A Novel Framework for Building Materials Knowledge Systems

This paper presents a novel mathematical framework for building a comprehensive materials knowledge system (MKS) to extract, store and recall hierarchical structure-property-processing linkages for a broad range of material systems. This new framework relies heavily on the use of computationally efficient FFT (Fast Fourier Transforms)-based algorithms for data-mining local structure-response-structure evolution linkages from large numerical datasets produced by established modelling strategies for microscale phenomena. Another salient feature of this new framework is that it facilitates flow of high fidelity information in both directions between the constituent length scales, and thereby offers a new strategy for concurrent multi-scale modelling of materials phenomena. The viability of this new approach is demonstrated in this paper with two selected case studies: (i) rigid-plastic deformation of a two-phase composite material, and (ii) spinodal decomposition of a binary alloy.     

On a multiscale strategy and its optimization for the simulation of combined delamination and buckling

This paper investigates a computational strategy for studying the interactions between multiple through‐the‐width delaminations and global or local buckling in composite laminates taking into account possible contact between the delaminated surfaces. To achieve an accurate prediction of the quasi‐static response, a very refined discretization of the structure is required, leading to the resolution of very large and highly nonlinear numerical problems. In this paper, a nonlinear finite element formulation along with a parallel iterative scheme based on a multiscale domain decomposition is used for the computation of three‐dimensional mesoscale models. Previous works by the authors already dealt with the simulation of multiscale delamination assuming small perturbations. This paper presents the formulation used to include geometric nonlinearities into this existing multiscale framework and discusses the adaptations that need to be made to the iterative process to ensure the rapid convergence and the scalability of the method in the presence of buckling and delamination. These various adaptations are illustrated by simulations involving large numbers of DOFs. Copyright © 2012 John Wiley & Sons, Ltd.     

Egg protein derived ultralightweight hybrid monolithic aerogel for water purification

The integration of 2D-graphitic carbon (G) with 1D-carbon nanofiber (CF) allows for the unique properties of 2D graphitic carbon to be combined with the low densities, mechanical performance, and high surface area required for applications across the energy and sustainability landscape. Through a combination of experiments and numerical modeling, we demonstrate the transformation of standard egg-white (EW) proteins into an ultralightweight G-CF aerogel with a multiscale structure. The resulting covalently-bonded hierarchical structure, derived from the complex underlying protein configuration, exhibits a density that is two orders of magnitude lower than existing state-of-the-art materials. We apply this material to the challenges of desalination and water purification, notably demonstrating that the G-CF aerogel significantly improves upon existing materials, capturing 98.2% of ionic impurities and 99.9% of nano/microplastic contamination from seawater.     

Discrete element modeling and experimental investigation of hot pressing of intermetallic NiAl powder

This paper presents the numerical and experimental analysis of hot pressing of NiAl powder with an emphasis on the best possible representation of its main stages: initial powder compaction and pressure-assisted sintering. The numerical study has been performed within the discrete element framework. In the paper, an original viscoelastic model of hot pressing has been used. In order to ensure that the applied values of material parameters in numerical simulations are appropriate, the reference literature has been reviewed. It produced the relations and equations to estimate the values of all required sintering material parameters of the considered viscoelastic model. Numerical simulations have employed the geometrical model of the initial dense specimen generated by a special algorithm which uses the real grain distribution of powder. The numerical model has been calibrated and validated through simulations of the real process of hot pressing of intermetallic NiAl material. The kinetics of compaction, sintering and cooling stage indicated by the evolution of density, shrinkage and densification rate have been studied. The comparison of numerical and experimental results has shown a good performance of the developed numerical model.     

Immersed stress method for fluid–structure interaction using anisotropic mesh adaptation

This paper presents advancements toward a monolithic solution procedure and anisotropic mesh adaptation for the numerical solution of fluid–structure interaction with complex geometry. First, a new stabilized three‐field stress, velocity, and pressure finite element formulation is presented for modeling the interaction between the fluid (laminar or turbulent) and the rigid body. The presence of the structure will be taken into account by means of an extra stress in the Navier–Stokes equations. The system is solved using a finite element variational multiscale method. We combine this method with anisotropic mesh adaptation to ensure an accurate capturing of the discontinuities at the fluid–solid interface. We assess the behavior and accuracy of the proposed formulation in the simulation of 2D and 3D time‐dependent numerical examples such as the flow past a circular cylinder and turbulent flows behind an immersed helicopter in a forward flight. Copyright © 2013 John Wiley & Sons, Ltd.     

Predictive multiscale theory for design of heterogeneous materials

A general multiscale theory for modeling heterogeneous materials is derived via a nested domain based virtual power decomposition. Three variations on the theory are proposed; a concurrent approach, a simplified hierarchical approach and a statistical power equivalence approach. Deformation at each scale of analysis is solved either (a) by direct numerical simulation (DNS) of the microstructure or (b) by higher order homogenization of the microstructure. If the latter approach is chosen, a set of multiscale homogenized constitutive relations must be derived. This is demonstrated using a computational cell modeling technique for a four scale metal alloy. In each variation of the theory, a transfer of information occurs between the scales giving a coupled formulation. The concurrent approach achieves a more comprehensive coupling than the hierarchical approach, making it more accurate for dynamic fast time scale simulations. The power equivalence approach is strongly coupled and is useful for performing larger scale simulations as the expensive multiple scale DNS boundary value problems are replaced with statistical higher order continua. Furthermore, these continua may be solved on a single spatial discretisation using an extended finite element framework, making the theory applicable within existing high performance computing codes. Submitted to a Special Issue of Computational Mechanics in Honor of Professor Ladeveze’s 60th Birthday.     

