International Journal of Computational Materials Science and Engineering

In this work, applicability of homogenization approach is verified with the micromechanics approach by considering wavy orthotropic fiber composite. Thermal conductivities of $T$-300 orthotropic wavy fiber composite are determined for micromechanical model and compared with the results obtained by two stage homogenized model over volume fraction ranging from 0.1 to 0.6. Also, a methodology is suggested for reducing percentage deviation between homogenization and micromechanical approaches. Effect of debond on the thermal conductivities of wavy orthotrophic fiber composite is studied and compared with perfectly aligned fiber composite for different volume fraction. It is observed that results obtained by the homogenization approach are in good agreement with the results obtained through micromechanics approach. Maximum percentage deviation between homogenized and micromechanics models is 2.13%.

Nonlinear buckling and postbuckling of orthogonal carbon nanotube-reinforced composite (Orthogonal CNTRC) cylindrical shells subjected to axial compression in thermal environments surrounded by elastic foundation are presented in this paper. Two layers of shell are reinforced by carbon nanotube (CNT) in two orthogonal directions (longitudinal and circumferential directions). Based on Donnell’s shell theory with von Karman’s nonlinearity and the Galerkin method, the governing equations are established to obtain the critical buckling loads and postbuckling load-deflection curves. The large effects of CNT volume fraction, temperature change, elastic foundation and geometrical parameters of cylindrical shells on the buckling load and postbuckling behavior of Orthogonal CNTRC cylindrical shells are obtained.

A structural genome (SG) is defined as the smallest structural building block of composite materials. In this study, we use the concept of structure genome to propose a simple approach for obtaining the equivalent mechanical properties of periodic heterogeneous composite plates. Firstly, an SG from the structural model of a periodic heterogeneous composite plate is extracted. Secondly, a python script is developed in commercial software ABAQUS to conveniently impose periodic boundary conditions and apply different loads on the SG as well as obtain the equivalent mechanical properties of the structural genome. To verify the proposed SG approach, numerical examples are presented and discussed for both linear and nonlinear elastic cases. The results show that this approach is efficient and the results are of sufficient precision to calculate the mechanical properties of both linear and nonlinear elastic periodic heterogeneous composite plates.

An element edge method is developed for the evaluation of stiffness matrix for the 8-node brick element. Handling of large data leads to take more computational time in finite element analysis. The new set of quadrature consist of 13 sampling points and weights out which 12 points are at the edges of the brick element and one point is considered at the center of the element. The new set of sampling points is a mimic of Gauss numerical integration method. Finally, the proposed element edge method is evaluated using the standard benchmarked problems and compared the results with conventional Gauss integration method and found that CPU execution time for the evaluation of finite element problems are found to be reduced considerably without compromising in the results mainly consist of accuracy of values and convergence rate.

A new and efficient semi-analytical iterative scheme is proposed in this work for solving the generalized Peierls–Nabarro model. The numerical method developed here exploits certain basic properties of the Hilbert transform to achieve a reduction of the nonlocal and nonlinear equations characterizing the generalized Peierls–Nabarro model to a local model which is then solved using a fixed point iteration scheme. This is in sharp contrast to existing schemes for solving the generalized Peierls–Nabarro model like the semi-discrete variational Peierls–Nabarro model, or methods involving the fitting of the slip distribution to a linear combination of predefined elementary slip distributions, all of which involve the solution of nonlinear and nonlocal equations using gradient-based optimization tools. The key idea behind the proposed technique is to transform the nonlocal Peierls–Nabarro model into an equivalent local model, called the inverse Peierls–Nabarro model. From a computational viewpoint, the resulting local model is attractive since it can be solved without recourse to any gradient based algorithms; combined with appropriate acceleration schemes, the proposed algorithm provides a computationally expedient alternative to solving the generalized Peierls–Nabarro model. Further, the fixed point iterative scheme developed here easily lends itself to parallelization, unlike iterative methods for the fully nonlocal and nonlinear models currently in use. The proposed numerical scheme is validated both with simple examples involving the 1D Peierls–Nabarro model corresponding to a sinusoidal stacking fault energy, and with realistic examples involving calculations of the core structure of both edge and screw dislocations on the close-packed $\{111\}$ planes in Aluminum. An approximate technique to incorporate external stresses within the framework of the proposed iterative scheme is also discussed with applications to the equilibration of a dislocation dipole. Finally, the advantages, limitations and avenues for future extension of the proposed method are discussed.

In this work, an efficient numerical method is proposed for solving generalized Burger’s type equations. The generalized Burger’s type equations are first converted into a nonlinear ordinary differential equation by choosing some suitable wave variable transformation. Linearize such nonlinear differential equations by using quasilinearization technique. For solving algebraic system of linear equations Haar wavelet-based collocation method is used. A distinct feature of the proposed method is their simple applicability in a variety of two- and three- dimensional nonlinear partial differential equations. Numerical experiments are performed to illustrate the accuracy and efficiency of the proposed method.