A mode-III crack embedded in a homogeneous isotropic elastic layer of nanoscale finite thickness is studied in this article. The classical elasticity incorporating surface elasticity is employed to reduce a nonclassical mixed boundary value problem, where the layer interior obeys the traditional constitutive relation and the surfaces of the layer and the crack are dominated by the surface constitutive

This paper compares simple interatomic potentials for carbon nanostructures with hexagonal lattice, by investigating the in-plane and the out-of-plane tensile behaviour of single-layer graphene sheets. Attention is given both to potentials already considered in the literature and to a new one, which we call the damped DREIDING potential, in which damping functions are added to the DREIDING potential

This paper investigates the bandgap properties of a piezoelectric periodic nano-beam considering size and surface effects using a modified couple stress theory. The nano-beam is made of some finite periodic arrays of piezoelectric (PZT-5H) and epoxy segments. The Bloch theorem for periodic materials together with the transfer matrix method are employed for analyzing the problem. The band structure

Microbeam resonators are widely used due to their scientific and engineering applications. The accurate prediction of thermoelastic damping (TED) is necessary to evaluate the performance of resonators at micro- and nanoscales with less energy dissipation. This article aims to present an analytical method for analyzing TED and dynamic behavior of microbeam resonators based on the Moore–Gibson–Thompson

In this paper, we research Noether’s theorems of fractional generalized Birkhoffian systems in terms of classical and combined Caputo derivatives. First, the generalized Pfaff–Birkhoff principle and Birkhoff’s equations with classical and combined Caputo derivatives are given. Then, in the case of without and with transforming time, respectively, we obtain two kinds of Noether symmetry and their conserved

An effective technique is proposed for identifying the track modulus, i.e., the foundation stiffness of the rails, using the contact-point response of the moving test vehicle. First, for a simple beam resting on an elastic foundation under a moving sprung mass, closed-form solutions are derived for the responses of the vehicle and its contact point with the rail. It is shown that the track modulus

Resonance phenomena in impacting systems can be defined as an amplitude increasing during periodically applied impacts. The wave cancellation phenomenon is defined as application of certain conditions to cancel the wave fully. The double impact system is defined as the application of the first impact with a certain duration \(\tau \) and then the application of a counter impact in a certain time \(\tau

An analytical solution is given to the problem of non-uniform torsion of an elliptical cylinder made of functionally graded anisotropic linear elastic material. The material moduli of the considered anisotropic non-homogeneous elastic bar are smooth functions of the axial coordinate. The contour of the elliptical cross section depends on the elastic constants. This dependence provides the zero warping

The stationary probability density function (PDF) solution of a variable-mass system is calculated under Gaussian white noises and Poisson white noises, respectively. For small mass disturbance, the corresponding Fokker–Planck–Kolmogorov equation and Kolmogorov–Feller equation of the system are derived. The solution procedure based on the exponential–polynomial closure (EPC) method is formulated to

This paper considers solutions that can determine the nature of the stress singularity in the vicinity of a singular point for two-dimensional and three-dimensional closed composite wedges. A comparative analysis of stress singularity exponents is carried out for closed composite wedges with perfectly bonded interfaces and homogeneous wedges with stress-free edges. Using analysis results, it is possible

The present article deals with the propagation of Rayleigh surface waves in a homogeneous orthotropic medium based on Eringen’s nonlocal thermoelasticity. This thermoelastic problem is studied under the purview of Green–Naghdi model type III of hyperbolic thermoelasticity in the presence of voids. The normal mode analysis is employed to obtain a vector matrix differential equation which is then solved

The temperature variation within two elastic bodies in perfect thermoelastic contact may cause the contact area to become convex and hence lead to a reduction in the size of the contacting surface. In receding thermoelastic contact problems, the final size of the contact zone is independent of the applied loads, being only affected by the thermomechanical properties of the solids. However, the final

In this article, a novel mathematical model is theoretically developed by incorporating a memory-dependent derivative (MDD) into the temperature-rate-dependent thermoelasticity theory (Green–Lindsay) on three mathematical aspects in order to study the spatial behavior of the thermal signals in an isotropic, homogeneous, thermoelastic continuum. Firstly, to ensure the thermodynamic consistency of the

The present work analyzes numerical simulations of long flexible fibers in two-dimensional flows. The focus is on the frequency at which caustics occur and the characterization of the collisions among fibers. The continuous flexible fibers are modeled as a set of connected rigid cylinders, where forces are applied to the center of mass of each cylinder determining their motion and fiber deformation

The present investigation is concerned with the reflection of plane waves at the free surface of a homogeneous, isotropic, nonlocal, micropolar rotating thermoelastic medium. The entire thermoelastic medium is rotating with a uniform angular velocity. It is observed that there exist four coupled plane waves, which travel through the medium with distinct speeds. Using appropriate boundary conditions

