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This paper aims to combine Eringen’s micromorphic and nonlocal theories and thus develop a comprehensive size-dependent beam model capable of capturing the effects of micro-rotational/stretch/shear degrees of freedom of material particles and nonlocality simultaneously.

To consider nonlocal influences, both integral (original) and differential versions of Eringen’s nonlocal theory are used. Accordingly, integral nonlocal-micromorphic and differential nonlocal-micromorphic beam models are formulated using matrix-vector relations, which are suitable for implementing in numerical approaches. A finite element (FE) formulation is also provided to solve the obtained equilibrium equations in the variational form. Timoshenko micro-/nano-beams with different boundary conditions are selected as the problem under study whose static bending is addressed.

It was shown that the paradox related to the clamped-free beam is resolved by the present integral nonlocal-micromorphic model. It was also indicated that the nonlocal effect captured by the integral model is more pronounced than that by its differential counterpart. Moreover, it was revealed that by the present approach, the softening and hardening effects, respectively, originated from the nonlocal and micromorphic theories can be considered simultaneously.

Developing a hybrid size-dependent Timoshenko beam model including micromorphic and nonlocal effects. Considering the nonlocal effect based on both Eringen’s integral and differential models proposing an FE approach to solve the bending problem, and resolving the paradox related to nanocantilever.

The purpose of this paper is to investigate a two dimensional problem of micropolar porous thermoelastic circular plate subjected to ramp type heating.

Three phase lag theory of thermoelasticity has been used to formulate the problem. A numerical inversion technique is applied to obtain the result in the physical domain. The numerical values of the resulting quantities are presented graphically to show the effect of porosity and dual phase lag model. Some particular cases are also presented.

The Laplace and Hankel transforms are employed followed by the eigen value approach to obtain the components of displacements, microrotation, volume fraction field, temperature distribution and stresses in the transformed domain.

This paper fulfils the need to study the two-dimensional problem of micropolar porous thermoelastic circular plate subjected to ramp type heating.

The purpose of this paper is to study of propagation of plane wave and the fundamental solution of the system of differential equations in the theory of a microstretch thermoelastic diffusion medium in phase-lag models for the case of steady oscillations in terms of elementary functions.

Wave propagation technique along with the numerical methods for computation using MATLAB software has been applied to investigate the problem.

Characteristics of waves like phase velocity and attenuation coefficient are computed numerically and depicted graphically. It is found that due to the presence of diffusion effect, these characteristics get influenced significantly. However, due to decoupling of CD-I and CD-II waves from rest of other, no effect on these characteristics can be perceived.

Basic properties of the fundamental solution are established by introducing the dual-phase-lag diffusion (DPLD) and dual-phase-lag heat transfer (DPLT) models.

The paper aims to presents a numerical analysis of free vibration of micromorphic structures subjected to various boundary conditions.

To accomplish this objective, first, a two-dimensional (2D) micromorphic formulation is presented and the matrix representation of this formulation is given. Then, two size-dependent quadrilateral and triangular elements are developed within the commercial finite element software ABAQUS. User element subroutine (UEL) is used to implement the micromorphic elements. These non-classical elements are capable of capturing the micro-structure effects by considering the micro-motion of materials. The effects of the side length-to-length scale parameter ratio and boundary conditions on the vibration behavior of 2D micro-structures are discussed in detail. The reliability of the present finite element method (FEM) is confirmed by the convergence studies and the obtained results are validated with the results available in the literature. Also, the results of micromorphic theory (MMT) are compared with those of micropolar and classical elasticity theories.

The study found that the size effect becomes very significant when the side length of micro-structures is close to the length scale parameter.

The study is to analyze the free vibrations of 2D micro-structures based on MMT; to develop a 2D formulation for micromorphic continua within ABAQUS; to propose quadrilateral and triangular micromorphic elements using UEL and to investigate size effects on the vibrational behavior of micro-structures with various geometries.

The propagation of free vibrations in microstretch thermoelastic homogeneous isotropic, thermally conducting plate bordered with layers of inviscid liquid on both sides subjected to stress free thermally insulated and isothermal conditions is investigated in the context of Lord and Shulman (L‐S) and Green and Lindsay (G‐L) theories of thermoelasticity. The secular equations for symmetric and skewsymmetric wave mode propagation are derived. The regions of secular equations are obtained and short wavelength waves of the secular equations are also discussed. At short wavelength limits, the secular equations reduce to Rayleigh surface wave frequency equations. Finally, the numerical solution is carried out for magnesium crystal composite material plate bordered with water. The dispersion curves for symmetric and skew‐symmetric wave modes are computed numerically and presented graphically.

