Sharif Digital Repository

In this paper, a computational counterpart of the experimental investigation is presented based on a nonlocal computational homogenization technique for extracting damage model parameters in quasi-brittle materials with softening behavior. The technique is illustrated by introducing the macroscopic nonlocal strain to eliminate the mesh sensitivity in the macroscale level as well as the size dependence of the representative volume element (RVE) in the first-order continuous homogenization. The macroscopic nonlocal strains are computed at each direction, and both the local and nonlocal strains are transferred to the microscale level. Two RVEs with similar geometries and material properties are... 

We study the homogenization of semilinear elliptic equations in divergence form with discontinuous oscillating coefficients in the whole ℝN. As is well known, the homogenization process in a classical framework is concerned with the study of asymptotic behavior of solutions u Isin; of boundary value problems when the period ∈ > 0 of the coefficients is small. By extending some of the classical homogenization results for quasi-linear elliptic equations to unbounded domains and, making use of various variational techniques, we shall establish some stability results under Γ-convergence of least energy solutions for such boundary value problems  

We present a universal model of brain tissue microstructure that dynamically links osmosis and diffusion with geometrical parameters of brain extracellular space (ECS). Our model robustly describes and predicts the nonlinear time dependency of tortuosity (λ=D/D∗) changes with very high precision in various media with uniform and nonuniform osmolarity distribution, as demonstrated by previously published experimental data (D = free diffusion coefficient, D∗ = effective diffusion coefficient). To construct this model, we first developed a multiscale technique for computationally effective modeling of osmolarity in the brain tissue. Osmolarity differences across cell membranes lead to changes... 

Designing meta-materials and cellular solids with biomimetic structures has received increasing attention in the past few years partially due to advances in additive manufacturing techniques that have enabled the fabrication of advanced materials with arbitrarily complex microarchitectures and novel functionalities. To impact on this trend, it is essential to develop our understanding about the role of microstructure on mechanical responses of these structures. Although a large literature exists on the general subject, the role of microstructure on the post-yield instability is not yet adequately documented. This research introduces a numerical approach to study the post-yield instability in... 

We have used a hierarchical multiscale modeling scheme for the analysis of carbon nanotube reinforced nanocomposites. This scheme consists of definition of two boundary value problems, one for macroscale (the scale in which the material exists homogeneously and we are interested in modeling the material behavior on that scale), and another for microscale (the scale in which the material becomes heterogeneous and microstructural constituents emerge). The coupling between these scales is done by using homogenization techniques. Using the presented scheme, we have studied carbon nanotube (CNT) reinforced composites behavior and the effects of an interphase layer between CNT and matrix material.... 

In this paper, a computational modeling tool is developed for fully coupled multiphase flow in deformable heterogeneous porous medium that consists of complex and non-uniform micro-structures using the dual continuum scales based on the computational homogenization approach. The first-order homogenization technique is employed to perform the multi-scale analysis. The governing equations of two-phase flow of immiscible fluids, including an equilibrium equation and two mass continuity equations, are considered based on the appropriate main variables. According to the well-known Hill–Mandel principle of macro-homogeneity, the proper energy types are defined instead of conventional stress power... 

In this paper, an atomistic–continuum homogenization multiscale method is developed to study the nonlinear behavior of heterogeneous nanomaterials. The atomistic representative volume element (RVE) with vacancy and/or void defects are analyzed by employing the fully atomistic method, in which the nucleation, migration, and elimination of dislocation, as well as the dislocation-vacancy interaction, are captured. The coarse-scale material domain is modeled within the framework of the nonlinear finite element method, and the impression of nanoscale material defects is investigated by upscaling the stress tensor and tangent modulus from the atomistic RVE based on the Hill-Mandel principle. The... 

The accuracy of static neutronic parameters in the nuclear reactors depends upon the determination of group constants of the diffusion equation in the desired geometry. Although several methods have been proposed for calculating these parameters, there is still the need for more reliable methods. In this paper a powerful and innovative method based on Spatial Homogenization and Temperature Variation (SHTV) of physical properties of a WWER-1000 nuclear reactor core for calculating the relative power distribution of Fuel Assemblies (FA) and the hot fuel rod, is presented. The method is based on replacing the heterogeneous lattices of materials with different properties by an equivalent... 

The microstructure of a transient liquid phase (TLP) bonded nickel base superalloy using B-containing filler metal after completion of isothermal solidification can usually be described by a eutectic-free joint centerline with extensive in-situ boride precipitation in the diffusion affected zone which in turn can affect the joint properties. Therefore, designing a proper post-bond heat treatment is needed to produce a robust joint. This paper addresses the microstructure evolution mechanism during post-bond heat treatment (PBHT) of TLP bonded wrought IN718 nickel base superalloy. PBHT at 1150 °C, which is lower than the solvus temperature of the borides, for 12 h resulted in boride-free... 

In this paper, a multiscale finite element framework is developed based on the first-order homogenization method for fully coupled saturated porous media using an extension of the Hill-Mandel theory in the presence of microdynamic effects. The multiscale method is employed for the consolidation problem of a 2-dimensional saturated soil medium generated from the periodic arrangement of circular particles embedded in a square matrix, which is compared with the direct numerical simulation method. The effects of various issues, including the boundary conditions, size effects, particle arrangements, and the integral domain constraints for the microscale boundary value problem, are numerically... 

This paper presents a bi-directional closed-form analytical solution, in the framework of nonlinear soft composites mechanics, for top-down hyperelastic characterization of brain white matter tissue components, based on the directional homogenized responses of the tissue in the axial and transverse directions. The white matter is considered as a transversely isotropic neo-Hookean composite made of unidirectional distribution of axonal fibers within the extracellular matrix. First, two homogenization formulations are derived for the homogenized axial and transverse shear moduli of the tissue, based on definition of the strain energy density function. Next, the rule of mixtures and... 

This paper presents a numerical multiscale formulation for analysis of the transient heat and fluid flow in deformable heterogeneous porous media. Due to the heterogeneity of the media, the direct numerical simulation of the micro-structures leads to high computational costs. Hence, the multi-scale method can provide an efficient computational procedure. To this end, the first-order computational homogenization is adopted for two-scale simulation of THM problems. The governing equations of the problem contain a stress equilibrium equation, a mass continuity equation and an advection–diffusion equation in a fully coupled manner. Accordingly, the proper virtual power relations are defined as a... 

In this paper, a micromechanical model for connective soft tissues based on the available histological evidences is developed. The proposed model constituents i.e. collagen fibers and ground matrix are considered as hyperelastic materials. The matrix material is assumed to be isotropic Neo-Hookean while the collagen fibers are considered to be transversely isotropic hyperelastic. In order to take into account the effects of tissue structure in lower scales on the macroscopic behavior of tissue, a strain energy density function (SEDF) is developed for collagen fibers based on tissue hierarchical structure. Macroscopic response and properties of tissue are obtained using the numerical... 

We have used a hierarchical multiscale modeling scheme for the analysis of cortical bone considering it as a nanocomposite. This scheme consists of definition of two boundary value problems, one for macroscale, and another for microscale. The coupling between these scales is done by using the homogenization technique. At every material point in which the constitutive model is needed, a microscale boundary value problem is defined using a macroscopic kinematical quantity and solved. Using the described scheme, we have studied elastic properties of cortical bone considering its nanoscale microstructural constituents with various mineral volume fractions. Since the microstructure of bone...