An interesting recent finding is that, in a medium of nearly linear elastic materials, the stem cell differentiation responds to the Young’s modulus of elasticity. It is discussed here that the more general mechanical identifier of differentiation is indeed the stiffness (rather than the Young’s modulus). Specifically, for nonlinear (and thus more realistic/physiologically mimetic) materials the stiffness

This work documents the first account of advanced mechanical properties of six commercial lipsticks, some of which serve as market leads. We systematically studied their nonlinear viscoelastic properties under large amplitude oscillatory shear deformations. At large strains, all lipsticks showed intercycle strain softening, the extent of which initially depended on the prototype in the nonlinear regime

The present work is devoted to the investigation of the free vibrations of a homogeneous isotropic nonlocal thermoelastic cylinder with void. Time-harmonic variations are used to reduce the governing partial differential equations to a system of ordinary differential equations. The frequency equation for the continuation of vibrations for the mode numbers in the considered cylinder is deduced in closed

A review is presented of measurement techniques to characterise dispersed multiphase flows, which are not accessible by means of conventional optical techniques. The main issues that limit the accuracy and effectiveness of optical techniques are briefly discussed: cross-talk, a reduced signal-to-noise ratio, and (biased) data drop-out. Extensions to the standard optical techniques include the use of

The paper focuses on the evaluation of the effective properties of linear viscoelastic composites with a periodic structure, containing long cylindrical fibers of circular cross-section and for two different cell arrangements: square and hexagonal unit cells. For this purpose, we use the two-scale asymptotic homogenization method (AHM) and a numerical homogenization method (NHM). Based on the correspondence

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The buckling and parametric resonance characteristics of laminated composite spherical sandwich shell panels with viscoelastic material (VEM) core are investigated in the present analysis considering full geometric nonlinearity in the Green–Lagrange sense. The study includes the longitudinal strain and normal strain in the transverse direction along with transverse shear deformation of the VEM core

In this paper, a weak form quadrature element formulation of a geometrically nonlinear shell model is proposed and applied for analysis of laminated composite shell structures. Thickness stretch parameters of the shell are incorporated for introducing 3D constitutive relations in the formulation. A drilling rotation constraint on the basis of polar decomposition of a modified deformation gradient is

The present work focuses on the effect of rotational restraints on the shear buckling of symmetrically laminated curved composite panels. The Sanders–Koiter shell theory and a first-order shear deformation scheme were used for the mathematical representation of the deformation kinematics of cylindrical shells. The eigenvalue buckling equations were obtained using the principle of minimum total potential

Surface-treated bodies are considered under the assumption that the plastic strain distribution is uniform along the surface and changes only with depth. The elastic problem of the surface-treated plate is solved. The obtained solution is used to derive the explicit exact reconstruction formulas for distributions of main tangential components of the plastic strain tensor. It has been proved that the

We present new nonlinear, one-dimensional equations of extended thermodynamics for temperature and heat flux that describe damped heat wave propagation and predict dependence of the second sound velocity on temperature and heat flux in a rigid thermal conductor. The aim of the present work is to investigate the implications of the considered nonlinearities on the process of heat propagation, especially

In this article, buckling analysis of a porous nanocomposite cylindrical shell reinforced with graphene platelets (GPLs) using first-order shear deformation theory is carried out. Internal pores and GPLs are scattered uniformly and/or nonuniformly in the thickness direction. The mechanical properties such as the effective modulus of elasticity through the thickness direction are computed by the modified

In this paper, the rolling contact fatigue crack growth in the presence of multiple cracks and their interactions is studied. The proposed formulation is based on linear elastic fracture mechanics and singular integral equations. The body under the rolling contact is modeled by a half-plane weakened by a set of surface, subsurface and surface–subsurface cracks. Rolling contact is simulated by translational

The nonlinear mechanics modeling is proposed to describe the nonlinear stiffness of the bolted joint interfaces induced by the stick-slip friction behaviors. By combining the microscale contact mechanics of the asperity interaction, the statistical analysis of the non-Gaussian surfaces is conducted to extract a four-parameter model to characterize the nonlinear softening stiffness and residual stiffness

Based on the modified couple stress theory and Gurtin–Murdoch surface elasticity theory, a size-dependent Timoshenko beam model is developed for investigating the nonlinear vibration response of functionally graded (FG) micro-/nanobeams. The model is capable of capturing the simultaneous effects of microstructure couple stress, surface energy, and von Kármán’s geometric nonlinearity. Sigmoid function

