Computational multiscale modelling of heterogeneous material layers

A computational homogenization procedure for a material layer that possesses an underlying heterogeneous microstructure is introduced within the framework of finite deformations. The macroscopic material properties of the material layer are obtained from multiscale considerations. At the macro level, the layer is resolved as a cohesive interface situated within a continuum, and its underlying microstructure along the interface is treated as a continuous representative volume element of given height. The scales are linked via homogenization with customized hybrid boundary conditions on this representative volume element, which account for the deformation modes along the interface. A nested numerical solution scheme is adopted to link the macro and micro scales. Numerical examples successfully display the capability of the proposed approach to solve macroscopic boundary value problems with an evaluation of the constitutive properties of the material layer based on its micro-constitution.     

Durability modelling of glass fibre reinforcement in cementitious environment

A main topic of consideration for glass-fibre reinforced cementitious composites is their durability. Recent developments of new cementitious matrices and advances in chemical composition and sizing of glass fibres lead to increased durability of cementitious composites with glass fibre reinforcement. Still, the relative importance of the main degradation mechanisms is not fully understood. A joint experimental program at RWTH-Aachen (Germany) and VUB-Brussels (Belgium) shows that the pH of the matrix has a considerable influence on the durability of the studied composite. Recent investigations on single filaments in high alkalinity solutions and on rovings in concrete show that filaments lose strength mainly due to chemical attack in local weak points of the glass structure. Once this chemical attack becomes diffusion controlled, further corrosion slows down to a considerably lower rate. The aim of these investigations is to finally build a model, allowing prediction of the long-term behaviour of textiles—made of glass filaments—in concrete, which is based on the physico-chemical background of degradation.     

Thermodynamic equilibrium calculations in cementitious systems

This review paper aims at giving an overview of the different applications of thermodynamic equilibrium calculations in cementitious systems. They can help us to understand on a chemical level the consequences of different factors such as cement composition, hydration, leaching, or temperature on the composition and the properties of a hydrated cementitious system. Equilibrium calculations have been used successfully to compute the stable phase assemblages based on the solution composition as well as to model the stable phase assemblage in completely hydrated cements and thus to asses the influence of the chemical composition on the hydrate assemblage. Thermodynamic calculations can also, in combination with a dissolution model, be used to follow the changes during hydration or, in combination with transport models, to calculate the interactions of cementitious systems with the environment. In all these quite different applications, thermodynamic equilibrium calculations have been a valuable addition to experimental studies deepening our understanding of the processes that govern cementitious systems and interpreting experimental observations. It should be carried in mind that precipitation and dissolution processes can be slow so that thermodynamic equilibrium may not be reached; an approach that couples thermodynamics and kinetics would be preferable. However, as many of the kinetic data are not (yet) available, it is important to verify the results of thermodynamic calculations with appropriate experiments. Thermodynamic equilibrium calculations in its different forms have been applied mainly to Portland cement systems. The approach, however, is equally valid for blended systems or for cementitious systems based on supplementary cementitious materials and is expected to further the development of new cementitious materials and blends.     

On multiscale approaches to three-dimensional modelling of morphogenesis.

In this paper we present the foundation of a unified, object-oriented, three-dimensional biomodelling environment, which allows us to integrate multiple submodels at scales from subcellular to those of tissues and organs. Our current implementation combines a modified discrete model from statistical mechanics, the Cellular Potts Model, with a continuum reaction-diffusion model and a state automaton with well-defined conditions for cell differentiation transitions to model genetic regulation. This environment allows us to rapidly and compactly create computational models of a class of complex-developmental phenomena. To illustrate model development, we simulate a simplified version of the formation of the skeletal pattern in a growing embryonic vertebrate limb.     

Computational modelling of multiscale morphologies in polymer-liquid crystal blends

Simulations of material architectures in polymer-liquid crystal blends driven by phase separation-phase ordering-texturing processes are presented. The study shows that mixtures of polymers and liquid crystals result in blend morphologies that organize at several scales. For thermally driven instabilities, morphologies of polymer droplets embedded in a liquid crystal matrix show colloidal crystallinity. Large polymer drops strongly affect the orientation of the matrix, producing textures consisting of defect lattices. This work shows that thermally driven phase separation-phase ordering-texturing processes can result in multiscale materials, with length scales cascading down from droplets to interfaces, and finally to nanoscale defects.     

