International Journal of Applied Mechanics

A method to relate the displacements of atoms within a representative volume element (RVE) of amorphous material to the deformation of the RVE is presented. The displacement relationship is expressed as a mapping matrix, T, which operates on the displacements of representative points in the RVE to return the atom displacements within it. While the mapping operation has the same mathematical form as an interpolation operation, the T matrix is not an interpolant. It is derived taking into account atom displacements in amorphous materials which cannot be simplified as a continuous, much less homogenous, field. It is shown that the computational domain of a material can be partitioned into nonintersecting sub-domains comprising representative cells — pseudo-amorphous cells (PAC) — and sub-domains of atoms for concurrent multiscale simulations of amorphous materials through the T matrix. Multiscale simulations of nanoindentation on a polymer substrate using the T matrix show good agreement with pure molecular mechanics simulations. When homogenization techniques commonly used for crystalline materials were employed for the same simulations, they gave much less accurate predictions.

A two-dimensional platform phase field model is founded to apply in the Fe-Cr-Al-Y alloy with crack and zirconium diboride ceramic as thermal barrier coatings treated by shot peening. This modal is used to simulate the oxidation growth stress distribution in the platform. The high temperature oxidation resistance and crack propagation of this composite are studied in the numerical simulation. The results show the characteristics of fracture and oxidation resistance properties of the alloy dealt with these promoted technology. The effects of thickness of ceramic layer, surface residual stress by shot peening and direction of crack on oxidation growth stress distribution are also investigated. In this paper, maximum stress is founded linear to the ceramic layer. The suitable thickness of the crack layer and the appropriate intensity of shot peening should be chosen, and the direction of the crack makes a big difference in stress distribution. The study provides a new powerful tool for the simulation of shot-peening process.

This paper investigates the nonlinear free vibration of a double layer graphene sheet (DLGS) embedded in a polymer matrix aroused by the nonlinear van der Waals (vdW) interactions based on the classic Kirchhoff plate theory. Harmonic balance method is used to predict the nonlinear relation between deflection amplitudes and resonant frequencies of the DLGS. The embedded DLGS presents a hardening nonlinearity in both in-phase vibration (IPV) and anti-phase vibration (APV) modes. The surrounding polymer medium is found to have significant effect on the resonant frequency, especially for the IPV mode. For example, the variation of the resonant frequencies of an embedded DLGS is less dependent on the graphene aspect ratio and mode numbers as compared with a free-standing one. Uni-axial and bi-axial in-plane load effects upon the vibrational behavior of DLGS are also investigated. It is concluded that due to the influence of the nonlinear interlayer and interfacial vdW forces on the DLGS, prediction on both linear and nonlinear resonant frequencies for the embedded DLGS is quite different from that for a free-standing one. This study is expected to be useful for understanding the nonlinear mechanical behavior of graphenes with their potential applications in nanocomposites.

The multiple scattering of plane compressional waves by two cylindrical fibers with interface effects is investigated. Based on surface elasticity theory, the wave fields in a nanoscale solid medium can be obtained by applying the eigenfunction expansion method and the Graf's addition theorem. Our results indicate that surface energy significantly affects the diffraction of elastic waves, as the radii of the fibers approach nanometers. The dynamic stress concentration factors at the interfaces between the fibers and the matrix under incident plane compressional waves at different frequencies are examined to determine the effects of surface energy, properties of inhomogeneous materials, and the interaction between fibers in multiple scattering phenomena. These results are helpful in understanding the dynamic mechanical properties of nanocomposites, and the proposed method for investigating the multiple scattering of plane compressional waves can be extended to the case of fiber-reinforced composites.

The present study is carried out to examine the effects of magnetic field-dependent viscosity on steady axi-symmetric ferrofluid flow due to rotating disk in porous medium. The momentum equations give rise to highly nonlinear partial differential equations, which are converted to a system of nonlinear coupled ordinary differential equations on using Karman's similarity transformation. Then a numerical technique, which is the combination of finite difference and shooting methods, is employed in MATLAB environment to get the numerical solution of the problem. Beside the velocity and pressure profiles, the effect of MFD viscosity parameter and porosity parameter are also examined on radial, tangential skin frictions and on boundary layer displacement thickness. The results thus obtained numerically over the entire range of physical parameters are presented graphically.

