A coupled thermo-chemo-mechanical reduced-order multiscale model for predicting process-induced distortions,residual stresses,and strength

We study residual stresses and part distortion induced by a manufacturing process of a polymer matrix composite and its effect on the component strength. Unlike most of the thermo-chemo-mechanical models in the literature where governing multiphysics equations are directly formulated on the macroscale, we present a multiscale-multiphysics approach. To address the enormous computational complexity involved, a reduced-order homogenization was originally developed for a single physics problem is employed. The proposed reduced-order two-scale thermo-chemo-mechanical model has been validated for predicting part distortion beam strength in three-point bending test. It is shown that while macroscopic stresses are relatively low, and therefore often ignored in practice, stresses at the scale of microconstituents are significant and may have an effect on the overall composite component strength.     

A multiscale model for predicting the viscoelastic properties of asphalt concrete

It is well known that the accurate prediction of long term performance of asphalt concrete pavement requires modeling to account for viscoelasticity within the mastic. However, accounting for viscoelasticity can be costly when the material properties are measured at the scale of asphalt concrete. This is due to the fact that the material testing protocols must be performed recursively for each mixture considered for use in the final design.In this paper, a four level multiscale computational micromechanics methodology is utilized to determine the accuracy of micromechanics versus directly measured viscoelastic properties of asphalt concrete pavement. This is accomplished by first measuring the viscoelastic dynamic modulus of asphalt binder, as well as the elastic properties of the constituents, and this comprised the first scale analysis. In the second scale analysis, the finite element method is utilized to predict the effect of mineral fillers on the dynamic modulus. In the third scale analysis, the finite element method is again utilized to predict the effect of fine aggregates on the dynamic modulus. In the fourth and final scale analysis, the finite element method is utilized to predict the effect of large aggregates on the dynamic modulus of asphalt concrete. This final predicted result is then compared to the experimentally measured dynamic modulus of two different asphalt concretes for various volume fractions of the constituents. Results reveal that the errors in predictions are on the order of 60 %, while the ranking of the mixtures was consistent with experimental results. It should be noted that differences between the “final predicted results” and the experimental results can provide fruitful ground for understanding the effect of interactions not considered in the multiscale approach, most importantly, chemical interactions.     

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.     

A nonlocal multiscale discrete‐continuum model for predicting mechanical behavior of granular materials

A three‐dimensional nonlocal multiscale discrete‐continuum model has been developed for modeling mechanical behavior of granular materials. In the proposed multiscale scheme, we establish an information‐passing coupling between the discrete element method, which explicitly replicates granular motion of individual particles, and a finite element continuum model, which captures nonlocal overall responses of the granular assemblies. The resulting multiscale discrete‐continuum coupling method retains the simplicity and efficiency of a continuum‐based finite element model, while circumventing mesh pathology in the post‐bifurcation regime by means of staggered nonlocal operator. We demonstrate that the multiscale coupling scheme is able to capture the plastic dilatancy and pressure‐sensitive frictional responses commonly observed inside dilatant shear bands, without employing a phenomenological plasticity model at a macroscopic level. In addition, internal variables, such as plastic dilatancy and plastic flow direction, are now inferred directly from granular physics, without introducing unnecessary empirical relations and phenomenology. The simple shear and the biaxial compression tests are used to analyze the onset and evolution of shear bands in granular materials and sensitivity to mesh density. The robustness and the accuracy of the proposed multiscale model are verified in comparisons with single‐scale benchmark discrete element method simulations. Copyright © 2015 John Wiley & Sons, Ltd.     

Modeling failure of heterogeneous viscoelastic solids under dynamic/impact loading due to multiple evolving cracks using a two-way coupled multiscale model

This paper presents a model for predicting damage evolution in heterogeneous viscoelastic solids under dynamic/impact loading. Some theoretical developments associated with the model have been previously reported. These are reviewed briefly, with the main focus of this paper on new developments and applications. A two-way coupled multiscale approach is employed and damage is considered in the form of multiple cracks evolving in the local (micro) scale. The objective of such a model is to develop the ability to consider energy dissipation due to both bulk dissipation and the development of multiple cracks occurring on multiple length and time scales. While predictions of these events may seem extraordinarily costly and complex, there are multiple structural applications where effective models would save considerable expense. In some applications, such as protective devices, viscoelastic materials may be preferred because of the considerable amount of energy dissipated in the bulk as well as in the fracture process. In such applications, experimentally based design methodologies are extremely costly, therefore suggesting the need for improved models. In this paper, the authors focus on the application of the newly developed multiscale model to the solution of some example problems involving dynamic and impact loading of viscoelastic heterogeneous materials with growing cracks at the local scale.     

