A general method, based on a multi-scale approach, is proposed to derive the effective elastic shear modulus of a rubber with 14\% of carbon black fillers from finite element (FE) and fast Fourier transform (FFT) methods. The complex multi-scale microstructure of such material was generated numerically from a mathematical model of its morphology which was identified from statistical moments out of

In this paper, we view homogenization within the framework of variational multiscale methods. The standard (primal) variational format lends itself naturally to the choice of Dirichlet boundary conditions on the Representative Volume Element (RVE). However, how to impose flux boundary conditions, treated as Neumann conditions in the standard variational format, is less obvious. Therefore, in this paper

In the present work, we have developed a numerical analysis to understand the influence that the Damköhler number has on the consumption of hydrogen sulfide (H2S) that develops on the surface of a biofilm for a mixture composed of methane gas and hydrogen sulfide that circulates laminarly through a thin microchannel. For this multiscale problem, because we are treating two physical regions, the dimensionless

Energy-based Matching Boundary Conditions (MBCs) are developed for both standard and stabilized non-ordinary peridynamics (NOPD) model in one space dimension. For a semi-infinite segment of the linear chain, we construct non-negative energy functions, and propose MBCs that guarantee the energy decay. Stability then holds except for the zero-energy mode. The coefficients in the MBCs are determined by

A statistically homogeneous random bar with the bond-based peridynamic properties of constituents is considered for a static case. For both statistically homogeneous composites and homogeneous remote loading, the effective properties of both the peridynamic composites and locally elastic ones are described by constant tensor of the local effective moduli. However, even for locally elastic composites

In this work, we present a multiscale model to characterize the constitutive behavior of a macroscale fluid accounting for microscale convective, transient, and obstacle effects. Thus, at the macroscale, a generalized continuum flow is considered, and the unsteady incompressible Navier-Stokes equation models the fine scale. From the concept of Representative Volume Element (RVE), we establish a connection

Diffusion in randomly dispersed, spherical, and ellipsoidal composite systems is studied using the random walk simulations. The outcome of the computational analysis is validated by finite element analyses. A Monte Carlo scheme is applied to generate the particulate system. The composite is assumed to have a lower diffusivity in the inclusions and a higher diffusivity in the matrix. The effective diffusion

We study residual stresses and strength induced by a manufacturing process of carbon fiber reinforced semi-crystalline polymer matrix composites and subsequent mechanical loading. Reduced-order homogenization (ROH) approach has been employed to address tremendous computational complexity stemming from analyzing complex thermo-chemo-mechanical processes at multiple scales. The proposed reduced-order

In this paper, we introduce a new computational approach for linking the information of mesoscale solder ball shapes to the macroscale drop test of a printed circuit board. The approach starts with a numerical prediction of mesoscale solder bump profiles using a novel full-implicit Lagrangian particle method to approximate the Navier-Stokes equations and efficiently simulate the incompressible free

The paper is devoted to the diffusion equation, with the Dirac-like periodic potential having different structure in two parts of the domain. The problem can be homogenized in one part of the domain while the standard homogenization does not work in the other. We introduce and test numerically the method of partial homogenization, combining in one multiscale model the homogenized and discrete description

This manuscript studies the mechanical response of amorphous silica based on data mining from molecular dynamics simulations. The temperature- and densification-dependent yield criteria have been established. The proposed modified Drucker-Prager-cap yield criterion adequately captures the temperature effect on the initial yield surface. The main focus of this study has been on understanding the critical

In this paper, we propose to use modified B-splines spanned on several macroelements as a basis for building the multiscale finite element method (MsFEM) trail functions. The main benefit of our approach is that the calculations of a multiscale function are done in one step on the whole support, in contrast to standard MsFEM shape functions that are evaluated coarse element by element and require a

The manuscript describes a multiscale paradigm for predicting post-cracking flexural behavior in ultrahigh performance fiber reinforced concrete (UHPFRC) structures. A comparative study was conducted to simulate the flexural behavior of reinforced UHPFRC beams used in the Malukou Bridge, China. In this study, UHPFRC was modeled as a heterogeneous composite medium made of a matrix and steel fibers using

A formal hierarchy of exact evolution equations is derived for physically relevant space-time averages of state functions of microscopic dislocation dynamics. While such hierarchies are undoubtedly of some value, a primary goal here is to expose the intractable complexity of such systems of nonlinear partial differential equations that, furthermore, remain "non-closed," and therefore subject to phenomenological

The model-free distance-minimizing data-driven computational method has recently become a novel paradigm for solving various mechanics problems. However, the paradigm may suffer from low efficiency since tremendous iterative searches of key data points in the material dataset are needed during the solution process. A fast data-driven solver is therefore proposed here for the accurate and efficient

The present work investigates the thermodynamic inconsistencies in the definition of the compatibility conditions on stress for constant and nonconstant material functions in one-dimensional modeling of shape memory alloys based on the first principles. In this work, simplifications are provided validating inconsistencies in the earlier proposed non-constant material functions used to satisfy compatibility

In the field of nanomedicine, there is a pressing need for predictive, quantitative tools to rationally design and optimize carriers for therapeutic and imaging applications. Current nano/microfabrication technologies allow us to control a large number of parameters, including the size, shape surface properties, and mechanical stiffness. These design parameters affect the biophysical behavior of nanomedicines

Heterogeneous media with several spatial scales are often found in heat transfer applications. For instance, two-phase nanofluids made of nanoparticles immersed in a fluid containing both individual particles and clusters, which exhibit at least three structural scales, have shown improved thermal conductivity over the individual constituents. In this work, a problem for the Fourier heat equation with

Microtomography images allow obtaining fully detailed microstructural descriptions of heterogeneous materials and structures. To evaluate the effects of local gradients induced by the boundary conditions, it might be of interest to perform direct numerical simulations (DNS) of such structures. In this paper, a multiscale method is developed to perform DNS on large, nonperiodic linear heterogeneous

We write to introduce our novel group formed to confront some of the issues raised by the COVID-19 pandemic. Information about the group, which we named "cure COVid for Ever and for All" (RxCOVEA), its dynamic membership (changing regularly), and some of its activities−described in more technical detail for expert perusal and commentary−are available upon request.