Journal of Multiscale Modelling

In this paper, we introduce a new discrete model by compounding two parameter discrete Weibull distribution with Beta distribution of first kind. The proposed model can be nested to different compound distributions on specific parameter settings. The model is a good competitive for zero-inflated models. In addition, we present the basic properties of the new distribution and discuss unimodality, failure rate functions and index of dispersion. Finally, the model is examined with real-life count data from medical sciences to investigate the suitability of the proposed model.

The vibrational behavior of polymer matrix nanocomposite plates reinforced with carbon fibers (CFs) and carbon nanotubes (CNTs) is studied using the finite element method based on a multi-scale modeling approach. The influences of nano- and micro-scale are coupled through a two-step procedure. First, CNTs are dispersed into the polymer matrix. In the selected representative volume element (RVE), interphase due to chemical interaction between CNT and polymer matrix is considered. Also, the state of dispersion of CNTs into the matrix is assumed to be random. In the second step, CFs are randomly distributed in the reinforced polymer with CNTs. The reinforcement is carried out for various volume fractions of CFs and CNTs. Two three-dimensional models including the brick and shell ones are used to generate the results. Moreover, the analysis is presented for square plates under different types of boundary conditions. The effect of nanocomposite thickness on its vibrational response is also investigated.

Inspired by nanotubes, a 3D finite element model was developed to simulate the influence of cylindrical inclusions on the polycrystalline mechanical behavior of Nickel alloys. A dislocation based strain hardening model, constructed in the so-called Kocks–Mecking framework, is used as the main strategy for the constitutive modeling of individual bulk grains. To determine the influence of the inclusions distribution, the direction of applied load and the size of the matrix phase on the inelastic stress–strain distribution, the digital microstructure code DREAM.3D was coupled to ABAQUS${}^{\circledR }$ finite element code through a MatLab${}^{\circledR }$ program. Four affordable computational representative volume elements (RVEs) meshes of two different edge sizes and two different inclusion distributions were tested to investigate the relation between micro and macro deformation and stress variables. The virtual specimens, subjected to continuous monotonic strain loading conditions, were constrained with random periodic boundary conditions. The difference in crystallographic orientation, which evolves in the process of straining, and the incompatibility of deformation between neighboring grains were accounted for by the introduction of single crystal averaged Taylor factors, single crystal Young’s modulus, single phase elastic modulus and the evolution of geometrically necessary dislocation density. The effects of single crystal Young’s modulus, inclusion distribution and direction of the applied load upon the aggregate local response are clearly observed. Results demonstrate a strong dependence of flow stress and plastic strain on phase type, Young’s modulus values and direction of the applied load, but slightly on matrix grain size. The stress–strain curve extension and the variation in the elastic limit of the individual inclusions depend on the inclusion-matrix Young’s modulus difference and applied load direction. The difference in curve extension and the difference in elastic limit decrease as the Young’s modulus of the single crystal inclusion approach the Young’s modulus of the matrix majoritary phase, while the resistance to flow increases when the applied load is perpendicular to the inclusion longitudinal axis.