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

The present volume is a special issue of selected papers from the 11th edition of a special symposium session, “Multiscale and Multiphysics Modeling for Complex Materials,” organized within the framework of the 9th International Conference on Computational Methods (ICCM2018), held in Rome, Italy, in August 2018, with Professor Trovalusci as chairman. The early focus of the symposium was to bridge the

Masonry structures constitutes a large portion of the built heritage around the world, from the past and still today. Therefore, understanding their structural behavior has a crucial role in preserving the historical characteristics of many of those structures and in addressing the requirements for housing and sustainable development. However, due to its composite and highly non-linear nature, it has

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 are 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.

A multiscale numerical solver called the seamless-domain method (SDM) is used in linear heat conduction analysis of nonperiodic simulated fields. The practical feasibility of the SDM has been verified for use with periodic fields but has not previously been verified for use with nonperiodic fields. In this paper, we illustrate the mathematical framework of the SDM and the associated error factors in

In many emerging applications, the controlled infiltration of specially designed particle-laden fluids into porous media is critical. The added materials are often chosen with the objective to mechanically, electrically, or magnetically functionalize the overall material. Because of the increased viscosity of particle-laden fluids and the pore-dependent permeability of the medium to be infiltrated

A micropolar phase field fracture model is implemented in an open source library FEniCS. This implementation is based on the theoretical study in Suh, H.S., Sun, W., and O’Connor, D. (under review) in which the resultant phase field model exhibits the consistent micropolar size effect in both elastic and damage regions identifiable via inverse problems for micropolar continua. By leveraging the automatic

This special issue of the International Journal for Multiscale Computational Engineering (IJMCE) is dedicated to the minisymposium “Computational Multi-Scale Modelling and Design of New Engineering Materials,” organized within the World Congress on Computational Mechanics, WCCM 2018, in New York. The issue contains seven papers selected from those presented during this symposium. The World Congress

In this paper, we develop a space-time upscaling framework that can be used for many challenging porous media applications without scale separation and high contrast. Our main focus is on nonlinear differential equations with multiscale coefficients. The framework is built on nonlinear nonlocal multi-continuum upscaling concept and significantly extends the results in the proceeding paper. Our approach

We developed a random walk model for solving the diffusion problem arising from composite materials of particulate inclusions with different shapes. Our two-phase material system contains circular or elliptical impermeable inclusions that are randomly embedded in a matrix material. A computational algorithm was developed for random walk simulation of molecules and to estimate the effective diffusion

High-performance concrete (HPC) has a complex mechanical performance due to its multiscale and multiphase com- posite structure. In this review, the various methods of multiscale modeling from different disciplines are summarized and discussed. The conjoint use of multiscale modeling and other methods such as image reconstruction technology for HPC is introduced. The failure mode modeling of HPC using

We present a dimensional-reduction framework based on proper orthogonal decomposition (POD) for the nondissipative explicit dynamic discrete element method (DEM) simulations. Through Galerkin projection, we introduce a finite dimensional space with lower number of degree of freedoms such that the discrete element simulations are not only faster but also free of high-frequency noises. Since this method

ADAPTIVE WAVELET ALGORITHM FOR SOLVING NONLINEAR INITIAL–BOUNDARY VALUE PROBLEMS WITH ERROR CONTROL C. Harnish,1 K. Matouš,1,∗ & D. Livescu2 1Department of Aerospace and Mechanical Engineering, Center for Shock Wave-processing of Advanced Reactive Materials, University of Notre Dame, Notre Dame, Indiana 46556, USA 2Computer and Computational Sciences Division, Los Alamos National Laboratory, Los Alamos

In this paper, we discuss multiscale methods for nonlinear problems. The main idea of these approaches is to use local constraints and solve problems in oversampled regions for constructing macroscopic equations. These techniques are intended for problems without scale separation and high contrast, which often occur in applications. For linear problems, the local solutions with constraints are used

This paper focuses on solving coupled problems of lumped parameter models. Such problems are of interest for the simulation of severe accidents in nuclear reactors~: these coarse-grained models allow for fast calculations for statistical analysis used for risk assessment and solutions of large problems when considering the whole severe accident scenario. However, this modeling approach has several

Complex materials play an essential role in many applications, ranging from turbine blades, car chassis, computer and cell phone cases, battery systems, and stretchable and wearable electronics to biomedical applications. Those materials often operate and must maintain their high performance in harsh environments. The advancement of computational methods at multiple scales opens new possibilities for

