Archives of Mechanics
type: channel
description: Archives of Mechanics Editor: Henryk Petryk Archives of Mechanics, a refereed international journal founded in 1949, provides a forum for original research on mechanics of solids, fluids and discrete systems, including the development of mathematical methods for solving mechanical problems. The journal encompasses all aspects of the field, with the emphasis placed on: mechanics of materials: elasticity, plasticity, time-dependent phenomena, phase transformation, damage, fracture; physical and experimental foundations, micromechanics, thermodynamics, instabilities; methods and problems in continuum mechanics: general theory and novel applications, thermomechanics, structural analysis, porous media, contact problems; dynamics of material systems; fluid flows and interactions with solids. Papers published in the Archives should contain original contributions dealing with theoretical, experimental, or numerical aspects of mechanical problems listed above.
publisher: Institute of Fundamental Technological Research, Polish Academy of Sciences (IPPT PAN)
language: en
publication name: Archives of Mechanics
issn: 0373-2029
copyright: Copyright © The Author(s). This work is licensed under the Creative Commons Attribution 4.0 International CC BY 4.0.
items: Problems of steady vibrations in the theory of Moore-Gibson-Thompson thermoviscoelasticity for materials with voids
items: An analytical model for ballistic performance prediction of elastoplastic materials with strain hardening
items: Point force in a plane in the context of fractional nonlocal elasticity
items: Simulation of transient fluid–structure interaction in flapping-wing micro aerial vehicles
items: Preface
items: Thermophoresis of a cylindrical particle embedded in a porous medium saturated by a micropolar fluid
items: Analytical solution of peridynamics for heat conduction with an external source
items: On the deformations of an electroactive solid subject to a uniform electric field in an orthogonal rheometer
items: Mechanical stability conditions for 3D and 2D crystals under arbitrary load
items: Characteristics of SH waves in multilayered piezoelectric semiconductor plates considering interfacial imperfection
items: Planar plasma source and a floating wall
items: Investigations of column separation influence on pressure waves severity based on results of water hammer experiments in elastically supported pipeline
items: Self-equilibrated residual based error estimation on 1-irregular meshes in finite elasticity
items: An analytical–numerical approach for the stability analysis of large strain thermo-elastoplastic material models
items: Evaluating compression and nanoindentation in FCC nickel: a methodology for interatomic potential selection
items: Influence of rotation and couple stresses on convective stability in Navier–Stokes–Voigt fluid
items: A simple quasi-3D theory for static stability analysis of imperfect FG beam
items: Improved three-dimensional refined plate theory
items: Two rigid non-circular inhomogeneities in an elastic matrix
items: Some explicit forrnulae for heteroclinic solutions to scalar second order ordinary differential equations
items: Mean-field/FMBEM homogenization of 3-D particulate composites
items: Thermal vibration analysis of carbon nanotubes embedded in two-parameter elastic foundation based on nonlocal Timoshenko's beam theory
items: Mechanical characterization of millimetric agarose spheres using a resonant technique
items: Hyperelastic behavior of cellular structures based on micromechanical modeling at small strain
items: Influence of mixed boundary conditions and heterogeneity on the vibration behavior of orthotropic truncated conical shells
items: A parametric study on the elastic-plastic deformation of a centrally heated two-layered composite cylinder with free ends
items: Inelastic behavior and numerical analysis in twin-roll casting process of AZ31 alloy
items: Vibration analysis of single-walled carbon nanotubes conveying nanoflow embedded in a viscoelastic medium using modified nonlocal beam model
items: Effect of hydrogen injection into natural gas on the mechanical strength of natural gas pipelines during transportation
items: Using stability analysis of discrete elastic systems to study the buckling of nanostructures

Problems of steady vibrations in the theory of Moore-Gibson-Thompson thermoviscoelasticity for materials with voids
type: item
description: In this paper, the linear theory of Moore-Gibson-Thompson (MGT) thermoviscoelasticity for materials with voids is examined and the basic boundary value problems (BVPs) of steady vibrations are investigated. The governing equations of motion and steady vibrations are formulated. The fundamental solution to the system of steady vibration equations is constructed explicitly using four elementary functions, and its key properties are analyzed. Then, Green's first identity is established and the uniqueness theorems for classical solutions of the associated basic BVPs are proved. The surface and volume potentials are defined, and their essential properties are established. Singular integral operators are introduced, and their symbolic determinants and indices are calculated. Finally, existence theorems for classical solutions of the basic internal and external BVPs are established using the potential method.
subject: Solids
  topic: section
subject: thermoviscoelasticity
  topic: keywords
subject: materials with voids
  topic: keywords
subject: steady vibrations
  topic: keywords
subject: potential method
  topic: keywords
subject: existence and uniqueness theorems
  topic: keywords
creator: M.M. Svanadze
rights: Copyright (c) 2026 M.M. Svanadze https://creativecommons.org/licenses/by/4.0
date: 2026-04-28
publication date: 2026-04-28
starting page: 33
ending page: 56
doi: 10.24423/aom.4847

An analytical model for ballistic performance prediction of elastoplastic materials with strain hardening
type: item
description: This study presents an analytical model to predict the ballistic performance of elastoplastic materials with strain hardening under normal impact by rigid penetrators. The model integrates the localized interaction model with the spherical cavity-expansion theory to account for dynamic material behaviour. Key parameters, including cavity-expansion pressure and strain hardening, are incorporated using the Ludwik and Voce hardening laws, enabling accurate predictions of residual velocity and ballistic limit. The model is validated using experimental data for various aluminium alloys and steel plates, demonstrating good agreement between predictions and observations. The proposed analytical approach offers a reliable and computationally efficient tool for evaluating ballistic performance, making it a valuable resource in armour design and impact mechanics research.
subject: Solids
  topic: section
subject: spherical cavity-expansion
  topic: keywords
subject: localized interaction model
  topic: keywords
subject: ballistic performance
  topic: keywords
creator: B.T. Phan
creator: V. Kulish
creator: V. Horák
rights: Copyright (c) 2026 B.T. Phan, V. Kulish, V. Horák https://creativecommons.org/licenses/by/4.0
date: 2026-04-28
publication date: 2026-04-28
starting page: 3
ending page: 31
doi: 10.24423/aom.4808

