Journal of Multiscale Modelling

A GTN-like model which yield function explicitly depends upon the third stress invariant is first described in this paper. Subsequently, a fully implicit stress integration procedure of this constitutive model based on the return-mapping algorithm is developed. The validity and the performance of the implementation of the considered algorithm within a finite element code are checked through simulations of single element test and three-element test under hydrostatic tensile conditions and simple shear loading as well. Afterwards, as a numerical example, the presented constitutive model and, for the purpose of comparison, the GTN isotropic hardening model, are used to analyze the classical tensile test of axisymmetric notched specimens. The obtained results highlight similarities, good agreement between both models as long as failure initiation of specimen is not reached, and discrepancy as soon as failure of specimen starts.

The quasi-stationary solitons for Langmuir waves in plasmas is obtained in this paper. This model is governed by the perturbed nonlinear Schrödinger's equation with cubic and power law nonlinearities. The perturbation terms are considered with full nonlinearity. A new generalized definition of the phase of the soliton is introduced. This leads to additional information at higher order level which soliton perturbation theory fails to capture.

This paper reviews the recent developments in the field of multiscale modelling of heterogeneous materials with emphasis on homogenization methods and strain localization problems. Among other topics, the following are discussed (i) numerical homogenization or unit cell methods, (ii) continuous computational homogenization for bulk modelling, (iii) discontinuous computational homogenization for adhesive/cohesive crack modelling and (iv) continuous-discontinuous computational homogenization for cohesive failures. Different boundary conditions imposed on representative volume elements are described. Computational aspects concerning robustness and computational cost of multiscale simulations are presented.

There has been increasing attention to utilizing carbon nanotubes (CNTs) as nano-fillers in polymers and polymer matrix composite materials, such as carbon fiber reinforced plastics. However, the understanding of how randomly oriented CNTs affect mechanical properties of such CNT-engineered composites is limited. This paper serves to develop an analytical model for determining the elastic properties of CNT-engineered composite materials using a mechanics of materials approach. Analysis of the properties was constructed progressively using material unit cells starting from the nano level, to the micro level, and finally, to the macro level. MATLAB programming platform was used to facilitate simulation of the modeling process. Typical simulation cases of the CNT-engineered composite materials are presented in comparison with published experimental and other data, where appropriate.