A micromechanics based multiscale model for nonlinear composites

A micromechanics model for fiber-reinforced composites that can be used at the subscale in a multiscale computational framework is established to predict the effective nonlinear composite response. Using a fiber–matrix concentric cylinder model as the basic repeat unit to represent the composite, micromechanics is used to relate the applied composite strains to the fiber and matrix strains by a six by six transformation matrix. The resolved spatial variations of the matrix fields are found to be in good agreement with corresponding finite element analysis results. The evolution of the composite nonlinear response is assumed to be governed by two scalar, strain-based variables that are related to the extreme value of an appropriately defined matrix equivalent strain, and the matrix secant moduli are used to compute the composite secant moduli for nonlinear analysis. The results from the micromechanics model are compared well with a full finite element analysis. The predictive capability of the proposed model is illustrated by two distinct fiber-reinforced material systems, carbon and glass, for the fiber volume fraction varying from 50 to 70 %. Since fully analytical solutions are utilized for the micromechanical analysis, the proposed method offers a distinct computational advantage in a multiscale analysis and is therefore suitable for large-scale progressive damage and failure analyses of composite material structures.     

A multiscale model of thrombus development

A two-dimensional multiscale model is introduced for studying formation of a thrombus (clot) in a blood vessel. It involves components for modelling viscous, incompressible blood plasma; non-activated and activated platelets; blood cells; activating chemicals; fibrinogen; and vessel walls and their interactions. The macroscale dynamics of the blood flow is described by the continuum Navier-Stokes equations. The microscale interactions between the activated platelets, the platelets and fibrinogen and the platelets and vessel wall are described through an extended stochastic discrete cellular Potts model. The model is tested for robustness with respect to fluctuations of basic parameters. Simulation results demonstrate the development of an inhomogeneous internal structure of the thrombus, which is confirmed by the preliminary experimental data. We also make predictions about different stages in thrombus development, which can be tested experimentally and suggest specific experiments. Lastly, we demonstrate that the dependence of the thrombus size on the blood flow rate in simulations is close to the one observed experimentally.     

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.     

A regularized phenomenological multiscale damage model

We present a regularized phenomenological multiscale model where elastic properties are computed using direct homogenization and subsequently evolved using a simple three‐parameter orthotropic continuum damage model. The salient feature of the model is a unified regularization framework based on the concept of effective softening strain. The unified regularization scheme has been employed in the context of constitutive law rescaling and the staggered nonlocal approach. We show that an element erosion technique for crack propagation when exercised with one of the two regularization schemes (1) possesses a characteristic length, (2) is consistent with fracture mechanics approach, and (3) does not suffer from pathological mesh sensitivity. Copyright © 2014 John Wiley & Sons, Ltd.     

A staggered nonlocal multiscale model for a heterogeneous medium

A staggered nonlocal multiscale model for a heterogeneous medium is developed and validated. The model is termed as staggered nonlocal in the sense that it employs current information for the point under consideration and past information from its local neighborhood. For heterogeneous materials, the concept of phase nonlocality is introduced by which nonlocal phase eigenstrains are computed using different nonlocal phase kernels. The staggered nonlocal multiscale model has been found to be insensitive to finite element mesh size and load increment size. Furthermore, the computational overhead in dealing with nonlocal information is mitigated by superior convergence of the Newton method. Copyright © 2012 John Wiley & Sons, Ltd.     

A multiscale finite element method for modeling fully coupled thermomechanical problems in solids

This article proposes a two‐scale formulation of fully coupled continuum thermomechanics using the finite element method at both scales. A monolithic approach is adopted in the solution of the momentum and energy equations. An efficient implementation of the resulting algorithm is derived that is suitable for multicore processing. The proposed method is applied with success to a strongly coupled problem involving shape‐memory alloys.Copyright © 2012 John Wiley & Sons, Ltd.     