Point force in a plane in the context of fractional nonlocal elasticity
type: item
description: Solutions to the point load problems for elastic solids have different applications in geomechanics, contact mechanics, tribology as well as in modeling of lattice defects in crystals. Nonlocal elasticity assumes an integral constitutive equation for the stress tensor, takes into account interatomic long-range forces, reduces to the classical theory of elasticity in the long wave-length limit and to the atomic lattice theory in the short wave-length limit. Often, the nonlocal kernel of a stress constitutive equation is selected as the Green function of the Cauchy problem for appropriate partial differential equation. In this paper, we obtain the solution of elasticity problems for a point force in a plane and for a point load on the boundary of a half-plane in the context of the new theory of nonlocal elasticity in which the nonlocal modulus is the Green function of the Cauchy problem for the fractional diffusion equation with the Caputo derivative with respect to the nonlocality parameter and the fractional Riesz derivative with respect to spatial coordinates.
subject: Solids
  topic: section
subject: point force
  topic: keywords
subject: Kelvin problem
  topic: keywords
subject: Flamant problem
  topic: keywords
subject: Cerruti problem
  topic: keywords
subject: nonlocal elasticity
  topic: keywords
subject: Caputo derivative
  topic: keywords
subject: Riesz derivative
  topic: keywords
creator: Y. Povstenko
creator: T. Kyrylych
creator: A. Yatsko
rights: Copyright (c) 2026 Y. Povstenko, T. Kyrylych, A. Yatsko https://creativecommons.org/licenses/by/4.0
date: 2026-04-28
publication date: 2026-04-28
starting page: 57
ending page: 73
doi: 10.24423/aom.4875

Simulation of transient fluid–structure interaction in flapping-wing micro aerial vehicles
type: item
description: The objective of this study is to investigate aeroelastic phenomena occurring during airflow around flapping wings of a micro aerial vehicle (MAV) inspired by insect anatomy. A numerical model of the wing and the flow configuration was developed based on an experiment conducted at ESPCI Paris. Transient fluid–structure interaction (FSI) simulations were carried out in the Ansys environment, employing independent solvers for fluid flow (CFD) and structural deformation (FEM), coupled through the System Coupling module. The analysis focused on the role of wing compliance in thrust generation, with particular attention to the effects of flapping frequency and wing stiffness, determined by the thickness of the membrane forming the lifting surface. The results demonstrate a strong dependence of thrust generation on the degree of wing deformation, in good agreement with the experimental findings. These findings highlight the importance of structural flexibility in enhancing aerodynamic performance and provide practical guidelines for the design of efficient flapping-wing micro aerial vehicles.
subject: Fluids
  topic: section
subject: fluid–structure interactions
  topic: keywords
subject: FSI
  topic: keywords
subject: aeroelasticity
  topic: keywords
subject: CFD
  topic: keywords
subject: MAV
  topic: keywords
subject: microdrone
  topic: keywords
subject: bio-inspired
  topic: keywords
subject: flapping wings
  topic: keywords
creator: W. Stankiewicz
creator: T. Krakowski
creator: K. Foltyński
rights: Copyright (c) 2026 W. Stankiewicz, T. Krakowski, K. Foltyński https://creativecommons.org/licenses/by/4.0
date: 2026-01-28
publication date: 2026-01-28
starting page: 573
ending page: 593
doi: 10.24423/aom.4688

Preface
type: item
description: This issue of the Archives of Mechanics contains a selection of papers presented at the 43rd Solid Mechanics Conference (SolMech 2024) held in Wrocław, 16–18 September 2024.
subject: Editorial Material
  topic: section
creator: J. Rojek
rights: Copyright (c) 2025 J. Rojek https://creativecommons.org/licenses/by/4.0
date: 2025-10-23
publication date: 2025-10-23
starting page: 435
ending page: 435
doi: 10.24423/aom.4809

Thermophoresis of a cylindrical particle embedded in a porous medium saturated by a micropolar fluid
type: item
description: The present study examines the thermophoresis of a cylindrical particle in a direction perpendicular to its axis in the Brinkman medium. To describe the behaviour of micropolar fluid driven by a thermal gradient within such a porous medium, the modified Brinkman’s equation is applied while considering low Reynolds and Péclet numbers. The governing equations for both the particle and the medium are solved using the separation of variables technique. The boundary conditions applied at the particle surface are thermal jump and heat flux continuity, with viscous slip, thermal creep, thermal stress slip and microrotation slip. The main objective of the research is to derive the expressions for thermophoretic velocity and thermophoretic force of a cylindrical particle. Graphical representations illustrate the thermophoretic velocity and force of the particle for various physical parameters, including the permeability, micropolarity parameter, thermal stress slip parameter, viscous slip parameter, Knudsen number, and thermal conductivity parameters. The results show that an increase in the micropolarity parameter decreases both the thermophoreti velocity and the force. Additionally, thermophoretic velocity increases with higher permeability, while the thermophoretic force decreases with increasing permeability and the thermal conductivity ratio. The findings of this research align with previously published studies and hold potential applications in industrial processes, including filtration, heat exchangers, air cleaning, and manufacturing thermal precipitators.
subject: Fluids
  topic: section
subject: thermophoresis
  topic: keywords
subject: cylindrical particle
  topic: keywords
subject: micropolar fluid
  topic: keywords
subject: porous medium
  topic: keywords
creator: S. Nishad
creator: K.P. Madasu
rights: Copyright (c) 2026 S. Nishad, K.P. Madasu https://creativecommons.org/licenses/by/4.0
date: 2026-01-28
publication date: 2026-01-28
starting page: 647
ending page: 678
doi: 10.24423/aom.4789

