In this part II , numerical solutions for two problems of Bingham and Herschel-Bulkley confined flows are presented. The solutions obtained validate the methodology proposed in part I of this work.

The commentary looks at two divergent trends which are broadening the definition of climate change to include security and shifting the focus of solutions from production to consumption patterns; both are expected to shape the debate. The security establishment has expressed views on the climate negotiations in, their deliberations in the North Atlantic Treaty Organization on 12 October, 2015. A recent report of the International Energy Agency, 8 October 2015, stresses energy efficiency as a key solution to deal with the causes of the problem. Twenty years after the climate treaty was negotiated in 1992, the climate debate has moved away from the sole focus on atmospheric sciences to the social sciences and also consider strategic concerns and consumption patterns, or politics and lifestyles.

It remains to be seen whether the new regime will adopt a broader sustainable development perspective or continue to view international cooperation and national action narrowly in terms of environmental risk.

Since 2008, our group, in cooperation with colleagues from Germany, Italy, Russia, Poland, Belgium, and Iceland, has been deeply involved in overcoming this challenge, by more deeply studying the X-ray physics underlying Computed Tomography: we developed increasingly mature methods to retrieve, from the grey value-defined voxel characteristics given in CT images, the actually underlying physical property, called X-ray attenuation coefficient. The latter contains information on the chemical composition of the material making up the considered voxel, and combining this information with known chemical characteristics of the material class making up the scanned object, gives access to important microstructural information inside the voxel, such as microporosity, or contents of known chemical substances. The latter then enter, as input values, experimentally validated micromechanical formulations representing the material inside the voxel, so as to reliably determine the voxel’s mechanical properties. Corresponding CT-to-mechanics conversion schemes will be presented in appropriate detail, with applications ranging from various ceramics and polymer-ceramic composites used in tissue engineering, to organs made up of the natural material bone.

Four examples of the model application for analysing transient chemo-hygro-thermo-mechanical processes in porous building materials are presented and discussed. The first example concerns the salt crystallization during drying of a wall made of concrete or ceramic brick, causing degradation of surface layer due to development of crystallization pressure. The second one deals with calcium leaching from a concrete wall due to chemical attack of pure water, exposed to gradients of temperature and pressure. The third one describes cracking of concrete element, caused by development of expanding products of ASR. The fourth example concerns freezing and thawing of a wet concrete wall in variable temperature and relative humidity.

We propose in this work a monolithic formulation where the complete problem is written in a fully Eulerian framework and the phases (fluid, solid,…) are separated by a level set function. The obtained system is solved using stabilized finite element methods. We combine this approximation with time-dependent anisotropic mesh adaptation to ensure accurate capturing of the discontinuities at the interfaces.

Different use of the levelset function ranging from, grain growth models for the evolutions of microstructure or void disclosure induced by forming operations, to the heat treatment of immersed metallic-alloys inside three-dimensional industrial furnaces will be presented. The advantages and the encountered numerical issues as well as the ongoing investigations related to these formulations will be discussed. 

On one hand, we will talk about how to deal in a parallel element-based environment with multiphysics simulations that involve interface coupling, e.g., fluid-structure interaction. Our approach is based on the partition of topological meshes, and ghost element information, in order to define locally the degrees of freedom and the unknowns that must be communicated among processors.

On the other hand, we will discuss how we deal with the resulting multiphysics (non)linear systems. We have two different approaches to the problem: block preconditioning and monolithic solvers. Block preconditioning techniques are interesting in the sense that they allow us to decouple complex multiphysics problems into simpler (probably) one physics simulations. However, in order for block preconditioners to be effective, we must define effective approximation of Schur complement systems, which can be a complicated (and very heuristic) task. We will show how we have implemented complex (recursive) block preconditioning strategies in FEMPAR using abstract definitions of operators, and how this framework has been applied to different multiphysics solvers.

We will also discuss how we can reach sustained scalability up to large core-counts (about 400,000 cores in a BG/Q). Our in-house numerical linear algebra solvers are based on multilevel domain decomposition techniques, and their very efficient practical implementations based on overlapped and asynchronous techniques. We will consider two different approaches, the first one being a combination of block-preconditioning and multilevel domain decomposition, whereas the second one will be a truly monolithic domain decomposition approach.