Analysis of SMA composite laminates using a multiscale modelling technique

The present work deals with the analysis of smart laminates, obtained as stacking sequence of fibre‐reinforced composite laminae and composite shape memory alloy (SMA) layers. The behaviour of composite SMA (CSMA) laminate is studied developing a full micro–macro approach. In fact, a non‐linear 4‐node mixed interpolation of tensorial components (MITC4) laminate finite element, based on the first‐order shear deformation theory, is developed. The SMA layer constitutive relationship is determined solving a non‐linear homogenization problem at each non‐linear iteration of each time step for each integration Gauss point. Some numerical applications are developed in order to investigate the influence of the CSMA on the buckling behaviour of plates and on the transversal displacement control of plates subjected to different loading conditions. Copyright © 2006 John Wiley & Sons, Ltd.     

Micromechanical modelling of strain hardening and tension softening in cementitious composites

This paper will describe a procedure for modelling the complete macroscopic response (including strain hardening and tension softening) of two short fibre reinforced cementitious composites and show how their microstructural parameters influence this response. From a mathematical point of view it is necessary to examine how bridging forces imposed by the fibres alter the opening of multiple cracks in elastic solids under unidirectional tensile loading. The strain hardening is essentially due to elastic bridging forces which are proportional to crack opening displacements. After a certain critical crack opening displacement is reached, some fibres progressively debond from the elastic matrix and thereafter provide a residual bridging force by frictional pull-out, while others continue to provide full bridging. This results in a kind of elasto-plastic bridging law which governs the initial tension softening response of the composite. Besides the usual square-root singularity at crack tips, the elasto-plastic bridging law introduces a logarithmic singularity at the point of discontinuity in the bridging force. These singularities have been analytically isolated, so that only regular functions are subjected to numerical integration. Unbridged multiple crack problems have in the past been solved using double infinite series which have been found to be divergent. In this paper a superposition procedure will be described that eliminates the use of double infinite series and thus the problem of divergence. It is applicable to both unbridged and bridged multiple cracks. The paper will end by showing how the model of multiple bridged cracks can accurately predict the prolonged nonlinear strain hardening and the initial tension softening response of two cementitious composites.     

Evaluation of early age cracking characteristics in cementitious systems

Early age cracking has re-emerged as an important issue in modern concretes, and it has its impact in developing new formulations for high strength and repair. Adequate performance with respect to cracking cannot be properly assessed on the basis of free shrinkage tests. More advanced methodologies need to be developed and applied, to consider in addition to the strains obtained also the stresses and stress relaxation. The present paper presents an overview of the testing techniques and methodologies of early age cracking. It classifies the tests into four categories: ring, plate, longitudinal and substrate restraint and assesses their significance and limitations.     

Opc-fly ash cementitious systems: study of gel binders produced during alkaline hydration

In the present paper, experiments were performed on blended cements containing 30% Portland cement clinker and 70% fly ash. The powdery material was mixed with deionised water for “normal” hydration, and with two different alkaline solutions for “normal” alkaline activation. The mechanical strength developed by this highly blended cement differed significantly depending on the hydrating solution used. XRD, FTIR and ²⁹Si MAS-NMR characterisation studies were conducted to obtain information on the complex structural nature of the hardened matrices, which in all cases consisted of a mixture of amorphous gels (C-S-H + N-A-S-H gel). These highly blended cements are able to comply with the specifications defined in the European Standard EN-197-1:2000.     

Service-based manufacturing systems: modelling and control

In service-based manufacturing systems, functionalities are independently developed as services and a central engine orchestrates their integration. As industrial processes tend to be very large, and performance and productivity are expected to be maximised, there is a constant interest in providing (in-advance) quality guarantees for services interactions, which contrasts with the usual non-automated workflow design. This paper provides an alternative to enhance service orchestration capabilities using supervisory control techniques. Initially, each component (atomic and composite activities) belonging to an orchestration language is modelled as a state-machine. Then, activity models are properly combined and composed, reproducing orchestrated workflows. Finally, supervisory control is used to calculate an optimal version of the orchestrator. Practical implications of handling large state-spaces are discussed and examples are provided.     