Analytical solution of peridynamics for heat conduction with an external source
type: item
description: This study provides a novel analytical approach for solving one- and two-dimensional heat conduction problems with an external heat source within the peridynamic framework. By employing Duhamel’s principle, the inhomogeneous governing equation with an external source is transformed into a homogeneous equation, enabling the derivation of peridynamic analytical solutions through separation of variables. An innovation involves introducing a nonlocal factor by ensuring compatibility between the spatial functions in the peridynamic solution and their classical continuum mechanics counterparts. Numerical examples demonstrate the methodology’s effectiveness for both one- and two-dimensional heat conduction problems subjected to sinusoidal and constant external sources, and the nonlocal effect is measured based on the nonlocal factor. Unlike peridynamic systems without external sources, these examples reveal that the nonlocal factor appears not only in the exponential term but also in other components of the solution, indicating persistent nonlocal effects even as time approaches infinity. Furthermore, the analysis shows that the kernel function with n = 0 exhibits the strongest nonlocal influence, while n = 2 results in the weakest nonlocal behavior. The findings demonstrate that peridynamic analytical solutions for heat conduction can be systematically derived from classical continuum mechanics solutions through appropriate incorporation of the nonlocal factor. This work significantly expands the scope of peridynamic analytical solutions and offers new insights into nonlocal heat conduction phenomena, providing a valuable foundation for future studies in this field.
subject: Solids
  topic: section
subject: peridynamics
  topic: keywords
subject: heat conduction
  topic: keywords
subject: analytical solution
  topic: keywords
subject: nonlocal effect
  topic: keywords
creator: S. Fan
creator: H. Liu
creator: X. Peng
rights: Copyright (c) 2025 S. Fan, H. Liu, X. Peng https://creativecommons.org/licenses/by/4.0
date: 2025-09-12
publication date: 2025-09-12
starting page: 401
ending page: 429
doi: 10.24423/aom.4700

On the deformations of an electroactive solid subject to a uniform electric field in an orthogonal rheometer
type: item
description: In this short paper, we extend the seminal study by Berker [4] of pseudoplanar flows that occur in an orthogonal rheometer, essentially two parallel disks rotating about non-coincident axes at the top and bottom, to the case of an electroactive elastic solid. We obtain the expression for the stress, which is a function of the deformation as well as the electric field, in an electroactive elastic solid using standard representation theorems. We show that in the case of elastic solids, pseudoplanar displacements can take place, with each layer z = constant rotating about a distinct center of rotation. We determine the nature of the locus of the centers of rotation, which can take on profiles that are distinctly different, based on the nature of the electric field, the applied pressure gradient and the rotation of the top and bottom plates.
subject: Solids
  topic: section
subject: electroactive solid
  topic: keywords
subject: orthogonal rheometer
  topic: keywords
subject: pseudo-planar motion
  topic: keywords
subject: rotation about non-coincident axes
  topic: keywords
creator: K.R. Rajagopal
creator: A. Wineman
creator: P. Alagappan
rights: Copyright (c) 2025 K.R. Rajagopal, A. Wineman, P. Alagappan https://creativecommons.org/licenses/by/4.0
date: 2025-07-14
publication date: 2025-07-14
starting page: 337
ending page: 353
doi: 10.24423/aom.4655

Mechanical stability conditions for 3D and 2D crystals under arbitrary load
type: item
description: The paper gathers and unifies mechanical stability conditions for all symmetry classes of 3D and 2D materials under arbitrary load. The methodology is based on the spectral decomposition of the fourth-order stiffness tensors mapped to secondorder tensors using orthonormal (Mandel) notation, and the verification of the positivity of the so-called Kelvin moduli. An explicit set of stability conditions for 3D and 2D crystals of higher symmetry is also included, as well as a Mathematica notebook that allows mechanical stability analysis for crystals, stress-free and stressed, of arbitrary symmetry under arbitrary loads.
subject: Solids
  topic: section
subject: mechanical stability
  topic: keywords
subject: Born’s stability
  topic: keywords
subject: 2D materials
  topic: keywords
subject: Kelvin moduli
  topic: keywords
subject: orthonormal notation
  topic: keywords
creator: M. Maździarz
rights: Copyright (c) 2025 M. Maździarz https://creativecommons.org/licenses/by/4.0
date: 2025-07-29
publication date: 2025-07-29
starting page: 379
ending page: 399
doi: 10.24423/aom.4679

Characteristics of SH waves in multilayered piezoelectric semiconductor plates considering interfacial imperfection
type: item
description: The dispersion and attenuation characteristics of SH waves in piezoelectric semiconductor multilayered plates with imperfect interfaces are investigated using the improved Legendre orthogonal polynomial method. The field quantities of each layer are expanded into individual Legendre polynomials. By incorporating the interface conditions, the imperfect interface model is integrated into the Legendre polynomials associated with the imperfect interface layer. This method ultimately converts the complex wave partial differential equations into a generalized eigenvalue problem, thereby eliminating the redundant integration operations typical of traditional polynomial methods and allowing for the derivation of complete solutions throughout the entire wave frequency domain. The solutions are then plotted in three-dimensional frequency-complex wavenumber space, thus gaining much deeper insight into the nature of modes. The study encompasses cases ranging from a single-layer ZnO plate, which serves to validate the method, to bilayered and sandwiched piezoelectric semi-conductor plates with imperfect interfaces. The effects of steady-state carrier concentration, imperfect interface coefficients, and stacking sequences on the phase velocity, dispersion, and attenuation curves of SH waves are illustrated. The findings can offer a theoretical foundation for controlling the wave characteristics of piezoelectric semiconductors and for the design of acoustic devices.
subject: Solids
  topic: section
subject: piezoelectric semiconductor
  topic: keywords
subject: multilayered plate
  topic: keywords
subject: SH wave
  topic: keywords
subject: imperfect interface
  topic: keywords
subject: Legendre orthogonal polynomial method
  topic: keywords
subject: dispersion and attenuation
  topic: keywords
creator: Y.H. Luo
creator: X.M. Zhang
creator: A.R. Gao
rights: Copyright (c) 2025 Y.H. Luo, X.M. Zhang, A.R. Gao https://creativecommons.org/licenses/by/4.0
date: 2025-08-20
publication date: 2025-08-20
starting page: 355
ending page: 378
doi: 10.24423/aom.4676