The complex variable moving least-squares (CVMLS) approximation is discussed in this paper, and the mathematical and physical meaning of the complex functional in the CVMLS approximation is presented. With the CVMLS approximation, the trial function of a two-dimensional problem is formed with a one-dimensional basis function. Then combining the CVMLS approximation and the Galerkin weak form, we investigate the complex variable element-free Galerkin (CVEFG) method for two-dimensional elastodynamics problems. The penalty method is used to apply the essential boundary conditions, and the implicit time integration method, which is the Newmark method, is used for time history analysis. Then the corresponding formulae of the CVEFG method for two-dimensional elastodynamics problems are obtained. For the purposes of demonstration, some selected numerical examples are solved using the CVEFG method. Compared with the EFG method, the CVEFG method has greater precision.

In this paper, employing an analytical method, optimum design of multi-layer compound cylinders is investigated. To this end, considering Tresca criterion, maximum shear stress in each layer is minimized. Analytical relations for optimum values of a layer dimension, residual pressures and radial interferences are derived. A technique for shrink-fitting of layers is also proposed and relationships for radial interferences, residual pressures and required temperature differences during the shrink-fitting process are derived. Three different examples are presented to show the effectiveness of the proposed method. It is shown that increasing the number of layers makes shear stress distribution near to uniform. As a result, with specified maximum shear stress and inner radius, the weight of compound cylinder is decreased when the number of layers is increased. Moreover, compound cylinders with more layers have lower maximum shear stress for a specified weight. It is also concluded that if the ratio of outer to inner radii be larger, increasing the number of layers is more effective.

The paper deals with the mathematical modeling of response amplitude operator (RAO) and frequency-based analysis for coupled roll and yaw motions in regular waves. Prior to obtaining the RAO expressions for linearly coupled conditions, hydrodynamic coefficients are computed by using the strip theory formulation. We consider sinusoidal wave with frequency (ω) varying between 0.3 rad/s and 1.2 rad/s acts on beam to the floating body for zero forward speed. Two limiting cases corresponding to ω → 0 and ω → ∞ are considered and general expressions of RAO for intermediate frequencies are derived. Analytical result shows that the norm of RAO is maximum when ω ≈ ω_n ≈ 0.74 for coupled roll and yaw motions. The asymptotic convergence of real part, imaginary part and norm of uncoupled yaw transfer functions are noticed with the increase of wave frequency. Using the normalization procedure and frequency based analysis; group based equations are formulated for each case. To understand the relative importance of the hydrodynamic coefficients, analytical solutions are obtained. The sensitivity analysis with respect to the initial conditions is investigated for roll and yaw motions. This study could be useful to model the floating body dynamics and corresponding wave loads in the design stage.

In this paper, a nodal integration method (NIM) is presented to deal with the static and dynamic problems of Timoshenko beam. In the present method, linear-shape functions are employed to approximate the displacement field, and smoothing domains based on the nodes are further formed for computing the stiffness matrix. Through a smoothing operation, the shear locking is effectively avoided and the computation gets much simpler. For static problems, the upper bounds for a set of benchmark examples are obtained by nodal integration. For dynamic problems, while keeping the shear stiffness matrix the same as NIM, integration based on elements is adopted to construct the bending stiffness matrix to improve the stability and diminish singular modes caused by pure nodal integration. Results computed in this way prove to be much better than pure nodal integration method for free vibration and forced vibration problems. Numerical examples indicate that very accurate results can be obtained when a reasonable number of nodes is used. Both computational efficiency and accuracy are achieved by above formulations.

In the context of the theory of generalized thermoelastic diffusion, a two-dimensional generalized electromagneto-thermoelastic problem with diffusion for a half-space is investigated. The half-space is placed in an external magnetic field with constant intensity and its bounding surface is subjected to a thermal shock and a chemical potential shock. The governing equations of the problem are formulated and solved numerically by means of finite element method. The derived finite element equations are solved directly in time domain. The nondimensional temperature, displacement, stress, chemical potential, concentration and induced magnetic field are obtained and illustrated graphically. The results show that all the considered variables have a nonzero value only in a bounded region and vanish identically outside this region, which fully demonstrates the nature of the finite speeds of thermoelastic wave and diffusive wave.

Pressure corrections for the viscoelastic potential flow analysis of capillary instability in the presence of axial electric field has been carried out. In viscoelastic potential flow theory, viscosity enters through normal stress balance and the effects of shearing stresses are completely neglected. We include the viscous pressure in the normal stress balance along with irrotational pressure and it is assumed that this viscous pressure will resolve the discontinuity of the tangential stresses at the interface for two fluids. A dispersion relation is derived for the case of axially imposed electric field and stability is discussed in terms of various parameters such as electric field, Deborah number, Ohnesorge number, permittivity ratio and conductivity ratio etc. Stability criterion is given in terms of critical value of wave number as well as critical value of applied electric field. The system is unstable when electric field is less than the critical value of electric field, otherwise it is stable. It has been found that irrotational shearing stresses have stabilizing effect on the stability of the system.