A multiscale theoretical model for fluid flow in cellular biological media

An integrated methodology is developed for the theoretical analysis of momentum transfer in cellular biological media, such as biofilms and tissues. First, the method of local spatial averaging via a weight function is used to establish the equations that describe momentum transfer at the cellular biological medium scale, starting with a continuum-based formulation of the process at finer spatial scales. The constitutive behavior of each constituent phase is postulated at the polymer- or cell-scale and, through the averaging procedure, appropriate constitutive relations are developed for the upscaled stress tensors and the fluid–structure interaction forces. Further, closure problems are developed for the theoretical calculation of the effective material properties that appear in the constitutive relations. The developed closure problem for the static hydraulic permeability tensor is solved using a finite element method in the context of a periodic spherocylinder-in-cell model, which accounts for salient geometric features of microbial aggregates and biofilms at the cell-scale. The degree of structural anisotropy resulting from the shape, orientation, and spatial arrangement of biological cells (from stack formation to nematic alignment), is examined and shown to affect strongly the permeability tensor. Very good agreement is observed with results from previous theoretical studies for sphere packings and experimental data for the hydraulic permeability of mycelial cakes.     

A heterarchical multiscale model for granular materials with evolving grainsize distribution

Naturally occurring granular flows, such as landslides, debris flows and avalanches typically have size ratios of up to \(10^{6}\) between the smallest and largest constituent particles. For the purposes of modelling, however, it is generally assumed that a single representative size can adequately describe the grains. Polydisperse flows are not described more completely primarily because of two reasons: The first is a lack of understanding of the physical mechanisms which affect polydisperse flows. The second is a lack of models with which to describe such systems. Here, we present a heterarchical multiscale model which accounts for both the microstructural evolution within representative elementary volumes, and also the associated changes in bulk flow properties. Three key mechanisms are addressed; segregation, comminution and mixing. Granular segregation is an important mechanism for industrial processes aiming at mixing grains. Additionally, it plays a pivotal role in determining the kinematics of geophysical flows. Because of segregation, the grainsize distribution in a granular medium varies in space and time during flow. Additional complications arise from the presence of comminution, where new particles are created, potentially enhancing segregation. This has a feedback on the comminution process, as particles change their local neighbourhood. Simultaneously, particles are generally undergoing remixing, further complicating the segregation and comminution processes. The interaction between these mechanisms is explored using a stochastic lattice model with three rules: one for each of segregation, comminution and mixing. The interplay between these rules creates complex patterns, as seen in segregating systems, and depth dependent log-normal grading curves, which have been observed in avalanche runout.     

Integrating a micromechanical model for multiscale analyses

The Chang‐Hicher micromechanical model based on a static hypothesis, not unlike other models developed separately at around the same epoch, has proved its efficiency in predicting soil behaviour. For solving boundary value problems, the model has now integrated stress‐strain relationships by considering both the micro and macro levels. The first step was to solve the linearized mixed control constraints by the introduction of a predictor–corrector scheme and then to implement the micro–macro relationships through an iterative procedure. Two return mapping schemes, consisting of the closest‐point projection method and the cutting plane algorithm, were subsequently integrated into the interparticle force‐displacement relations. Both algorithms have proved to be efficient in studies devoted to elementary tests and boundary value problems. Closest‐point projection method compared with cutting plane algorithm, however, has the advantage of being more intensive cost efficient and just as accurate in the computational task of integrating the local laws into the micromechanical model. The results obtained demonstrate that the proposed linearized method is capable of performing loadings under stress and strain control. Finally, by applying a finite element analysis with a biaxial test and a square footing, it can be recognized that the Chang‐Hicher micromechanical model performs efficiently in multiscale modelling.     

Variational multiscale enrichment for modeling coupled mechano‐diffusion problems

In this paper, a new multiscale–multiphysics computational methodology is devised for the analysis of coupled diffusion–deformation problems. The proposed methodology is based on the variational multiscale principles. The basic premise of the approach is accurate fine‐scale representation at a small subdomain where it is known a priori that important physical phenomena are likely to occur. The response within the remainder of the problem domain is idealized on the basis of coarse‐scale representation. We apply this idea to evaluate a coupled mechano‐diffusion problem that idealizes the response of titanium structures subjected to a thermo–chemo–mechanical environment. The proposed methodology is used to devise a multiscale model in which the transport of oxygen into titanium is modeled as a diffusion process, whereas the mechanical response is idealized using concentration‐dependent elasticity equations. A coupled solution strategy based on operator split is formulated to evaluate the coupled multiphysics and multiscale problem. Numerical experiments are conducted to assess the accuracy and computational performance of the proposed methodology. Numerical simulations indicate that the variational multiscale enrichment has reasonable accuracy and is computationally efficient in modeling the coupled mechano‐diffusion response. Copyright © 2011 John Wiley & Sons, Ltd.     

