Viscoelastic and Viscoplastic Materials

This book introduces numerous selected advanced topics in viscoelastic and viscoplastic materials. The book effectively blends theoretical, numerical, modeling and experimental aspects of viscoelastic and viscoplastic materials that are usually encountered in many research areas such as chemical, mechanical and petroleum engineering. The book consists of 14 chapters that can serve as an important reference for researchers and engineers working in the field of viscoelastic and viscoplastic materials

Identification of material properties and phase distribution of heterogeneous materials through data-driven computational methods : towards an enhanced constitutive space

Tesi en modalitat de cotutela: Universitat Politècnica de Catalunya i École Centrale de NantesIdentifying the constitutive relations of materials is an essential task to understand their behavior. Classical methods like testing can be effective in understanding these relationships, but introducing models can lead to biased formulations and errors. Furthermore, not all constitutive relations can be determined directly by mathematical expressions or there might be parameters that we cannot obtain easily through common techniques. Data-Driven Identification (DDI), developed by Leygue et al. (2018), is an algorithm in which the constitutive relation of elastic materials is defined by a database of material points that need to be computed based on measured strain fields, applied forces and known geometry of tested samples of the material. The algorithm simultaneously estimates the corresponding values of the stress fields that emerge due to the deformations measured in the samples. In this thesis, we focus on departing from elasticity to cover more complex material behaviors with the DDI algorithm. In a first step, the method is applied to heterogeneous samples, where a post-process is performed with Correspondence Analysis to separate the different phases in a sample and identify their sepa-rated behavior. Then, DDI was also applied to linear viscoelastic materials, where an extended phase-space approach is used to account for the time dependence of the behavior. Finally, different variations of the algorithm are considered by combining DDI with different statistical techniques such as the Principal Component Analysis, in a search for speed and accuracy of the predictions through dimensionality reduction. Parallel to this, the method is tested in heterogeneous composite samples and compared to expected results obtained by classical methods.L’identification des relations constitutives des matériaux est une tâche essentielle pour comprendre leur comportement. Les méthodes classiques sont efficaces pour comprendre ces relations, mais l'introduction de modèles peut conduire à des formulations biaisées. En plus, il n’est pas possible de formaliser toutes les relations constitutives par des expressions mathématiques ou il peut y avoir des paramètres difficilement identifiables par des techniques courantes. L'identification pilotée par les données (DDI), développée par Leygue et al. (2018), est un algorithme dans lequel la relation constitutive des matériaux élastiques est définie par une base de données de points matériels qui sont calculés en fonction des champs de déformation mesurés, des forces appliquées et de la géométrie connue des échantillons du matériau. L'algorithme estime simultanément les champs de contraintes associés aux déformations mesurées dans les échantillons. Dans cette thèse, nous étendons l’algorithme DDI pour couvrir des comportements de matériaux plus complexes. Dans un premier temps, la méthode est appliquée à des échantillons hétérogènes, où un post-traitement est effectué avec l'analyse des orrespondances pour séparer les différentes phases de l’échantillon et identifier leur comportement individuel. Ensuite, la DDI a également été appliquée à des matériaux viscoélastiques linéaires, où une approche étendue de l'espace de phase est utilisée pour tenir compte de la dépendance temporelle du comportement. Enfin, différentes variantes de l'algorithme sont envisagées en combinant la DDI avec différentes techniques statistiques telles que l'analyse en composantes principales, dans une recherche de rapidité et de précision des prédictions par réduction de la dimensionnalité. Parallèlement, la méthode est testée sur des échantillons composites hétérogènes et comparée aux résultats obtenus par les méthodes classiques.Identificar las relaciones constitutivas de los materiales es una tarea esencial para entender su comportamiento. Los métodos clásicos como los ensayos, pueden ser eficaces para comprender estas relaciones, pero la introducción de modelos puede conducir a formulaciones sesgadas y errores. Además, no todas las relaciones constitutivas pueden determinarse directamente mediante expresiones matemáticas o puede haber parámetros que se obtengan fácilmente a través de técnicas habituales. La identificación impulsada por datos (DDI), desarrollada por Leygue et al. (2018), es un algoritmo en el que la relación constitutiva de los materiales elásticos se define mediante una base de datos de puntos materiales que deben ser calculados a partir de los campos de deformación medidos, las fuerzas aplicadas y la geometría conocida de las muestras ensayadas del material. El algoritmo estima simultáneamente los valores correspondientes de los campos de tensión que surgen debido a las deformaciones medidas en las muestras. En esta tesis nos enfocamos en apartarnos de la elasticidad para abarcar comportamientos de materiales más complejos con el algoritmo DDI. En un primer paso, el método se aplica a muestras heterogéneas, donde se realiza un postproceso con Análisis de Correspondencias para separar las diferentes fases de una muestra e identificar su comportamiento separado. A continuación, el DDI se aplica también a materiales con viscoelasticidad lineal, donde se utiliza un enfoque de espacio de fases ampliado para tener en cuenta la dependencia temporal del comportamiento. Finalmente, se consideran diferentes variaciones del algoritmo combinando DDI con diferentes técnicas estadísticas como el Análisis de Componentes Principales, en una búsqueda por mejorar la velocidad y precisión de las predicciones a través de la reducción de dimensiones. Paralelamente, el método fue probado en muestras heterogéneas de materiales compuestos y fueron comparadas con los resultados esperados obtenidos a través de métodos clásicos.Postprint (published version