Hydration kinetics of high-performance cementitious systems under different curing conditions

Curing plays an essential role in the modern concrete technology, since it has a crucial effect on the development of concrete properties. High-performance cementitious systems are especially sensitive to the applied curing methods because of self-desiccation and high sensitivity to early-age cracking. Thus, it is of particular interest to compare the efficiency of internal curing and traditional curing techniques such as sealing and water ponding. In this study, the efficiency of different types of curing was estimated by means of isothermal calorimetry. Four different water to cement (w/c) ratios in the range of 0.21–0.45 and four types of curing were studied, including sealing, water ponding with different amount of water, internal curing by saturated lightweight aggregate and super-absorbent polymer. The hydration degree was determined using heat of hydration data. Compressive strength of the tested specimens was measured and analyzed. The results indicate that efficiency of different types of curing strongly depends on w/c ratio.     

Finite element modelling of inverse design problems in large deformations anisotropic hyperelasticity

This paper introduces a finite element model for the inverse design of pieces with large displacements in the elastic range. The problem consists in determining the initial shape of the piece, such that it attains the designed shape under the effect of service loads. The model is particularly focused on the design of parts with a markedly anisotropic behavior, like laminated turbine blades. Although the formulation expresses equilibrium on the distorted configuration, it uses a standard constitutive equations library that is expressed as usual for measures attached to the undistorted configuration. In this way, the modifications to a standard finite elements code are limited to the routines for the computation of the finite element internal forces and tangent matrix. Two examples are given, the first one for validation purposes, while the second is an application which has industrial interest for the design of turbine blades. Copyright © 2007 John Wiley & Sons, Ltd.     

Properties of cementitious systems containing silica fume or nonreactive microfillers

The object of this work was to explore the effects of silica fume on the microstructure of hardened paste and of the transition zone between paste and aggregates in concrete. The significance of aggregates as reinforcing fillers and their impact on some properties of the transition zone and bulk paste were resolved. The experimental procedure was based on simultaneous studies of model concretes and paste matrices extracted from fresh model concrete mixes. In addition, continuously graded aggregate concretes were prepared. Three sizes of a nonreactive microfiller (carbon black) and one reactive microfiller (silica fume) were applied. On the basis of microstructural studies and compressive strength tests, it was concluded that the primary effect of silica fume was generated by its physical (microfiller) properties, since the strengthening provided by reactive silica fume was similar to that obtained with nonreactive carbon black of similar size and shape. This effect was more significant from the point of view of the concrete strength enhancement than the chemical (pozzolanic) activity of the silica fume. In concretes containing either silica fume or carbon black, aggregates of high quality could serve as reinforcing filler. This could take place when sufficient densification of the transition zone occurred in the presence of silica fume or carbon black. Significant refinement of pore structure was observed in both types of paste matrices (containing silica fume or carbon black). However, this led to a relatively small influence on the paste strength. Concretes containing reactive silica fume or an inert carbon black microfiller behaved as a composite material, unlike conventional concrete.     

Multiscale modelling of particle debonding in reinforced elastomers subjected to finite deformations

Interfacial damage nucleation and evolution in reinforced elastomers subjected to finite strains is modelled using the mathematical theory of homogenization based on the asymptotic expansion of unknown variables. The microscale is characterized by a periodic unit cell, which contains particles dispersed in a blend and the particle matrix interface is characterized by a cohesive law. A novel numerical framework based on the perturbed Petrov–Galerkin method for the treatment of nearly incompressible behaviour is employed to solve the resulting boundary value problem on the microscale and the deformation path of a macroscale particle is predefined as in the micro‐history recovery procedure. A fully implicit and efficient finite element formulation, including consistent linearization, is presented. The proposed multiscale framework is capable of predicting the non‐homogeneous micro‐fields and damage nucleation and propagation along the particle matrix interface, as well as the macroscopic response and mechanical properties of the damaged continuum. Examples are considered involving simple unit cells in order to illustrate the multiscale algorithm and demonstrate the complexity of the underlying physical processes. Copyright © 2005 John Wiley & Sons, Ltd.     