Tension-stiffening model for FRP-strenghened RC concrete two-way slabs

The main focus of this paper is to present a tension-stiffening model that is suitable for finite element analysis (FEA) aimed at investigating the effect of FRP strengthening on the tensile behaviour of concrete slabs. Available experimental results of the FRP-strengthened reinforced concrete slabs are used to calibrate the finite element model based on the ultimate load carrying capacity of the two-way slabs. The proposed tension-stiffening model is implemented into the constitutive concrete model defined in a general-purpose finite element code. Reinforced concrete behaviour in tension can signifcantly be changed due to strengthening. An overall increase in the post-peak stiffness based on the tensile stress-strain relationship is observed. A simplified bilinear model is introduced to define the behaviour of the FRP-strengthened concrete in tension. An expression of the fracture energy density is introduced to define the area under the concrete tensile stress-strain relationship. The tensile stress-strain relationship of concrete is referred to as the tension-stiffening model. It is shown numerically that the ultimate load capacity of two-way slab specimens is sensitive to the fracture energy density. Hence, a distinction has to be made between the definitions of the tension-stiffening model of FRP-strengthened and un-strengthened concrete. This distinction is the focus of this paper.

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Résumé L'objectif principal de cet article est de présenter un modèle approprié de raidissement en traction pour l'analyse d'éléments finis (AEF). L'analyse est destinée pour l'étude de l'effet du renforcement en polymère renforcé de fibres (PRF) sur le comportement en traction des dalles en béton armé. Les résultats expérimentaux des dalles renforcées sont employés pour calibrer le modèle d'éléments finis basés sur la capacité ultime des dalles bidirectionnelle. Le modèle de raidissement en traction proposé, est appliqué dans un code général d'élément finis. Le comportement du béton armé renforcé en traction peut être changé d'une manière significative due au renforcement. On observe une augmentation en tension de la rigidité du poteau crête basée sur la relation contrainte-déformation. Un modèle bilinéaire simplifié est présenté pour définir le comportement du béton renforcé de PRF en traction. Une expression de la densité d'énergie de rupture est présentée pour définir l'aire sous la courbe contrainte-déformation. La relation contrainte-déformation du béton en tension est appelée modèle raidissement en traction. On montre numériquement que la capacité de la charge ultime de spécimens bi-directionnels de dalle est affectée par densité d'énergie de rupture. Par conséquent, une distinction doit être faite entre les définitions du modèle raidissement en traction du béton renforcé de PRF est béton non renforcé. Cette distinction est l'objet de cet article.

     

A thermodynamic model for predicting the stability of thaumasite

A model based on the phase rule has been used to predict the hydrate phase mineralogy and phase proportions from the chemical composition of hydrated Portland cement altered by sulfate attack. The eight-component system on which the model is based consists of CaO, SiO₂, Al₂O₃, Fe₂O₃, MgO, CaSO₄, CaCO₃ and H₂O. The phases included in the model are C–S–H, portlandite, ettringite, hydroxy-AFm, monosulfate, monocarbonate, calcite, gypsum, thaumasite, brucite and the pore solution. The model predicts, among other things, that thaumasite, which forms at low temperature, is unstable in the presence of AFm phases, and can only form in systems that would otherwise form gypsum at higher temperatures. The model has been tested experimentally on cement pastes containing 15 and 30 wt.% limestone dust stored at 5 °C, and which were either mixed with different amounts of gypsum and stored in water, or stored in solutions of different MgSO₄ concentrations. The fully hydrated pastes have been analysed by XRD and ²⁹Si CP/MAS NMR, whilst the remaining solution was analysed by ICP. Thaumasite is only found in regions where it has been predicted to form as a stable phase.     

Ballistic performance study of fabric armor based on numerical simulations with multiscale material model

Based on a multiscale model for fabric materials, dynamic simulations of the fabric ballistic performance were implemented. Through parameter research, it was found that the ballistic performance and mechanical behavior of the fabric materials are determined by a combination of factors and conditions rather than by the material properties alone. The material mechanical properties reflect the inherent strength of the fabric; the fabric weaving structure, boundary conditions, material orientation, and projectile shape also play important roles and have a significant influence on the ballistic performance of the fabric. The multiscale material model incorporates not only the membrane‐like properties of the fabric but also the underlying weaving structure, yarn interaction, and yarn composition. The simulations results show good agreement with the experimental data. Various physical phenomena can be observed in the simulations, such as yarn decrimping, material anisotropy, and two types of damage modes. Copyright © 2011 John Wiley & Sons, Ltd.