Planar plasma source and a floating wall
type: item
description: The Debye sheath that forms at the plasma-wall interface is discussed by means of the one dimensional collisionless kinetic model. We pay special attention to the simplification often adopted both in theoretical descriptions and numerical simulations, treating the wall as a perfect absorber. We show that this assumption, although it greatly simplifies the considerations, is too restrictive from the physical point of view as it leads to an overdetermined problem. This becomes somewhat understandable if we notice that this assumption does not allow for taking into account any properties of the wall.
subject: Fluids
  topic: section
subject: Debye sheath
  topic: keywords
subject: collisionless plasma
  topic: keywords
subject: plasma-wall interactions
  topic: keywords
subject: collisionless kinetic model
  topic: keywords
creator: A. Riazantsev
creator: Z. Peradzyński
rights: Copyright (c) 2019 A. Riazantsev, Z. Peradzyński https://creativecommons.org/licenses/by/4.0
date: 2026-01-28
publication date: 2026-01-28
starting page: 595
ending page: 620
doi: 10.24423/aom.4713

Investigations of column separation influence on pressure waves severity based on results of water hammer experiments in elastically supported pipeline
type: item
description: Water hammer (WH) events are involved in pipelines when the flow is disturbed by any reason changing its velocity, which produces pressure variations and elastic waves propagating in liquid along a pipeline at the acoustic wave-speed. These phenomena stay more complex if dynamic fluid-structure interaction takes place. More dangerous scenarios may happen in the case of liquid cavitation, which appears when the instantaneous local pressure drops down to the level of the liquid vapor pressure. Bubbles of vapor are created, which can be distributed in specific areas of pipes (distributed cavitation) or may form one larger vapor space between two parts of water column (column separation = CS). In the paper analyses of CS effects are presented based upon experiments performed in the laboratory of the Institute of Fluid-Flow Machinery. Water hammer runs in a copper pipeline fixed to the foundation with elastic supports were generated while pressure oscillations and pipeline vibrations were being measured. For certain initial and boundary conditions CS effects were observed. Analyses of these events were performed for varying initial conditions and support stiffness. The general conclusion is that, more elastic pipeline fixing allows to reduce CS behaviors, more effectively. Further discussion and conclusions are also presented, specifically on WH energy dissipation effects.
subject: Fluids
  topic: section
subject: water hammer
  topic: keywords
subject: column separation
  topic: keywords
subject: fluid-structure interaction
  topic: keywords
subject: cavitation
  topic: keywords
subject: severity index
  topic: keywords
subject: experimental measurements
  topic: keywords
creator: S. Henclik
rights: Copyright (c) 2019 S. Henclik https://creativecommons.org/licenses/by/4.0
date: 2026-01-28
publication date: 2026-01-28
starting page: 621
ending page: 645
doi: 10.24423/aom.4741

Self-equilibrated residual based error estimation on 1-irregular meshes in finite elasticity
type: item
description: We consider well-established techniques for the residual error estimation of finite element approximations applied to problems in finite elasticity. The element implicit residual method and the method of self-equilibration are applied to nearly incompressible and anisotropic finite strain elastic cases. Our contribution regarding the residual error estimation concerns generalising the approach to 1-irregular meshes. That is, we recover equilibrating element tractions in the presence of compatibility enforcing constraints. The generalisations are illustrated using numerical experiments. The considered variants of the estimators are compared.
subject: SolMech2024 conference
  topic: section
subject: error estimation
  topic: keywords
subject: finite element approximation
  topic: keywords
subject: finite elasticity
  topic: keywords
subject: residual
  topic: keywords
subject: self-equilibrated
  topic: keywords
creator: W. Rachowicz
creator: A. Zdunek
rights: Copyright (c) 2019 W. Rachowicz, A. Zdunek https://creativecommons.org/licenses/by/4.0
date: 2025-10-23
publication date: 2025-10-23
starting page: 493
ending page: 531
doi: 10.24423/aom.4643

An analytical–numerical approach for the stability analysis of large strain thermo-elastoplastic material models
type: item
description: The paper deals with the notion of stability for thermo-elastoplastic materials undergoing large strains. The stability analysis is performed by using the perturbation approach applied to a comprehensive material model derived in a thermodynamic format. As the main contribution of this paper a stability condition for a material model incorporating geometrical and material non-linearities under full thermo-mechanical coupling, without typical simplifying assumptions, is derived, and a hybrid analytical-numerical verification of the stability condition at a material point is investigated for the three-dimensional case. Special emphasis is placed on the quasi-static case, for which a specific stability criterion is derived. The theoretical analysis is followed by the numerical verification of the obtained condition. The implementation of the model in the finite element method, using the numerical-symbolic package AceGen, is also presented in the paper. Two representative three-dimensional examples are solved, namely a cube under simple shear and a plate with imperfection, subjected to tension. The obtained results reveal that the type of softening, i.e., thermal or material softening, has a significant influence on the stability at a material point level.
subject: SolMech2024 conference
  topic: section
subject: material stability
  topic: keywords
subject: localization
  topic: keywords
subject: thermo-elastoplasticity
  topic: keywords
subject: large strains
  topic: keywords
subject: finite element method
  topic: keywords
creator: B. Wcisło
creator: J. Pamin
creator: K. Kowalczyk-Gajewska
creator: A. Menzel
rights: Copyright (c) 2025 B. Wcisło, J. Pamin, K. Kowalczyk-Gajewska, A. Menzel https://creativecommons.org/licenses/by/4.0
date: 2025-10-23
publication date: 2025-10-23
starting page: 533
ending page: 568
doi: 10.24423/aom.4661