A framework for implementation of RVE‐based multiscale models in computational homogenization using isogeometric analysis

This study presents an isogeometric framework for incorporating representative volume element–based multiscale models into computational homogenization. First‐order finite deformation homogenization theory is derived within the framework of the method of multiscale virtual power, and Lagrange multipliers are used to illustrate the effects of considering different kinematical constraints. Using a Lagrange multiplier approach in the numerical implementation of the discrete system naturally leads to a consolidated treatment of the commonly employed representative volume element boundary conditions. Implementation of finite deformation computational strain‐driven, stress‐driven, and mixed homogenization is detailed in the context of isogeometric analysis (IGA), and performance is compared to standard finite element analysis. As finite deformations are considered, a numerical multiscale stability analysis procedure is also detailed for use with IGA. Unique implementation aspects that arise when computational homogenization is performed using IGA are discussed, and the developed framework is applied to a complex curved microstructure representing an architectured material.     

Micromechanical modeling of crack-aggregate interaction in concrete materials

A new condition for crack penetration into the aggregate phase in concrete materials is developed based on numerical simulations. The numerical simulation utilizes a newly developed micromechanical model which considers the concrete internal structure as a three-phase material, viz. matrix, aggregate and interfaces between them. The micromechanical model is capable of capturing the entire load-deformation response of a concrete specimen under monotonic loading including softening. The new condition for crack penetration is developed based on a simple specimen configuration where a crack is driven towards an aggregate particle. Results from numerical simulations are implemented to relate the relative properties of both aggregate and matrix phases (represented by the characteristic length ratio) to their tensile strength ratio. It is shown that the tensile strength ratio between the aggregate and the matrix plays the dominant role in determining the penetration condition. Predictions based on this condition agree with direct tensile simulations using different specimen configuration.     

Setting manufacturing strategy for a company's international manufacturing network

Manufacturing strategy is a plan for moving a company from where it is to where it wants to be. Determining the best manufacturing strategy is not easy because of the wide range of choices and constraints a company faces. Manufacturing strategy frameworks or models are helpful because they identify the objects that comprise manufacturing strategy and organise these objects into a structure that enables a company to understand and use the objects to develop strategy. This paper examines a company's international manufacturing network. It identifies and examines six manufacturing strategy objects (generic international strategies, manufacturing networks, network manufacturing outputs, network levers, network capability, and factory types), linkages between objects, and the manufacturing strategy framework that follows from these objects and linkages. Then the paper applies the framework to the manufacturing networks of three companies in the global steel industry: Arcelor (Luxembourg), Mittal (India), and Dofasco (Canada).     

Residual-based variational multiscale simulation of free surface flows

In this work we apply the residual-based variational multiscale method (RB-VMS) to the volume-of-fluid (VOF) formulation of free-surface flows. Using this technique we are able to solve such problems in a Large Eddy Simulation framework. This is a natural extension of our Navier–Stokes solver, which uses the RB-VMS finite element formulation, edge-based data structures, adaptive time step control, inexact Newton solvers and supports several parallel programming paradigms. The VOF interface capturing variable is advected using the computed coarse and fine scales velocity field. Thus, the RB-VMS technique can be readily applied to the free-surface solver with minor modifications on the implementation. We apply this technique to the solution of two problems where available data indicate complex free-surface behavior. Results are compared with numerical and experimental data and show that the present formulation can achieve good accuracy with minor impacts on computational efficiency.     

A hybrid variationally consistent homogenization approach based on Ritz's method

Multiscale approaches based on homogenization theory provide a suitable framework to incorporate information associated with a small‐scale (microscale) problem into the considered large‐scale (macroscopic) problem. In this connection, the present paper proposes a novel computationally efficient hybrid homogenization method. Its backbone is a variationally consistent FE² approach in which every aspect is governed by energy minimization. In particular, scale bridging is realized by the canonical principle of energy equivalence. As a direct implementation of the aforementioned variationally consistent FE² approach is numerically extensive, an efficient approximation based on Ritz's method is advocated. By doing so, the material parameters defining an effective macroscopic material model capturing the underlying microstructure can be efficiently computed. Furthermore, the variational scale bridging principle provides some guidance to choose a suitable family of macroscopic material models. Comparisons between the results predicted by the novel hybrid homogenization method and full field finite element simulations show that the novel method is indeed very promising for multiscale analyses.Copyright © 2013 John Wiley & Sons, Ltd.     

