Analytical and Computational Mechanics of Advanced Materials and Functional Structures

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Mathematics and Computer Science".

Deadline for manuscript submissions: closed (25 March 2022) | Viewed by 11421

Special Issue Editor

Special Issue Information

Dear Colleagues,

Advanced materials (composites, functionally graded materials, shape memory materials, multi-phase materials, active materials, piezoelectrics, biomaterials, etc.) and functional structures (conductors, actuators, sensors, MEMS, 4D printed structures, etc.) play a key role in modern engineering and biomedical applications where they are often exposed to severe environmental conditions and experience complex multi-axial loadings. In many occasions, new analytical and computational methods are needed to characterise novel features of these materials and to model their mechanical behaviours as well as to analyse their mechanical performance.

The objective of this Special Issue is to promote the dissemination of significant developments dealing with analytical and computational mechanics of advanced materials and functional structures. This Special Issue creates a forum for research contributions covering a broad spectrum of topics ranging from analytical methods, numerical simulations and experimental investigations to hybrid techniques that combine computational and experimental approaches in the research and study of advanced materials and functional structures. Mechanics of advanced materials like biological materials, ceramics, functionally graded materials, carbon-fibre and polymer/metal-matrix composites, nanocomposites, smart materials, shape memory materials, multi-phase materials, active materials, piezoelectrics, meta-materials, electromagnetic materials, 3D/4D printed materials are of interests. All researchers/investigators are invited to contribute to this Special Issue with their original research articles, short communications, and review articles.

Dr. Mahdi Bodaghi
Guest Editor

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Keywords

  • Solid mechanics
  • Fluid mechanics
  • Biomechanics
  • Analytical solutions
  • Numerical methods
  • Finite element methods
  • Multiscale methods
  • Beams, plates and shells
  • Composite materials
  • Smart materials
  • 3D/4D printing

Published Papers (5 papers)