Evaluating compression and nanoindentation in FCC nickel: a methodology for interatomic potential selection
type: item
description: We performed molecular dynamics simulations to investigate the mechanical response of face-centered cubic (FCC) nickel under uniaxial compression and nanoindentation using traditional interatomic potentials, including the embedded atom method (EAM) and the modified embedded atom method (MEAM). By calculating the generalized stacking fault energy (GSFE), we analyzed the dissociated slip paths responsible for stacking fault formation and partial Shockley dislocations during mechanical loading. Our findings highlight the critical importance of selecting appropriate interatomic potentials to model compression and nanoindentation tests accurately, aligning simulations with experimental observations. We propose a practical methodology for identifying empirical interatomic potentials suitable for mechanical testing of single-element materials. This approach establishes a benchmark for FCC nickel simulations and provides a basis for extending these methods to more complex Ni-based alloys, facilitating comparisons with experimental results such as those from electron microscopy.
subject: SolMech2024 conference
  topic: section
subject: mechanical test
  topic: keywords
subject: MD simulations
  topic: keywords
subject: nickel
  topic: keywords
subject: nanoindentation
  topic: keywords
subject: compression
  topic: keywords
creator: K. Cichocki
creator: F.J. Dominguez-Gutierrez
creator: E. Wyszkowska
creator: L. Kurpaska
creator: K. Muszka
rights: Copyright (c) 2019 K. Cichocki, F.J. Dominguez-Gutierrez, E. Wyszkowska, L. Kurpaska, K. Muszka https://creativecommons.org/licenses/by/4.0
date: 2025-10-23
publication date: 2025-10-23
starting page: 437
ending page: 459
doi: 10.24423/aom.4611

Influence of rotation and couple stresses on convective stability in Navier–Stokes–Voigt fluid
type: item
description: This study investigates the influence of rotation and couple stresses on the convective stability of the Navier–Stokes–Voigt fluid under various boundary conditions, employing both nonlinear (via the energy method) and linear (using the normal mode analysis method) approaches. The eigenvalue problem is derived for both analyses and solved using the Galerkin method to obtain the Rayleigh number. It has been observed that the critical Rayleigh number is identical for both analyses, confirming global stability and the absence of subcritical instabilities. Notably, we find that increasing the couple stress parameter significantly narrows the spectrum of wave numbers for oscillatory modes. Conversely, higher Taylor numbers and Kelvin–Voigt parameters expand the wave number spectrum for oscillatory convection. While couple stresses and rotational effects provide stabilizing influences, the Kelvin–Voigt parameter acts as a destabilizing factor for oscillatory convection. These findings offer valuable insights with potential applications in improving fluid stability and thermal management across a wide array of industries, including industrial cooling systems, aerospace engineering, biomedical devices, energy systems, and environmental engineering.
subject: Fluids
  topic: section
subject: nonlinear and linear analyses
  topic: keywords
subject: couple stresses
  topic: keywords
subject: rotation
  topic: keywords
subject: Navier–Stokes–Voigt fluid
  topic: keywords
creator: D. Kumar
creator: Sunil
creator: R. Devi
rights: Copyright (c) 2025 D. Kumar, Sunil, R. Devi https://creativecommons.org/licenses/by/4.0
date: 2025-05-19
publication date: 2025-05-19
starting page: 305
ending page: 332
doi: 10.24423/aom.4650

A simple quasi-3D theory for static stability analysis of imperfect FG beam
type: item
description: This study introduces a simplified approach to assess the buckling and static bending of advanced composite beams, including those composed of functionally graded materials (FGMs) with various porosity models. The technique utilizes a straightforward integral quasi-3D approach based on the advanced shear deformation theory. This approach offers several advantages: it simplifies the analysis by reducing the number of unknowns and equations required, improves accuracy by considering the stretch effect across the entire depth of the beam, resulting in more reliable results, and accurately represents shear by satisfying the zero-traction boundary conditions on the beam’s surfaces without the need for a shear correction factor. Additionally, it captures the parabolic pattern of transverse shear strain and stress throughout the depth of the beam. The governing equations are obtained by applying the concept of virtual work, and the Navier solution is employed to calculate analytical solutions for the buckling and static bending of FGM porous beams under different boundary conditions. The approach is in line with and builds upon existing research on FGMs and other sophisticated composite beams, further enhancing its validity and reliability. Finally, computational analyses demonstrate how the distribution of materials, such as power-law functionally graded materials (FGMs), geometry, and porosity, affect the deflections, stresses, and critical buckling load of the beam.
subject: Solids
  topic: section
subject: higher-order shear deformation theory
  topic: keywords
subject: FG beam
  topic: keywords
subject: integral quasi-3D
  topic: keywords
subject: bending
  topic: keywords
subject: buckling
  topic: keywords
subject: porosity
  topic: keywords
subject: virtual work principle
  topic: keywords
subject: Navier solution
  topic: keywords
creator: A. Menasria
creator: R. Slimani
creator: A. Bouhadra
creator: S. Refrafi
creator: M. Chitour
creator: M. Ali Rachedi
creator: N. Himeur
creator: K. Zerari
rights: Copyright (c) 2025 A. Menasria, R. Slimani, A. Bouhadra, S. Refrafi, M. Chitour, M. Ali Rachedi, N. Himeur, K. Zerari https://creativecommons.org/licenses/by/4.0
date: 2025-06-02
publication date: 2025-06-02
starting page: 263
ending page: 287
doi: 10.24423/aom.4642

Improved three-dimensional refined plate theory
type: item
description: The paper presents improvements over an earlier developed three-dimensional refined plate theory. The improved theory removes the disadvantage of the earlier theory in that it does not properly satisfy transverse shear stress conditions, and deficiency in being suitable only for flexure problems. The improved theory is suitable for use in flexure, as well as, for vibrations and stability problems of plates. The theory is simple, easy to use and accurate. The number of unknown variables involved are the same as those associated with thin plates, viz. only one in the case of flexure and vibrations; and three in the case of stability. The theory is based on displacement. The theory, to keep it as simple as possible, uses the concept of targeted displacements (which contribute only towards specific stresses, moments, shear forces, axial forces). All the stresses are represented realistically. The theory uses all strain displacement relations, and satisfies, as accurately as possible, all constitutive relations. The moments and forces satisfy gross equilibrium equations. The theory has some noteworthy similarities with the earlier developed well known theories. Due to these similarities, the experience of dealing with the earlier developed theories can be harnessed. Illustrative examples bring out the eficacy of the theory.
subject: Solids
  topic: section
subject: plate theory
  topic: keywords
subject: thick plate theory
  topic: keywords
subject: exact plate theory
  topic: keywords
subject: three-dimensional plate theory
  topic: keywords
subject: refined plate theory
  topic: keywords
creator: R.P. Shimpi
rights: Copyright (c) 2025 R.P. Shimpi https://creativecommons.org/licenses/by/4.0
date: 2025-06-26
publication date: 2025-06-26
starting page: 217
ending page: 262
doi: 10.24423/aom.4564