Many multiphysics simulations are also multiscale, and the use of adaptively refined meshes can reduce even orders of magnitude the computational cost of simulations with respect to uniformly refined meshes. The possibility to reach extremely scalable adaptive multiphysics solvers would open the door to unprecedented simulations of challenging problems that are out of reach nowadays. In this sense, we will show how we are dealing with scalable adaptive solvers in FEMPAR, via a combination of the p4est library for parallel mesh refinement and dynamic load balancing in our element-based framework. Further, we will show how we modify our solvers to deal with nonconforming meshes through interfaces, and the effect of cheap space-filling curve partitions on solver robustness. 

In this presentation, the modelling, simulation and visualization methods are presented for tsunami waves. The stabilized finite element methods are employed for 2D and 3D tsunami simulations based on the shallow water equation, Boussinesq equation and Navier-Stokes equation. In order to realize an efficient tsunami simulation, a combination method using 2D and 3D models is presented. We also propose a visualization system linked to the evacuation simulation using virtual reality technology to understand the power of tsunami and the importance of the evacuation. The present modelling, simulation and visualization methods are shown to be useful tools to realize the high quality computing for large scale tsunami simulation. 

The talk will review recent activities on topology optimization of thermofluidic problems within the TopOpt group. On the parameterization side we discuss pros and cons between element-based (fictitious domain) and boundary tracking topology optimization formulations as well as comparisons between Finite Element and Lattice Boltzman formulations. On the application side we discuss recent applications within systematic design of active and passive (natural convection) cooling devices, heat exchangers, as well as simplified models for fire-protection of structures. 

For the case of fluid-structure interactions (FSI) with or without free-surfaces or for the case of fluid with moving internal interfaces (multi-fluids), it is well known that in the explicit integrations, the time-step to be used in the solution is stable only for time-step smaller than two critical values: the Courant-Friedrichs-Lewy (CFL) number and the Fourier number. The first one is concerning with the convective terms and the second one with the diffusive ones. Both numbers must be less than one to have stable algorithms. For convection dominant problems the condition CFL<1 becomes crucial and limit the use of explicit methods or outdistance its to be efficient. On the other hand, implicit integrations using Eulerian formulations are restricted in the time-step size due to the lack of convergence of the non-linear terms. Both time integrations, explicit or implicit are, in most cases, limited to CFL no much larger than one.

In this lecture we will present a Particle Method to solve coupled problems like FSI or multi-fluid problems that use in all the domain (solid and fluid) a Lagrangian formulation with explicit or implicit time integration without the CFL<1 restriction. This allows large time-steps, independent of the spatial discretization, having equal or better precision that an Eulerian integration.

The proposal will be tested numerically for FSI and multi-fluid flows problems using the Particle Finite Element Method second generation (PFEM2). The results show than this Particle Method is largely more efficient compared as well in accuracy as in computing time with other more standard Eulerian formulations.

Here, we will discuss one such coarse-graining scheme, viz. a fully-nonlocal energy-based QC technique which excels by minimal approximation errors and vanishing force artefacts (a common problem in concurrent scale-coupling methods). Our model is equipped with automatic adaptation techniques to effectively tie atomistic resolution to regions of interest while efficiently coarse-graining the remaining solid. We review both mesh-based and meshless formulations. The former adopts methods from finite elements (using an affine interpolation on a Delaunay triangulation), whereas the latter is based on local maximum-entropy interpolation schemes. In both cases, the result is a computational toolbox for coarse-grained atomistic simulations, whose computational challenges are quite similar to those of molecular dynamics. Finite temperature extensions as well as coarse-graining in time can be incorporated in the presented framework.

We will review the underlying theory and give an overview of the state of the art, followed by a suite of numerical examples demonstrating the benefits and limitations of the nonlocal energy-based QC method. Examples range from nanoindentation and material failure to defect interactions and nanoscale mechanical size effects. 

One of the main drawback of the time integrations using Eulerian formulations are the restricted time-step size that is necessary to use due to the lack of accuracy of the convective terms. Both time integrations, explicit or implicit are, in most cases, limited to small CFL numbers. The cases in which the problem to be solved include free-surfaces or moving internal interfaces, like multi-fluids of fluid-structure interactions this time-step limitation is even worse.

The objective of this presentation is to make an overview of recent examples solved using PFEM-2 and to demonstrate why this method based on particles that move in a Lagrangian frame projecting the results on a fixed mesh is faster than a classical Eulerian Finite Element Method. The authors claim that nowadays, the best way to improve the efficiency of the majority of the CFD problems is the use of a particle-based method like PFEM-2.