The purpose of this paper is to extend and generalize the precise integration method (PIM) and the Wittrick–Williams (W–W) algorithm to analyze the dispersion of guided waves in multilayered anisotropic piezoelectric structures. The analysis shows that the W–W algorithm cannot be directly applied to piezoelectric materials. This is due to the fact that a submatrix of the Hamiltonian matrix is not positive

In the present paper, constitutive equations accounting for coupled damage-thermo-elasto-(visco)plastic and diffusion at small deformation are proposed in the standard thermodynamics of irreversible processes framework. One main objective is to include the diffusion phenomenon in the models with ductile damage. The model is developed in the framework of thermodynamics of irreversible processes with

The design equations of a neutral coated inhomogeneity with confocal elliptic interfaces are derived, when the elastic matrix is subjected to a longitudinal shear. The neutrality of such an inhomogeneity is achieved by inserting an appropriate coating between inhomogeneity and matrix provided that the longitudinal shear applied to the matrix is parallel to one of the elliptical semi-axes. The above

In the present paper, a study is performed in an irregular earth crust, layered over a semi-infinite half-space under the effect of gravity. The irregularities at the interface are possible combinations of geometric shapes such as rectangular, paraboic and triangular notches. The aim of the study is to come up with the influence of these irregularities on the phase velocity of shear horizontal waves

The deformation of a rotating elastic cylinder moving on an elliptic orbit is discussed analytically. Firstly, one solution method is developed for a coupled displacement equation, which includes the centrifugal force and the 2D-Coriolis effects fully. Secondly, the obtained general solution is applied to a rotating cylinder moving on an elliptic orbit. For a rotating hollow cylinder, the non-circular

This paper aims at a fundamental perspective of multiple cracks’ interaction on the fracture behavior of magnetoelastic materials. A theoretical study is performed on a soft ferromagnetic solid weakened by an array of periodic cracks under an in-plane magnetic loading. By using the conformal mapping technique and the analytic function boundary value theory, a rigorous analytical solution of the magnetic

The vibration of a functionally graded axisymmetric nonlocal thermoelastic hollow sphere with dual-phase-lag effect is addressed in this paper. Surfaces of the sphere are assumed to be thermally insulated or isothermal and stress free. According to a simple power law, the material is assumed to be graded in the radial direction. The linear theory of modified thermoelasticity with a dual phase lag based

A new stabilized method is presented for coupled chemo-mechanical problems involving chemically reacting fluids flowing through deformable elastic solids. A mixture theory model is employed wherein kinematics is represented via an independent set of balance laws for each of the interacting constituents. A significant feature of the mixture model is the interactive force field in the momentum balance

A biologically microscopic system presenting a highly scientific interest is the microtubule (MT). Our research endeavor revolves around the eigenfrequencies’ analysis of an MT embedded in the cytoplasm of the cell by means of the nonlocal integral elasticity for the first time. The MT is simulated as a beam and the cytoplasm as a Pasternak-type elastic foundation, respectively. The responses of the

In this study, the nonlinear forced vibration of simply supported multilayered nanoplates in the framework of the first-order shear deformation of Mindlin plate theory based on the nonlocal strain gradient elasticity theory is investigated. The nonlinear von Karman strain–displacement relation is employed. The interaction of van der Waals forces between adjacent layers of a multilayered nanoplate is

In the present paper, a flexible framework is developed for the optimization of composite laminate plates. In this framework, an optimization algorithm is employed to find the optimal stacking sequence design of the FE models by interfacing the Abaqus solver with MATLAB through a Python script. The Python script submits dimension, orientation, and diameter of the cutout combinations to Abaqus/CAE.

The aim of the present study is to analyze the propagation behavior of an SH wave in a layered structure constituted of a functionally graded piezo-poroelastic material (FGPPM) layer imperfectly bonded to an FGPPM half-space influenced by a stress point source of disturbance situated at the interface. Mass loading sensitivity of the considered structure is also analyzed by assuming a deposition of

Ubiquitiform geometry, as an important tool to study complex and irregular configurations, provides an important theoretical basis for solving nonlinear problems. In this paper, considering the ubiquitiformal characteristics of crack propagation, two key ubiquitiformal parameters of complexity and yardstick length were introduced into the theoretical derivation of Mode I crack propagation. The effects

Smart materials respond to external stimuli, e.g., electric fields, which enables their use as sensors and actuators. The electromechanical coupling of the direct and converse piezoelectric effects, for instance, is used for both actuation and sensing in diverse engineering applications. The response of ferroelectric materials depends on their state of remanent polarization and the presence of an external

Trajectory tracking problems for underactuated manipulators represent an actual research topic, which is sustained by the interest in a lighter and faster automatic class of mechanical systems, bringing some benefits as lower energy consumption, higher productivity and a more convenient human–machine interaction. This work presents a feedforward design method, which is based on the inverse dynamics