Simulation of single mode Rayleigh–Taylor instability by SPH method

A smoothed particle hydrodynamics (SPH) solution to the Rayleigh–Taylor instability (RTI) problem in an incompressible viscous two-phase immiscible fluid with surface tension is presented. The present model is validated by solving Laplace’s law, and square bubble deformation without surface tension whereby it is shown that the implemented SPH discretization does not produce any artificial surface tension. To further validate the numerical model for the RTI problem, results are quantitatively compared with analytical solutions in a linear regime. It is found that the SPH method slightly overestimates the border of instability. The long time evolution of simulations is presented for investigating changes in the topology of rising bubbles and falling spike in RTI, and the computed Froude numbers are compared with previous works. It is shown that the numerical algorithm used in this work is capable of capturing the interface evolution and growth rate in RTI accurately.     

A multiscale overlapped coupling formulation for large-deformation strain localization

We generalize the multiscale overlapped domain framework to couple multiple rate-independent standard dissipative material models in the finite deformation regime across different length scales. We show that a fully coupled multiscale incremental boundary-value problem can be recast as the stationary point that optimizes the partitioned incremental work of a three-field energy functional. We also establish inf-sup tests to examine the numerical stability issues that arise from enforcing weak compatibility in the three-field formulation. We also devise a new block solver for the domain coupling problem and demonstrate the performance of the formulation with one-dimensional numerical examples. These simulations indicate that it is sufficient to introduce a localization limiter in a confined region of interest to regularize the partial differential equation if loss of ellipticity occurs.     

三维离散元与壳体有限元耦合的时空多尺度方法

壳体结构的局部失效及其对整体结构稳定性影响涉及到跨宏细观多尺度力学问题。该文推导出元/网格动量传递的多尺度算法,建立了三维离散元与壳体有限元耦合的时空多尺度数值计算方法。通过激光辐照下充内压圆柱壳局部失效算例的数值模拟,验证该多尺度方法能够完善地并行实现时间多尺度与空间多尺度计算,不仅能够准确模拟壳体结构局部细观非均匀演化及其对整体结构的影响,而且计算时间很少,有效地发挥了时空多尺度模拟高效率优势。     

Fully coupled hydromechanical multiscale model with microdynamic effects

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 investigated to illustrate the performance of a representative volume element in the proposed computational homogenization method of fully coupled saturated porous media. This study is aimed to clarify the effect of scale separation and size dependence, and to introduce characteristics of a proper representative volume element in multiscale modeling of saturated porous media.     

Multiscale space–time fluid–structure interaction techniques

We present the multiscale space–time techniques we have developed for fluid–structure interaction (FSI) computations. Some of these techniques are multiscale in the way the time integration is performed (i.e. temporally multiscale), some are multiscale in the way the spatial discretization is done (i.e. spatially multiscale), and some are in the context of the sequentially-coupled FSI (SCFSI) techniques developed by the Team for Advanced Flow Simulation and Modeling (T \bigstar AFSM){({\rm T} \bigstar {\rm AFSM})}. In the multiscale SCFSI technique, the FSI computational effort is reduced at the stage we do not need it and the accuracy of the fluid mechanics (or structural mechanics) computation is increased at the stage we need accurate, detailed flow (or structure) computation. As ways of increasing the computational accuracy when or where needed, and beyond just increasing the mesh refinement or decreasing the time-step size, we propose switching to more accurate versions of the Deforming-Spatial-Domain/Stabilized Space–Time (DSD/SST) formulation, using more polynomial power for the basis functions of the spatial discretization or time integration, and using an advanced turbulence model. Specifically, for more polynomial power in time integration, we propose to use NURBS, and as an advanced turbulence model to be used with the DSD/SST formulation, we introduce a space–time version of the residual-based variational multiscale method. We present a number of test computations showing the performance of the multiscale space–time techniques we are proposing. We also present a stability and accuracy analysis for the higher-accuracy versions of the DSD/SST formulation.     

Micropolar hyper‐elastoplasticity: constitutive model,consistent linearization,and simulation of 3D scale effects

A computational model for micropolar hyperelastic‐based finite elastoplasticity that incorporates isotropic hardening is developed. The basic concepts of the non‐linear micropolar kinematic framework are reviewed, and a thermodynamically consistent constitutive model that features Neo‐Hooke‐type elasticity and generalized von Mises plasticity is described. The integration of the constitutive initial value problem is carried out by means of an elastic‐predictor/plastic‐corrector algorithm, which retains plastic incompressibility. The solution procedure is developed carefully and described in detail. The consistent material tangent is derived. The micropolar constitutive model is implemented in an implicit finite element framework. The numerical example of a notched cylindrical bar subjected to large axial displacements and large twist angles is presented. The results of the finite element simulations demonstrate (i) that the methodology is capable of capturing the size effect in three‐dimensional elastoplastic solids in the finite strain regime, (ii) that the formulation possesses a regularizing effect in the presence of strain localization, and (iii) that asymptotically quadratic convergence rates of the Newton–Raphson procedure are achieved. Throughout this paper, effort is made to present the developments as a direct extension of standard finite deformation computational plasticity. Copyright © 2012 John Wiley & Sons, Ltd.