The NSCD method has been developed for dealing with large collections of packed bodies and then for simulating the behaviour of granular materials. The Nonlinear Gauss-Seidel (NLGS) algorithm is the generic solver applied to the NSCD formulation. This combination allows simulation of the behaviour of a collection of (especially rigid) bodies involving different and mixed regimes: static, slow dynamics (solid), fast dynamics (fluid). Some examples illustrate the ability of the Moreau’s approach for dealing with a large range of granular problems.

For illustrating the limits of the NSCD approach we focus our attention on dense granular systems that are strongly confined. In order to respect the “elegant rusticity” of the Moreau’s approach we restrict the analysis to a collection of rigid bodies without considering global or local deformations of the grains. Some simple examples highlight the issue of inconsistencies, i.e. some configurations for which no solution exists, as well as indeterminacies, i.e. configurations that lead to non-uniqueness of solutions. We recover here the Painlevé paradox underlined at the beginning of the twentieth century. The non existence of solutions is the more important challenge we have to face. We can first identify the situations leading to this non existence among them the granular systems submitted to moving walls. If such a case may not be avoided another response consists in changing the Coulomb friction law.

The NSCD approach is well adapted to inelastic shocks that predominate in granular media. However J.J. Moreau introduced the concept of formal velocity to account for an elastic restitution. This concept is richer than a restitution coefficient (Newton or Poisson type) involving a binary shock; this permits to deal with multicontact situations without introducing either deformable grains or elastic-plastic contact laws. However this does not allow to reproduce shock propagation as it occurs for instance in the famous Newton’s cradle. Is it then possible to propose an algorithmic solution in the NSCD framework?

In this talk, a framework for computational modelling of discretized single or polycrystal grain structures subjected to thermal-mechanical loading conditions is presented. The model is general for finite deformations with the crystal plasticity model based on dislocation motion and interactions. A parallel finite element implementation is briefly described. Then, applications including predicting microstructure evolution during large deformation processing, fatigue crack initiation, and defect formation during single crystal AlN crystal growth will be presented

Void nucleation, growth and coalescence are important mechanisms responsible for spall and ductile failure. By simulating individual nano-voids and collections of voids under hydrostatic and multiaxial loading, we investigate (i) the nucleation of defects and the associated failure mechanisms at sufficiently-large loads, and (ii) the importance of coarse-grained atomistic techniques to avoid modeling artefacts and size effects in small representative volume elements treated by conventional atomistic methods.

Grain boundaries (GBs) play a central role in polycrystal plasticity through their interactions with lattice defects as well as through GB relaxation mechanisms. We will use the aforementioned coarsegrained atomistic technique to study the behavior of GBs in three-dimensional crystals with a particular focus on the GB strength and the interaction with dislocations. As in the case of void expansion, the QC simulations enable us to consider sample sizes outside the realm of conventional atomistic techniques.

This talk gives an overview of computational techniques that have been developed within the frame of the first author’s doctoral research for solving large dynamic SSI problems. A domain decomposition approach is employed, where finite elements for the structure(s) are coupled to boundary elements for the soil, accounting for the soil’s stratification. A fast boundary element method is developed, resulting in a significant reduction of the required memory and CPU time with respect to traditional formulations. This allows for an increase of the problem size by at least one order of magnitude. Furthermore, innovative algorithms for an efficient coupling of finite and boundary elements are presented, considering three–dimensional as well as two–and–a–half– dimensional formulations. The computational performance of the proposed procedures is assessed and their suitability is illustrated through numerical examples.

The novel techniques are subsequently employed for the solution of challenging problems related to the prediction of railway induced ground vibrations. In particular, the efficiency of a stiff wave barrier for impeding the propagation of Rayleigh waves from the railway track to the surrounding buildings is studied in detail, providing fundamental insight in the underlying physical mechanism. The numerical results are validated by means of a full scale experimental test, confirming the efficacy of the proposed type of barrier.

Accordingly, the discrete dislocation dynamics (DDD) coupling with finite element method (FEM), so a discrete-continuous crystal plastic model (DCM) is developed. Three kinds of plastic deformation mechanisms for the single crystal pillar at submicron scale are investigated. (1) Single arm dislocation source (SAS) controlled plastic flow. It is found that strain hardening is virtually absent due to continuous operation of stable SAS and weak dislocation interactions. When the dislocation density finally reaches stable value, a ratio between the stable SAS length and pillar diameter obeys a constant value. A theoretical model is developed to predict DDD simulation results and experimental data. (2) Confined plasticity in coated micropillars. Based on the simulation results and stochastic distribution of SAS, a theoretical model is established to predict the upper and lower bounds of stress-strain curve in the coated micropillars. (3) Dislocation starvation under low amplitude cyclic loading. This work argued that the dislocation junctions can be gradually destroyed during cyclic deformation, even when the cyclic peak stress is much lower than that required to break them under monotonic deformation. The cumulative irreversible slip is found to be the key factor of leading to junction destruction and promoting dislocation starvation under low amplitude cyclic loadings. Based on this mechanism, a proposed theoretical model successfully reproduces dislocation annihilation behavior observed experimentally for small pillar and dislocation accumulation behavior for large pillar. The predicted critical conditions of dislocation starvation agree well with the experimental data.

