximum stress are significantly influenced by the exponential parameter governing material gradients. Unlike axial stretch, torsion induces a more intricate longitudinal stress distribution, with large twisting producing two extrema that shift toward the cylinder’s center and outer surface. Longitudinal stress primarily governs von Mises stress and strain energy density variations across the radial direction. A critical axial stretch is identified, below which torsion-induced axial force transitions to compression, elongating the cylinder during twisting. Beyond this stretch, the axial force shifts from tensile to compressive with increasing twist, causing initial shortening before further elongation.
Keywords: extension–torsion of rubber-like cylinder; functionally graded material; hyperelastic material; invariant-based analytical solution; finite element method extension–torsion of rubber-like cylinder; functionally graded material; hyperelastic material; invariant-based analytical solution; finite element method

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MDPI and ACS Style

Shojaeifard, M.; Valiollahi, A.; Rahmatabadi, D.; Taheri, A.; Choi, E.; Ostadrahimi, A.; Baghani, M. Analytical and Finite Element Solution for Functionally Graded Pressure Vessels Subjected to Finite Strain Coupled Axial and Torsional Deformations. Materials 2025, 18, 2136. https://doi.org/10.3390/ma18092136

AMA Style

Shojaeifard M, Valiollahi A, Rahmatabadi D, Taheri A, Choi E, Ostadrahimi A, Baghani M. Analytical and Finite Element Solution for Functionally Graded Pressure Vessels Subjected to Finite Strain Coupled Axial and Torsional Deformations. Materials. 2025; 18(9):2136. https://doi.org/10.3390/ma18092136

Chicago/Turabian Style

Shojaeifard, Mohammad, Arash Valiollahi, Davood Rahmatabadi, Ali Taheri, Eunsoo Choi, Alireza Ostadrahimi, and Mostafa Baghani. 2025. "Analytical and Finite Element Solution for Functionally Graded Pressure Vessels Subjected to Finite Strain Coupled Axial and Torsional Deformations" Materials 18, no. 9: 2136. https://doi.org/10.3390/ma18092136

APA Style

Shojaeifard, M., Valiollahi, A., Rahmatabadi, D., Taheri, A., Choi, E., Ostadrahimi, A., & Baghani, M. (2025). Analytical and Finite Element Solution for Functionally Graded Pressure Vessels Subjected to Finite Strain Coupled Axial and Torsional Deformations. Materials, 18(9), 2136. https://doi.org/10.3390/ma18092136

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