Two rigid non-circular inhomogeneities in an elastic matrix
type: item
description: We derive analytical solutions to the plane elasticity problem of two interacting identical rigid non-circular inhomogeneities embedded in an infinite isotropic elastic matrix subjected to uniform remote in-plane normal and shear stresses. Explicit expressions for the pair of analytic functions due to remote normal and shear stresses are obtained with the aid of analytic continuation and a conformal mapping function for the doubly connected quadrature domain occupied by the matrix. The rigid body rotation of each rigid inhomogeneity induced by a uniform remote shear stress is determined once three corresponding regular integrals are evaluated. The remote asymptotic behaviors of the pair of analytic functions are determined once five associated regular integrals are evaluated.
subject: Solids
  topic: section
subject: two rigid non-circular rigid inhomogeneities
  topic: keywords
subject: quadrature domain
  topic: keywords
subject: conformal mapping
  topic: keywords
subject: analytic continuation
  topic: keywords
subject: rigid body rotation
  topic: keywords
subject: analytical solution
  topic: keywords
creator: X. Wang
creator: P. Schiavone
rights: Copyright (c) 2025 X. Wang, P. Schiavone https://creativecommons.org/licenses/by/4.0
date: 2025-06-02
publication date: 2025-06-02
starting page: 289
ending page: 304
doi: 10.24423/aom.4663

Some explicit forrnulae for heteroclinic solutions to scalar second order ordinary differential equations
type: item
description: We derive some explicit formulae for heteroclinic pairs for scalar ordinary differential equations of the form u" + vλ(u)u' - su(u - a)(u - 1)(1 + ϕ(u)) = 0, where λ is an arbitrary polynomial in ϕ and is properly chosen. The results are used in a simple model of plasma sustained by a laser beam.
subject: Articles
  topic: section
creator: B. Kaźmierczak
rights: Copyright (c) 1996 B. Kaźmierczak https://creativecommons.org/licenses/by/4.0
date: 1996-01-01
publication date: 1996-01-01
starting page: 211
ending page: 215
doi: 10.24423/aom.1338

Mean-field/FMBEM homogenization of 3-D particulate composites
type: item
description: An approach to homogenization of particulate composite materials is proposed. The mean-field assumption for averaging over phases is combined with numerical calculations of strain-concentration tensors, thus making it independent from the analytical Eshelby solution for ellipsoidal inclusions. The fast multipole boundary element method (FMBEM) is applied to 3-D elasticity and two-phase composites. As opposed to the finite element method (FEM), this method allows for easy modeling of large structures without the need to discretize volumes. Single-inhomogeneity problems are solved, and the calculated strain concentration tensors are used in the averaging formula under the assumption of the Mori–Tanaka approach. An interpolative scheme involving the inverse Mori–Tanaka assumption, known from the literature, is also applied to increase the accuracy of the approximation for higher volume fractions of particles. Examples include composites with spherical and cubic particles, and hybrid materials with auxetic components. The results are consistent with analytical solutions and RVE/FEM models.
subject: SolMech2024 conference
  topic: section
subject: 3-D particulate composites
  topic: keywords
subject: linear elasticity
  topic: keywords
subject: mean-field homogenization
  topic: keywords
subject: strain concentration tensor
  topic: keywords
subject: fast multipole boundary element method
  topic: keywords
creator: J. Ptaszny
rights: Copyright (c) 2019 J. Ptaszny https://creativecommons.org/licenses/by/4.0
date: 2025-10-23
publication date: 2025-10-23
starting page: 461
ending page: 491
doi: 10.24423/aom.4640

Thermal vibration analysis of carbon nanotubes embedded in two-parameter elastic foundation based on nonlocal Timoshenko's beam theory
type: item
description: This paper presents a new model to consider the thermal effects, Pasternak's shear foundation, transverse shear deformation and rotary inertia on vibration analysis of a single-walled carbon nanotube. Nonlocal elasticity theory is implemented to investigate the small-size effect on thermal vibration response of an embedded carbon nanotube. Based on Hamilton's principle, the governing equations are derived and then solved analytically, in order to determine the nonlocal natural frequencies. Results show that unlike the Pasternak foundation, the influence of Winkler's constant on nonlocal frequency is negligible for low temperature changes. Moreover, the nonlocal frequencies are always smaller as compared to their local counterparts. In addition, in high shear modulus along with an increase in aspect ratio, the nonlocal frequency decreases.
subject: Solids
  topic: section
subject: carbon nanotube
  topic: keywords
subject: Pasternak's foundation
  topic: keywords
subject: temperature change
  topic: keywords
subject: nonlocal elasticity
  topic: keywords
subject: Timoshenko's beam theory
  topic: keywords
creator: B. Amirian
creator: R. Hosseini-Ara
creator: H. Moosavi
rights: Copyright (c) 2013 B. Amirian, R. Hosseini-Ara, H. Moosavi https://creativecommons.org/licenses/by/4.0
date: 2013-01-04
publication date: 2013-01-04
starting page: 581
ending page: 602
doi: 10.24423/aom.718