In this work, coarse-grained atomistic simulations via the concurrent atomistic-continuum (CAC) method are performed to investigate compressive deformation of nano-/submicron-sized pillars in body-centered cubic (BCC) tungsten. Two models with different surface roughness are considered. All pillars have the same height-to-diameter aspect ratio of 3, with the diameter ranging from 27.35 to 165.34 nm;

Damage of materials inherently involves coupling of deformation and failure mechanisms at multiple length and time scales. This paper develops self-consistent elastic constitutive relations of crystalline materials containing atomistic scale cracks, from observations made in a concurrent multi-scale simulation system coupling atomistic and continuum domain models. The self-consistent constitutive model

This paper reports the unsteady magnetohydrodynamic (MHD) natural convection flow of nanofluid over a permeable stretching sheet with buoyancy effects. Effects of Brownian motion and thermophoresis using a revised model are present. Entropy and heat transfer analysis is performed in the presence of viscous dissipation, Joule heating, and chemical reaction. Transformations techniques are applied to

This manuscript presents a multi-yield surface model to idealize the mechanical behavior of viscoplastic solids subjected to cyclic loading. The multi-yield surface model incorporates the evolution of nonlinear viscoplastic flow through a piece-wise linear hardening approximation. A kinematic hardening law is employed to account for the evolution of backstress with respect to the viscoplastic strain

In this paper, we develop a Bayesian multiscale approach based on a multiscale finite element method. Because of scale disparity in many multiscale applications, computational models can not resolve all scales. Various subgrid models are proposed to represent un-resolved scales. Here, we consider a probabilistic approach for modeling un-resolved scales using the Multiscale Finite Element Method (cf

Sintering is an essential stage of powder metallurgy processes in which solid parts are manufactured from metal or ceramic powder mixtures. Sintering consists in consolidation of loose or weakly bonded powders at elevated temperatures, close to the melting temperature with or without additional pressure. Sintering is a complex process affected by many factors. Modelling can be used to optimize and

This special issue of the International Journal for Multiscale Computational Engineering is dedicated to symposium MS806, “Multiscale Modelling of Materials and Structures,” organized within the ECCOMAS 2016 Congress on Crete Island. The issue contains ten papers selected from those presented during the symposium. The European Congress on Computational Methods in Applied Sciences (ECCOMAS) brings together

We present a new eigendeformation-based reduced order homogenization approach for simulating progressive degradation and failure in brittle composite materials. A new reduced model basis construction strategy is proposed, where the bases are based on numerically calculated “failure paths” within the material microstructure subjected to a pre-selected set of load configurations. The failure paths are

Unlike a conventional first-order continuum model, the material parameters of which can be identified via an inverse problem conducted at material point that exhibits homogeneous deformation, a higher-order continuum model requires information from the derivative of the deformation gradient. This study concerns an integrated experimental-numerical procedure designed to identify material parameters

This special issue of the International Journal of Multiscale Computational Engineering (IJMCE) comprises seven papers and aims to present recent advances and emerging cros s-disciplinary approaches in the broad field of uncertainty modeling and propagation in engineering mechanics w th a focus on multiscale techniques. The papers include developments at both levels of fundament al research and engineering

This special issue of the International Journal for Multiscale Computational Engineering is dedicated to the field of computational poromechanics. We refer to the term poromechanics as a discipline that studies the coupled responses of multiphase materials that contain voids filled with one or multiple types of fluids. Materials fitting this description include many geological materials (e.g., sand

Using the dynamics of information propagation on a network as our illustrative example, we present and discuss a systematic approach to quantifying heterogeneity and its propagation that borrows established tools from Uncertainty Quantification, specifically, the use of Polynomial Chaos. The crucial assumption underlying this mathematical and computational “technology transfer” is that the evolving

Albany is a multiphysics code constructed by assembling a set of reusable, general components. It is an implicit, unstructured grid finite element code that hosts a set of advanced features that are readily combined within a single analysis run. Albany uses template-based generic programming methods to provide extensibility and flexibility; it employs a generic residual evaluation interface to support

Modelling and simulation of manufacturing processes may require the capability to account for localization behavior, often associated with damage/fracture. It may be unwanted localization indicatin ...