In this presentation we intend focusing on some recent works and associated possibilities and difficulties regarding:

• the extension of the method in explicit and implicit-explicit coupling in dynamics
• the coupling between plate and 3D models for bolted and multi-bolted plates
• the treatment of complex non-linear visco-plastic structures 

This work is partially funded by the French National Research Agency as part of project ICARE (ANR-12-MONU-0002-04). 

A major advantage in the first topic is that macroscopic inelastic constitutive models for a variety of composite materials can easily be determined with reference to the material models assumed for periodic microstructures (unit cells), if the small strain assumption is valid. However, NMTs with finite deformation of resins often cause some trouble. That is, even though isotropic multiplicative finite visco-plastic models is originally developed and introduced for NMTs, the formulation of the corresponding anisotropic model for macroscopic analyses is not always possible.

The second topic arises from the method of NPT for composite plates, which enables us to evaluate the relationship between macroscopic resultant stresses and generalized strains. The originally formulated microscopic problem is featured by the in-plane periodic boundary conditions, which properly reproduces all the plate’s deformation modes. If we confine ourselves to linearly elastic material behavior, even the topology optimization of microscopic plate’s cross-sections is successfully conducted to maximize the performance at macro-scale. Nonetheless, we may not meet a macroscopic plate model that can accommodate the NPT results of nonlinear material behavior assumed for the in-plane unit cell.

The third subject of study is related to the method of isogeometric analyses (IGA) for NMT and NPT. Since the treatment of the combination of different materials in IGA models is not trivial especially along with periodicity constraints, the first priority is to clearly specify points at issue in the numerical modeling, or equivalently mesh generation, for IG homogenization analysis (IGHA). The most important issue is how to generate patches for NURBS representation of the geometry of a rectangular parallelepiped unit cell to realize appropriate deformations in consideration of the convex-full property of IGA and the in-plane periodicity. A promising coping technique is proposed and numerically demonstrated. 

Included in this presentation is the design of macroscopic constitutive equations with only few parameters that are obtained from homogenization of polycrystal assemblies. The results are validated at micro and macro scale by means of experiments. These include as well results from microstructural observation as from classical pullout tests. Typical and important industrial applications range from ceramic to ductile materials.

We are developing a novel technique, called Proper Generalized Decomposition (PGD) based on the assumption of a separated form of the unknown fields that has demonstrated its capabilities in dealing with high-dimensional problems overcoming the strong limitations of classical approaches. But the main opportunity given by this technique is that it allows for a completely new approach for addressing standard problems, not necessarily high dimensional. Many challenging problems can be efficiently cast into a multidimensional framework opening new possibilities to solve old and new problems with strategies not envisioned until now. For instance, parameters in a model can be set as additional extra-coordinates of the model. In a PGD framework, the resulting model is solved once for life, in order to obtain a general solution that includes all the solutions for every possible value of the parameters, that is, a sort of “Computational Vademecum”. Under this rationale, optimization of complex problems, uncertainty quantification, simulation-based control and real-time simulation are now at hand, even in highly complex scenarios, by combining an off-line stage in which the general PGD solution, the “vademecum”, is computed, and an on-line phase in which, even on deployed, handheld, platforms such as smartphones or tablets, real-time response is obtained as a result of our queries. 

In this work, an integrated approach for multi-scale topological design of structural linear materials is proposed. The approach features the following properties:

• The “topological derivative” is considered the basic mathematical tool to be used for the purposes of determining the sensitivity of the cost function to material removal. In conjunction with a level-set-based “algorithm” it provides a robust and well-founded setting for material distribution optimization.
• The computational cost associated to the multiscale optimization problem is dramatically reduced by resorting to the concept of the online/offline decomposition of the computations. A “Computational Vademecum” containing the micro-scale solution for the topological optimization problem in a RVE for a large number of discrete macroscopic stress-states, is used for solving that problem by simple consultation.
• Coupling of the optimization problem at both scales is solved by a simple iterative “fixedpoint” scheme, which is found to be robust and convergent.
• The proposed technique is enriched by the concept of “manufacturability”, i.e.: obtaining sub-optimal solutions of the original problems displaying homogeneous material over finite sizes domains at the macrostructure: the “structural components”.