Mechanical characterization of millimetric agarose spheres using a resonant technique
type: item
description: This paper presents a methodology for the mechanical characterization of agarose millimetric spheres using resonant principles. Detection of the modes of vibration was conducted using a low-cost experimental setup based on an electret microphone adapted with a thin latex elastic membrane for the sensing stage and a piezoelectric actuator driven by a conventional transformer for the excitation stage. The identification of vibration modes is supported through an ANSYS Finite Element model of the experimental setup. Experimental and numerical results demonstrate that two modes of vibration, known as Quadrupole and Octupole, appear in the amplitude spectrum and can be used to obtain stiffness values for the samples. Following this approach, Young's modulus of 209 ± 19.80, 338 ± 35.30 and 646 ± 109 kPa for 2%, 3% and 4% agarose millimetric spheres were calculated.
subject: Solids
  topic: section
subject: agarose spheres
  topic: keywords
subject: resonance experiment
  topic: keywords
subject: bulk mechanical properties
  topic: keywords
subject: tissue engineering
  topic: keywords
subject: Young's modulus
  topic: keywords
subject: 3D scaffolds
  topic: keywords
creator: J. Yescas
creator: P. Mandal
creator: J. Sinha
creator: R. Snook
creator: J. Hawkes
creator: P. Moreno Garibaldi
creator: R. Carrera-Espinoza
rights: Copyright (c)
date: 2020-06-30
publication date: 2020-06-30
starting page: 217
ending page: 233
doi: 10.24423/aom.3499

Hyperelastic behavior of cellular structures based on micromechanical modeling at small strain
type: item
description: The present paper extends recent effective, linear anisotropic elasticity model [6, 7] for cellular materials by implying geometric nonlinearity, which is built as the constitutive relation between Green's Lagrangean strain in the tensor and the second Piola–Kirchhoff stress tensor and strain potential formulation. Cellular materials may easily experience large deformations due to large pores-to-volume ratio, since such a deformation on the macroscopic level usually requires smaller deformations of the individual struts constituting the skeleton. The formulation based on micromechanical modeling assumes that essential macroscopic features of mechanical behavior on a macro scale, can be inferred from the deformation response of a representative volume element. Open-cell materials with diverse regular skeleton structures are considered. The initial stiffness tensor components for anisotropic continuum are expressed as fuctions of microstructural parameters, such as skeleton geometric data of representative volume element and skeleton material properties. Since large strains in skeleton structure are characteristic for elasto-plastic behavior, interest is focused on the large displacement and small strain cases. Examples involving numerical tests on cellular materials under homogenoeous strain, relevant to simple shearing and to uniaxial or biaxial loading in the tensile and compressive range, are considered.
subject: Solids
  topic: section
subject: cellular materials
  topic: keywords
subject: anisotropy
  topic: keywords
subject: effective model
  topic: keywords
subject: micromechanical modeling
  topic: keywords
subject: hyperelasticity
  topic: keywords
subject: dissymetry in tension-compression
  topic: keywords
creator: M. Janus-Michalska
rights: Copyright (c) 2011 M. Janus-Michalska https://creativecommons.org/licenses/by/4.0
date: 2011-02-28
publication date: 2011-02-28
starting page: 3
ending page: 23
doi: 10.24423/aom.464

Influence of mixed boundary conditions and heterogeneity on the vibration behavior of orthotropic truncated conical shells
type: item
description: This paper presents the vibration behavior analysis of heterogeneous orthotropic conical shells with mixed boundary conditions. Basic equations of heterogeneous orthotropic truncated conical shells are derived using Donnell–Mushtari shell theory. Employing the separation of variables and Galerkin's method, the expressions for frequency of heterogeneous orthotropic conical shells with two mixed boundary conditions are obtained. The results are validated through numerical comparisons with available results in the literature. The influences of truncated shell characteristics, heterogeneity, material orthotropy and mixed boundary conditions on dimensionless frequency parameters are investigated.
subject: Solids
  topic: section
subject: vibration
  topic: keywords
subject: frequency parameter
  topic: keywords
subject: heterogeneity
  topic: keywords
subject: orthotropic material
  topic: keywords
subject: mixed boundary conditions
  topic: keywords
subject: truncated conical shell
  topic: keywords
creator: A.H. Sofiyev
creator: S.E. Huseynov
creator: N. Kuruoglu
rights: Copyright (c) 2015 A.H. Sofiyev, S.E. Huseynov, N. Kuruoglu https://creativecommons.org/licenses/by/4.0
date: 2015-08-03
publication date: 2015-08-03
starting page: 331
ending page: 348
doi: 10.24423/aom.1890

A parametric study on the elastic-plastic deformation of a centrally heated two-layered composite cylinder with free ends
type: item
description: In this paper, an elastic-plastic deformation of a centrally heated two-layered composite cylinder with free ends subjected to uniformly distributed internal energy generation within an inner cylinder is studied using Tresca's yield condition and its associated flow rule. Stress, strain and displacement distributions in the composite cylinder made of elastic-perfectly plastic material are derived considering the influence of geometric parameters as well as material properties such as yield strength, modulus of elasticity, Poisson's ratio, coefficient of thermal conduction and coefficient of thermal expansion. Yielding starts at the outer boundary or at the axis corresponding to an ‘edge regime’ of Tresca's prism in both cases. Propagations of the plastic regions are studied due to an increase of a heat generation.
subject: Solids
  topic: section
subject: elastic-plastic stress analysis
  topic: keywords
subject: thermal stress
  topic: keywords
subject: composite cylinder
  topic: keywords
subject: Tresca's criterion
  topic: keywords
subject: yielding
  topic: keywords
creator: F. Yalçın
creator: A. Ozturk
creator: M. Gulgec
rights: Copyright (c) 2016 F. Yalçın, A. Ozturk, M. Gulgec https://creativecommons.org/licenses/by/4.0
date: 2016-06-29
publication date: 2016-06-29
starting page: 203
ending page: 228
doi: 10.24423/aom.2159