A coupled FEM/DEM approach for hierarchical multiscale modelling of granular media

A hierarchical multiscale framework is proposed to model the mechanical behaviour of granular media. The framework employs a rigorous hierarchical coupling between the FEM and the discrete element method (DEM). To solve a BVP, the FEM is used to discretise the macroscopic geometric domain into an FEM mesh. A DEM assembly with memory of its loading history is embedded at each Gauss integration point of the mesh to serve as the representative volume element (RVE). The DEM assembly receives the global deformation at its Gauss point from the FEM as input boundary conditions and is solved to derive the required constitutive relation at the specific material point to advance the FEM computation. The DEM computation employs simple physically based contact laws in conjunction with Coulomb's friction for interparticle contacts to capture the loading‐history dependence and highly nonlinear dissipative response of a granular material. The hierarchical scheme helps to avoid the phenomenological assumptions on constitutive relation in conventional continuum modelling and retains the computational efficiency of FEM in solving large‐scale BVPs. The hierarchical structure also makes it ideal for distributed parallel computing to fully unleash its predictive power. Importantly, the framework offers rich information on the particle level with direct link to the macroscopic material response, which helps to shed lights on cross‐scale understanding of granular media. The developed framework is first benchmarked by a simulation of single‐element drained test and is then applied to the predictions of strain localisation for sand subject to monotonic biaxial compression, as well as the liquefaction and cyclic mobility of sand in cyclic simple shear tests. It is demonstrated that the proposed method may reproduce interesting experimental observations that are otherwise difficult to be captured by conventional FEM or pure DEM simulations, such as the inception of shear band under smooth symmetric boundary conditions, non‐coaxial granular response, large dilation and rotation at the edges of shear band and critical state reached within the shear band. Copyright © 2014 John Wiley & Sons, Ltd.     

Finite element modelling of wooden structures at large deformations and brittle failure prediction

This paper presents a constitutive wood model that accounts for both hardening associated with material densification at large compressive deformations and brittle failure modes. The model is adapted from previous work by the authors and has been modified to deal with wood behaviours. The main novelty of the model is the coupling between the anisotropic plasticity and the ductile densification. The model developed is successfully implemented in the commercial ABAQUS software. Validation was made for uniaxial compressive loadings and an application on a three-points bending test. The results obtained, for the uniaxial compressive loadings, demonstrate the capability of the model to simulate the wood behaviour at large compressive deformations and show clearly the effect of the densification on the plastic behaviour. The result obtained for the three-points bending test shows a good implementation of the brittle failure criterion and demonstrates the suitability of the developed model to analyse and design wooden structures.     

Durability of proprietary cementitious materials for use in wastewater transport systems

Several methods and materials, such as high performance coatings, fiber glass reinforced linings, special mortars, brick or ceramic linings, etc., are used to protect concrete from sulfuric acid attack in a sewage environment. Two proprietary high alumina cementitious lining materials, CC and SC, are recent additions to the list of protective materials used in the Arabian Gulf. This paper documents the findings of a laboratory study under accelerated conditions as well as a two-year field study of CC and SC in a wastewater lift station in Jubail, Saudi Arabia. In the laboratory investigations, 50 mm cube mortar specimens prepared using: (1) SC, (2) CC, (3) Type I+8% silica fume cement, (4) Type I+20% fly ash cement and (5) Type I cement were exposed to 2% sulfuric acid for 150 days. The laboratory specimens were tested for weight reduction, compressive strength, sulfate content, and alkalinity. In the field, the walls and ceiling of a wastewater manhole were coated using the proprietary lining materials, SC and CC, and were exposed to a normal sewage service environment. Performance of the liner materials was monitored for sulfate content and alkalinity after 6, 12 and 24 months of exposure. The analysis and evaluation test data generated from the accelerated laboratory study and the field study, which lasted for 24 months, showed that SC performed better than other materials tested in this investigation.     

A multiscale and multiphysics numerical framework for modelling of hygrothermal ageing in laminated composites

In this work, a numerical framework for modelling of hygrothermal ageing in laminated composites is proposed. The model consists of a macroscopic diffusion analysis based on Fick's second law coupled with a multiscale FE² stress analysis in order to take microscopic degradation mechanisms into account. Macroscopic material points are modelled with a representative volume element with random fibre distribution. The resin is modelled as elasto‐plastic with damage, and cohesive elements are included at the fibre/matrix interfaces. The model formulations and the calibration of the epoxy model using experimental results are presented in detail. A study into the representative volume element size is conducted, and the framework is demonstrated by simulating the ageing process of a unidirectional specimen immersed in water. The influence of transient swelling stresses on microscopic failure is investigated, and failure envelopes of dry and saturated micromodels are compared. Copyright © 2017 John Wiley & Sons, Ltd.