The approach is tested by application to some engineering examples, involving minimum compliance design of material and structure topologies, which show the capabilities of the proposed framework.

The DEM model is calibrated to represent Fontaineblau sand. The resulting granular assembly is incrementally tested starting from an initial oedometric (no lateral deformation) condition. The incremental behavior of the numerical models is studied by performing axisymmetric stress probes of equal magnitude but varying direction. Recent advances to enhance the efficiency of the numerical procedure are adopted. The cascading nature of crushing events complicates stress probe control but damping is effectively used to overcome this problem.

The contribution of grain crushing to the incremental irreversible strain is identified and separately measured. Three components of the incremental strains are distinguished: elastic, plastic-unbreakable and plastic-crushing. Particular focus is placed on the effects of crushing on the direction of plastic flow.

In the context of finite element simulations for fluids, a second problem is the apparition of numerical instabilities. These can be avoided by the use of stabilized formulations, in which the problem is modified to ensure that it has a stable solution. Since stabilization methods typically introduce numerical dissipation, the relation between numerical and physical dissipation plays a crucial role in the accuracy of turbulent flow simulations. We investigate this issue by studying the behavior of stabilized finite element formulations based on the Variational Multiscale framework and on Finite Calculus, analyzing the results they provide for well-known turbulent problems, with the final goal of obtaining a method that both ensures numerical stability and introduces physically correct turbulent dissipation.

Given that, even with the use of turbulence models, turbulent flow problems require significant computational resources, we also focused on programming and parallel implementation aspects of finite element codes, and in particular in ensuring that our solver can perform efficiently on distributed memory architectures and high-performance computing clusters.

Finally, we have developed an adaptive mesh refinement technique to improve the quality of unstructured tetrahedral meshes, again with the goal of enabling the simulation of large turbulent flow problems. This technique combines an error estimator based on Variational Multiscale principles with a simple refinement procedure designed to work in a distributed memory context and we have applied it to the simulation of both turbulent and non-Newtonian flow problems.

In patients with moderate symptomatic or severe asymptomatic carotid stenosis, prior to an endarterectomy it is recommended to do a detailed study, in which the complet set of morphological and hemodynamic parameters are included.

In this work the effect that the location and shape of the stenosis has on the distribution of wall shear stresses and their impact on clinical diagnosis in these cases is analyzed.

Materials and methods

First the model of the area to study is generated and the numerical simulation is done. Then the wall shear stress, the oscilation index and the wall shear stress exposure time are established, and the impact of the results for embolization risk or the growth of arterial plaque because of intimal hiperpasia are analysed. The methodology is applied to three idealized carotids with different localization and geometrical slope of the stenosis.

Results

For the idealized carotids it is obtained that stenosis close to bifurcation present a higher embolization risk that the most distant one and has more risk as more stenosis slope it has. For the clinical case, the results show a high risk of embolization by break located near the atheromatous plaque. As well, it is obtained that the risk the arterial plaque to continue growing is low.

Conclusions

The results show that the location of a moderate stenosis related to carotid bifurcation and their geometry they are factors that aid to complete the diagnosis of lesion.

Viscoplastic fluids are characterized by a minimum shear stress called yield stress. Above this yield stress, the fluid is able to flow. Below this yield stress, the fluid behaves as a quasi-rigid body, with zero strain-rate.

First, the Navier-Stokes equations for incompressible fluid are presented. A review of the viscoplastic rheological models is included, with a detailed description of these models. The regularized viscoplastic models due to Papanastasiou are described. Double viscosity regularized models are proposed as an alternative to the models commonly used.

The discrete model is developed, and the Algebraic SubGrid Scale (ASGS) stabilization method, the Orthogonal Subgrid Scale (OSS) method and the split orthogonal subscales method are introduced.

The methodology proposed in this work provides a computational tool to study confined viscoplastic flows, common in industry.

The developed fluid-structure interaction solver is based, on one side, on an implicit iteration algorithm, communicating pressure forces and displacements of the seals at memory level and, on the other side, on an innovative wetting and drying scheme able to predict the water action on the seals. The stability of the iterative scheme is improved by means of relaxation, and the convergence is accelerated using Aitken’s method.

Several validations against experimental results have been carried out to demonstrate the developed algorithm.