Inelastic behavior and numerical analysis in twin-roll casting process of AZ31 alloy
type: item
description: In this paper, Anand's model, a unified visco-plasticity constitutive model, was employed to simulate the highly nonlinear behavior in the twin-roll casting process. Anand model's parameters were regressed based on compression tests at various temperatures and strain rates for magnesium alloy AZ31. To calculate the thermal mechanical stresses, the thermal ﬂow of twin-roll casting process was simulated firstly; then the stresses were calculated by the imposed thermal flow as the body load, and a small displacement load along roller's tangential direction was imposed simultaneously in order to simulate the rolling action. The stresses and deformation results were compared with experimental data. Based on the stresses analysis and experimental tests, it reveals that separating force should be strictly controlled in the twin roll casting process in order to avoid cracks caused by thermal and deformation stresses.
subject: Articles
  topic: section
subject: twin roll casting
  topic: keywords
subject: visco-plasticity constitutive model
  topic: keywords
subject: stress and deformation analysis
  topic: keywords
subject: magnesium alloy
  topic: keywords
creator: D.Y. Ju
creator: X.D. Hu
creator: H.Y. Zhao
rights: Copyright (c)
date: 2009-05-01
publication date: 2009-05-01
starting page: 229
ending page: 239

Vibration analysis of single-walled carbon nanotubes conveying nanoflow embedded in a viscoelastic medium using modified nonlocal beam model
type: item
description: In this study, the vibration and stability analysis of a single-walled carbon nanotube (SWCNT) coveying nanoflow embedded in biological soft tissue are performed. The effects of nano-size of both fluid flow and nanotube are considered, simultaneously. Nonlocal beam model is used to investigate flow-induced vibration of the SWCNT while the small-size effects on the flow field are formulated through a Knudsen number (Kn), as a discriminant parameter. Pursuant to the viscoelastic behavior of biological soft tissues, the SWCNT is assumed to be embedded in a Kelvin–Voigt foundation. Hamilton's principle is applied to the energy expressions to obtain the higher-order governing differential equations of motion and the corresponding higher-order boundary conditions. The differential transformation method (DTM) is employed to solve the differential equations of motion. The effects of main parameters including Kn, nonlocal parameter and mechanical behaviors of the surrounding biological medium on the vibrational properties of the SWCNT are examined.
subject: Solids
  topic: section
subject: single-walled carbon nanotube
  topic: keywords
subject: small size effects
  topic: keywords
subject: Knudsen number
  topic: keywords
subject: nonlocal parameter
  topic: keywords
subject: viscoelastic medium
  topic: keywords
subject: differential transformation method
  topic: keywords
creator: M. Hosseini
creator: M. Sadeghi-Goughari
creator: S.A. Atashipour
creator: M. Eftekhari
rights: Copyright (c) 2014 M. Hosseini, M. Sadeghi-Goughari, S.A. Atashipour, M. Eftekhari https://creativecommons.org/licenses/by/4.0
date: 2014-07-28
publication date: 2014-07-28
starting page: 217
ending page: 244
doi: 10.24423/aom.1108

Effect of hydrogen injection into natural gas on the mechanical strength of natural gas pipelines during transportation
type: item
description: The aim of this paper is to study the effect of hydrogen injection into natural gas transient flows on the mechanical strength of natural gas pipelines. The governing equations of hydrogen-natural gas mixtures are two nonlinear partial differential equations. The fluid pressure and velocity are considered as two principal dependent variables. The fluid is a homogeneous hydrogen-natural gas mixture for which the density is defined by an expression averaging the two gas densities where an adiabatic process is admitted for the two components. The problem has been solved by the nonlinear method of characteristics. By the use of Laplace's law, the pipe's circumferential stress has been analyzed for different hydrogen mass fraction in the mixture. It was then compared to the allowable stress of different grade pipeline steels used to transport natural gas. The obtained results have shown that the allowable stress for the natural gas pipelines is exceeded for some fractions of hydrogen in the hydrogen-natural gas mixtures.
subject: Fluids
  topic: section
subject: hydrogen-natural gas mixtures
  topic: keywords
subject: transient flow
  topic: keywords
subject: method of characteristics
  topic: keywords
subject: circumferential stress
  topic: keywords
creator: S. Elaoud
creator: B. Abdulhay
creator: E. Hadj-Taieb
rights: Copyright (c) 2014 S. Elaoud, B. Abdulhay, E. Hadj-Taieb https://creativecommons.org/licenses/by/4.0
date: 2014-07-28
publication date: 2014-07-28
starting page: 269
ending page: 286
doi: 10.24423/aom.1219

Using stability analysis of discrete elastic systems to study the buckling of nanostructures
type: item
description: Stubility/instability criteria of discrete elastic systems are used to study the buckling of nanostructures. The deformation of nanostructures is simulated by solving the nonlinear equations of molecular mechanics. The external forces applied to the nanostructure are assumed to be dead (that is the directions of their action remain constant throughout nanostructure deformation). We note that the positive-definiteness property of the tangential stiffness matrix of a nanostructure is a universal sufficient stability criterion for both equilibrium states and quasi-static/dynamic motions of the nanostructure. The equilibrium configurations are stable in Lyapunov's sense, and quasi-static/dynamic motions are stable in a finite time interval t "isin" (0, Tcr) in which the positive-definiteness property of this matrix is preserved. For dynamic motions of nanostructures, the stability property in this time interval follows from Lee's criterion of quasi-bifurcation of solutions of second order ODEs. The non-positive definiteness of the tangential stiffness matrix of nanostructures at a time t > Tcr corresponds to both unstable equilibrium configurations and unstable dynamic motions. Computer procedures for determining the critical time and buckling mode(s) are developed using this criterion and are implemented in the PIONER FE code. This code is used to obtain new solutions for the deformation and buckling of twisted (10, 10) armchair and (10, 0) zigzag single-walled carbon nanotubes.
subject: Solids
  topic: section
subject: nanostructure
  topic: keywords
subject: single-walled carbon nanotube
  topic: keywords
subject: buckling criteria
  topic: keywords
subject: van der Waals forces
  topic: keywords
creator: S.N. Korobeynikov
creator: V.V. Alyokhin
creator: B.D. Annin
creator: A.V. Babichev
rights: Copyright (c) 2012 S.N. Korobeynikov, V.V. Alyokhin, B.D. Annin, A.V. Babichev https://creativecommons.org/licenses/by/4.0
date: 2012-08-28
publication date: 2012-08-28
starting page: 367
ending page: 404
doi: 10.24423/aom.548