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Research

13 pages, 2269 KiB  
Article
Hybrid Finite Element Method to Thermo-Elastic Interactions in a Piezo-Thermo-Elastic Medium under a Fractional Time Derivative Model
by Tareq Saeed
Mathematics 2022, 10(4), 650; https://doi.org/10.3390/math10040650 - 19 Feb 2022
Cited by 3 | Viewed by 1370
Abstract
In this work, the effect of the fractional time derivative on the piezo-thermo-elastic medium is studied, using the hybrid Laplace transform and finite element methods (LFEM). The generalized fractional piezoelectric–thermoelastic basic equations for piezo-thermo-elastic medium are formulated. The Laplace transforms are used for [...] Read more.
In this work, the effect of the fractional time derivative on the piezo-thermo-elastic medium is studied, using the hybrid Laplace transform and finite element methods (LFEM). The generalized fractional piezoelectric–thermoelastic basic equations for piezo-thermo-elastic medium are formulated. The Laplace transforms are used for the time derivatives, and the finite element method is used to discretize for the space derivatives. The inversions process is performed using the Stehfest numerical technique. The finite element approach is used to obtain the solutions of complex coupled formulations of this problem. The effects of fractional time derivative and thermal relaxation time on piezoelectric–thermoelastic mediums are studied. It can be seen from the distribution that the thermal-induced displacement, the temperature and the stress of the medium increase at a high fractional parameter. Full article
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15 pages, 4180 KiB  
Article
Series Solution-Based Approach for the Interlaminar Stress Analysis of Smart Composites under Thermo-Electro-Mechanical Loading
by Salman Khalid, Jaehun Lee and Heung Soo Kim
Mathematics 2022, 10(2), 268; https://doi.org/10.3390/math10020268 - 16 Jan 2022
Cited by 8 | Viewed by 1964
Abstract
This paper introduces a new loading condition considering the combined thermo-electro-mechanical coupling effect in a series solution-based approach to analyze the free-edge interlaminar stresses in smart composite laminates. The governing equations are developed using the principle of complementary virtual work. The assumed stress [...] Read more.
This paper introduces a new loading condition considering the combined thermo-electro-mechanical coupling effect in a series solution-based approach to analyze the free-edge interlaminar stresses in smart composite laminates. The governing equations are developed using the principle of complementary virtual work. The assumed stress fields satisfy the traction-free and free-edge boundary conditions. The accurate stress states of the composite structures are acquired through the procedure of generalized eigenvalue problems. The uniform temperature is employed throughout the laminate, and the electric field loading is applied to the symmetric piezo-bonded actuators to examine the combined effect of thermal and electrical stresses on the overall deformation of smart composite laminates. It was observed that the magnitude of the peeling stresses generated by mechanical loading was reduced by the combined thermal and electric excitation loading (up to 25.3%), which in turn resulted in expanding the service life of the smart composite structures. The proposed approach is implemented on three different layup configurations. The efficiency of the current methodology is confirmed by comparing the results with the 3D finite element (FEM) solution computed by ABAQUS. Full article
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23 pages, 564 KiB  
Article
Slip Effects on MHD Squeezing Flow of Jeffrey Nanofluid in Horizontal Channel with Chemical Reaction
by Nur Azlina Mat Noor, Sharidan Shafie and Mohd Ariff Admon
Mathematics 2021, 9(11), 1215; https://doi.org/10.3390/math9111215 - 27 May 2021
Cited by 23 | Viewed by 1583
Abstract
The heat and mass transfer characteristics on hydromagnetic squeeze flow of Jeffrey nanofluid between two plates over a permeable medium by slip condition with the influences of viscous dissipation and chemical reaction is examined. Buongiorno’s nanofluid model, which includes Brownian motion and thermophoresis [...] Read more.
The heat and mass transfer characteristics on hydromagnetic squeeze flow of Jeffrey nanofluid between two plates over a permeable medium by slip condition with the influences of viscous dissipation and chemical reaction is examined. Buongiorno’s nanofluid model, which includes Brownian motion and thermophoresis impacts, is implemented in this research. The governing nonlinear partial differential equations are transformed to the nonlinear ordinary differential equations via asimilarity transformation. The transformed equations are solved by employing numerical techniques of Keller-box. A comparison of the skin friction coefficient, Nusselt and Sherwood numbers with reported outputs in the journals are carried out to validate the present outputs. An excellent agreement is found. The results show that the squeezing of plates accelerates the velocity and wall shear stress. Furthermore, the velocity, temperature and concentration profile decrease when the Hartmann number and ratio of relaxation and retardation times increases. The raise in thermophoresis and viscous dissipation elevate the temperature profile and the heat transfer rate. Furthermore, the mass transfer rate declines due to the strong Brownian motion in the nanofluid, whereas it increases with the addition of chemical reaction and thermophoresis. Full article
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22 pages, 4088 KiB  
Article
Analytical Solutions of Upper Convected Maxwell Fluid with Exponential Dependence of Viscosity under the Influence of Pressure
by Constantin Fetecau, Dumitru Vieru, Tehseen Abbas and Rahmat Ellahi
Mathematics 2021, 9(4), 334; https://doi.org/10.3390/math9040334 - 7 Feb 2021
Cited by 9 | Viewed by 2817
Abstract
Some unsteady motions of incompressible upper-convected Maxwell (UCM) fluids with exponential dependence of viscosity on the pressure are analytically studied. The fluid motion between two infinite horizontal parallel plates is generated by the lower plate, which applies time-dependent shear stresses to the fluid. [...] Read more.
Some unsteady motions of incompressible upper-convected Maxwell (UCM) fluids with exponential dependence of viscosity on the pressure are analytically studied. The fluid motion between two infinite horizontal parallel plates is generated by the lower plate, which applies time-dependent shear stresses to the fluid. Exact expressions, in terms of standard Bessel functions, are established both for the dimensionless velocity fields and the corresponding non-trivial shear stresses using the Laplace transform technique and suitable changes of the unknown function and the spatial variable in the transform domain. They represent the first exact solutions for unsteady motions of non-Newtonian fluids with pressure-dependent viscosity. The similar solutions corresponding to the flow of the same fluids due to an exponential shear stress on the boundary as well as the solutions of ordinary UCM fluids performing the same motions are obtained as limiting cases of present results. Furthermore, known solutions for unsteady motions of the incompressible Newtonian fluids with/without pressure-dependent viscosity induced by oscillatory or constant shear stresses on the boundary are also obtained as limiting cases. Finally, the influence of physical parameters on the fluid motion is graphically illustrated and discussed. It is found that fluids with pressure-dependent viscosity flow are slower when compared to ordinary fluids. Full article
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28 pages, 1310 KiB  
Article
Application of Multi-Parameter Perturbation Method to Functionally-Graded, Thin, Circular Piezoelectric Plates
by Xiao-Ting He, Zhi-Xin Yang, Yang-Hui Li, Xue Li and Jun-Yi Sun
Mathematics 2020, 8(3), 342; https://doi.org/10.3390/math8030342 - 4 Mar 2020
Cited by 11 | Viewed by 2037
Abstract
In this study, a multi-parameter perturbation method is used for the solution of a functionally-graded, thin, circular piezoelectric plate. First, by assuming that elastic, piezoelectric, and dielectric coefficients of the functionally-graded materials vary in the form of the same exponential function, the basic [...] Read more.
In this study, a multi-parameter perturbation method is used for the solution of a functionally-graded, thin, circular piezoelectric plate. First, by assuming that elastic, piezoelectric, and dielectric coefficients of the functionally-graded materials vary in the form of the same exponential function, the basic equation expressed in terms of two stress functions and one electrical potential function are established in cylindrical coordinate system. Three piezoelectric coefficients are selected as perturbation parameters, and the established equations are solved by the multi-parameter perturbation method, thus obtaining up to first-order perturbation solutions. The validity of the perturbation solution obtained is verified by numerical simulations, based on layer-wise theory. The perturbation process indicates that adopting three piezoelectric coefficients as perturbation parameters follows the basic idea of perturbation theory—i.e., if the piezoelectricity may be regarded as a kind of introduced disturbance, the zero-order solution of the disturbance system corresponds exactly to the solution of functionally-graded plates without piezoelectricity. The result also indicates that the deformation magnitude of piezoelectric plates is smaller than that of plates without piezoelectricity, due to the well-known piezoelectric stiffening effect. Full article
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