The aim of the present paper is to study the combined influence of textured surface and micropolar lubricant behaviour on the performance of two-lobe hole-entry hybrid journal bearing system. The bearing performance parameters of the textured circular/two-lobe hole-entry hybrid journal bearing system have been computed against the constant vertical external load supported by the bearing.

In this work, Eringen’s micropolar fluid theory has been used to derive the governing Reynolds equation. The consequent solution of the governing Reynolds equation has been obtained by using finite element method (FEM) numerical technique.

The present study indicates that the use of the textured surface, two-lobe profile of bearing and micropolar lubricant, significantly enhances the bearing performance as compared to non-textured circular journal bearing.

The present study concerning the influence of surface texturing on the behaviour of the two-lobe hole-entry hybrid journal bearing lubricated with micropolar lubricant is original. The theoretically simulated results of the present study will be useful to design an efficient journal bearing system.

The purpose of this paper is to study the reflection of a plane harmonic wave at the interface of thermo-microstretch elastic half space. The modulus of elasticity is taken as a linear function of reference temperature. The formulation is applied to generalized thermoelasticity theories, the Lord-Shulman and Green-Lindsay theories, as well as the classical dynamical coupled theory. Using potential function, the governing equations reduce to ten-order differential equation.

Coefficient ratios of reflection of different waves with the angle of incidence are obtained using continuous boundary conditions. By numerical calculations, the variation of coefficient ratios of reflection with the angle of incidence is illustrated graphically for magnesium crystal micropolar material under three theories.

The effect of different temperature-dependent constants and frequency on the coefficient ratios of reflection is illustrated graphically in context of Lord-Shulman theory.

The reflection coefficient ratios are given analytically and illustrated graphically. The effects of thermal relaxation times are very small on reflection coefficient ratio. The temperature-dependent constant and wave frequency have a strong effect on the reflection coefficient ratios.

The present paper aims to study the effect of rotation on the general model of the equations of generalized thermo‐microstretch for a homogeneous isotropic elastic half‐space solid whose surface is subjected to a thermal shock is considered. The problem is in the context of the generalized thermoelasticity Lord‐Şhulman's theory with one relaxation time, as well as the classical dynamical coupled theory.

The normal mode analysis is used to obtain the exact expressions.

For the displacement components, force stresses, temperature, couple stresses and microstress distribution.

The variations of the considered variables through the horizontal distance are illustrated graphically. Comparisons are made with the results in the presence and absence of rotation and in the presence and absence of microstretch constants between the two theories.

The purpose of this paper is to study the effect of gravity on the general model of the equations of generalized magneto‐thermo‐microstretch for a homogeneous isotropic elastic half‐space solid whose surface is subjected to a mode‐I crack. The problem is in the context of the Green and Naghdi theory of both types (II and III).

The normal mode analysis is used to obtain the expressions for the displacement components, the force stresses, the temperature, the couple stress and the microstress distribution.

The variations in variables against distance components are given graphically in 2D and 3D.

The linear theory of elasticity is of paramount importance in the stress analysis of steel, which is the commonest engineering structural material. To a lesser extent, the linear elasticity describes the mechanical behavior of the other common solid materials, e.g. concrete, wood and coal. However, the theory does not apply to the behavior of many of the newly synthetic materials of the elastomer and polymer type, e.g. polymethyl‐methacrylate (Perspex), polyethylene and polyvinyl chloride.

Comparisons are made with the results in the presence and absence of gravity and initially applied magnetic field with two cases: the first for the generalized micropolar thermoelasticity elastic medium (without stretch constants) between both types (II, III); and the second for the generalized magneto‐thermoelastic medium with stretch (without micropolar constants) between both types (II, III).

An analysis is presented to study the effects of buoyancy on forced convection in an axisymmetric stagnation flow of micropolar fluids over a vertical cylinder with constant or linear variation of surface heat flux conditions. Numerical solutions are given for the governing momentum, angular momentum and energy equations. Two flow regions, namely the buoyancy‐assisted and buoyancy‐opposed cases are analysed. It is observed that the wall shear stress and surface heat transfer rate increase or decrease with the buoyancy force parameter depending on the flow regime being buoyancy‐assisted or buoyancy‐opposed respectively.