A new, general hp-version axisymmetric finite element is derived for the boundary value problems of thin linearly elastic shells of revolution, applying a complementary strain energy-based three-field dual-mixed variational principle. For the interpolation of the mid-surface geometry, non-uniform rational B-splines—NURBS—is used. The independent field variables of the weak formulation are the a priori

This paper investigates the buckling analysis of periodic beams by a geometrically nonlinear equivalent micro-polar model that is built through the results of the unit cell transfer matrix eigenanalysis. The periodic system considered is the Vierendeel girder under compressive axial loads. The stiffness properties of the equivalent model are evaluated by an averaging process of unit cell strain energies

In this paper, we present a high-order polynomial free energy for the phase-field model of two-phase incompressible fluids. The model consists of the Navier–Stokes (NS) equation and the Cahn–Hilliard (CH) equation with a high-order polynomial free energy potential. In practice, a quartic polynomial has been used for the bulk free energy in the CH equation. It is well known that the CH equation does

The state-space approach is developed to analyze the dynamic behaviors of a multilayered two-dimensional piezoelectric quasicrystal circular cylinder filled with the compressible fluid. With simple support at both ends, the hollow cylindrical shell has imperfect bonding between the layers. The analytical solution of a homogeneous cylindrical shell has been derived based on the state equations. The

For the first time, explicit closed form relations between overall elastic properties of two composite materials with the same microstructure and properties of inhomogeneities but different matrices are derived. Based on this result, we developed an innovative methodology that allows evaluation of the elastic properties of small particles—the problem of crucial importance in geophysics, mechanics of

In this paper, a lattice Boltzmann model based on the phase-field Cahn–Hilliard-based approach is proposed to deal with ternary fluid flows in the axisymmetric coordinate system. The present model can handle both high density and viscosity ratios for partial and total spreading scenarios. A variety of numerical tests, including a static droplet test, a breakup of a liquid thread test, a spreading of

The present study is concerned with the dynamic response of an anisotropic composite structure due to a normal moving load on its irregular rough surface. The composite structure is comprised of an irregular incompressible heterogeneous transversely isotropic fluid-saturated poroelastic layer lying over a transversely isotropic substrate. The mathematical formulation of this structure gives rise to

In the present work, a continuum-based material model has been developed for an isotropic magneto-active elastomer (MAE) to investigate its behavior under small deformations. Firstly, the governing magneto-mechanical equations are formulated for the flexible magneto-active medium. Subsequently, a linearization scheme is used to construct constitutive equations for the small-deformation analysis of

The technique of numerical simulation of laser surface evaporation of small particles ranging in size from tens to several millimeters falling into the field of laser radiation is developed. The interaction of a laser beam with solid or liquid particles freely flying in a gas-dispersed stream is accompanied by heating and evaporation of the material, which occurs only from the irradiated part of the

Propagation of the torsional surface waves in a medium consisting of a functionally graded (FG) substrate bonded to a thin piezoelectric over-layer has been analytically formulated in the mathematical framework of surface/interface elasticity theory. In the cases where the wavelength and/or the thickness of the over-layer are comparable to the surface/interface characteristic length, then the surface/interface

This paper presents a systematic computational study to investigate the effects of crystal orientation, strain rate (impact velocity), and size (thickness) on plasticity and damage behavior of copper single crystals during the penetration process at the atomistic scale. For the penetration analysis, copper single crystals with different crystal orientations and thicknesses were impacted and penetrated

Discrete mechanics makes it possible to formulate any problem of fluid mechanics or fluid-structure interaction in terms of velocity and potentials of acceleration; the equation system consists of a single-vector equation and potential updates. The scalar potential of the acceleration represents the pressure stress, and the vector potential is related to the rotational shear stress. The formulation

Supersonic flows around diamond airfoils, under large-amplitude step motion, are analytically studied. Nine regions with distinct flow structures are identified on each side. These regions include intricate wave structures and significantly shape the indicial response. The novelty of this work is to develop theoretical models, capable of describing each region’s wave speed, pressure, and force. We

Nanoindentation of single microscale fibers is a challenging task due to the dimensional similarity of the probing instruments to the single-fiber cross sections. Algorithms customarily used in nanoindentation equipment assume that the indentation occurs in flat surfaces, thus simplifying the local geometry and approximating material properties in curved specimens. A modified Curved Area Function (mCAF)

A shear deformable beam moving along a straight path is considered as an idealization of the problem of stationary operation of a belt drive. The partial contact with a traveling surface results in the shear deformation of the beam. The tangential contact force grows near the end of the contact zone. Assuming perfect adhesion of the lower fiber of the beam to the traveling surface (no slip), we analytically