Automated discovery of generalized standard material models with EUCLID

We extend the scope of our approach for unsupervised automated discovery of material laws (EUCLID) to the case of a material belonging to an unknown class of behavior. To this end, we leverage the theory of generalized standard materials, which encompasses a plethora of important constitutive classes. We show that, based only on full-field kinematic measurements and net reaction forces, EUCLID is able to automatically discover the two scalar thermodynamic potentials, namely, the Helmholtz free energy and the dissipation potential, which completely define the behavior of generalized standard materials. The a priori enforced constraint of convexity on these potentials guarantees by construction stability and thermodynamic consistency of the discovered model; balance of linear momentum acts as a fundamental constraint to replace the availability of stress-strain labeled pairs; sparsity promoting regularization enables the automatic selection of a small subset from a possibly large number of candidate model features and thus leads to a parsimonious, i.e., simple and interpretable, model. Importantly, since model features go hand in hand with the correspondingly active internal variables, sparse regression automatically induces a parsimonious selection of the few internal variables needed for an accurate but simple description of the material behavior. A fully automatic procedure leads to the selection of the hyperparameter controlling the weight of the sparsity promoting regularization term, in order to strike a user-defined balance between model accuracy and simplicity. By testing the method on synthetic data including artificial noise, we demonstrate that EUCLID is able to automatically discover the true hidden material model from a large catalog of constitutive classes, including elasticity, viscoelasticity, elastoplasticity, viscoplasticity, isotropic and kinematic hardening

Application of the multi-level time-harmonic fast multipole BEM to 3-D visco-elastodynamics

Engineering Analysis with Boundary elements (accepted, to appear)International audienceThis article extends previous work by the authors on the single- and multi-domain time-harmonic elastodynamic multi-level fast multipole BEM formulations to the case of weakly dissipative viscoelastic media. The underlying boundary integral equation and fast multipole formulations are formally identical to that of elastodynamics, except that the wavenumbers are complex-valued due to attenuation. Attention is focused on evaluating the multipole decomposition of the viscoelastodynamic fundamental solution. A damping-dependent modification of the selection rule for the multipole truncation parameter, required by the presence of complex wavenumbers, is proposed. It is empirically adjusted so as to maintain a constant accuracy over the damping range of interest in the approximation of the fundamental solution, and validated on numerical tests focusing on the evaluation of the latter. The proposed modification is then assessed on 3D single-region and multi-region visco-elastodynamic examples for which exact solutions are known. Finally, the multi-region formulation is applied to the problem of a wave propagating in a semi-infinite medium with a lossy semi-spherical inclusion (seismic wave in alluvial basin). These examples involve problem sizes of up to about $3\,10^{5}$ boundary unknowns

Linear Stability Analyses of Poiseuille Flows of Viscoelastic Liquids

The linear stability of the Giesekus and linear Phan-Thien Tanner (PTT) fluid models is investigated for a number of planar Poiseuille flows in single, double and triple layered configurations. The Giesekus and PTT models involve parameters that can be used to fit shear and extensional data, thus making them suitable for describing both polymer solutions and melts. The base flow is determined using a Chebyshev-tau method. The linear stabil-ity equations are also discretized using Chebyshev approximations to furnish a generalized eigenvalue problem which is then solved using the QZ-algorithm. The eigenspectra are shown to comprise of continuous parts and discrete parts. The theoretical and numerical results are validated for the Oldroyd-B model, which is a simplified case of the Giesekus and PTT models, by comparing with results in the literature. The continuous and discrete parts of the eigenspectra are determined using a purely numerical scheme to solve the discretized eigenvalue problem. The continuous spectra are then more accurately determined using a semi-analytical scheme which uses an analytical solution of the Orr-Sommerfeld equation alongside a numerical solution for the base flow. A comprehensive survey of the effect of each shear thinning and extensional fluid pa

Numerical study of convective fluid flow in porous and non-porous media.

Ph. D. University of KwaZulu-Natal, Pietermaritzburg 2015.Abstract available in PDF file

Numerical study for non-Newtonian fluid-structure interaction problems

In this work, we consider non-Newtonian fluid structure problems, which have significant applications in biology and industry. Numerical approximation schemes are developed based on the Arbitrary Lagrangian-Eulerian (ALE) formulation of the flow equations. A spatial discretization is accomplished by the finite element method, and the time discretization is carried out by the implicit Euler method. We first consider a fluid-structure interaction problem that consists of a two-dimensional viscoelastic flow and a one-dimensional structure equation. We show how the system can be decoupled and how each subproblem can be solved using interface conditions. Numerical results of different algorithms are presented, showing the comparison between non-Newtonian and Newtonian fluids. We then extend the FSI problem into the 2D-2D case of a quasi-Newtonian fluid and a linear elastic structure. In this case, we present the stability and error estimation for both semi-discrete and fully discrete formulation. For the last part of this work, a 2D-2D viscoelastic FSI problem is considered with both monolithic algorithm and decoupled algorithm under Robin condition

Proceedings of the YIC 2021 - VI ECCOMAS Young Investigators Conference

The 6th ECCOMAS Young Investigators Conference YIC2021 will take place from July 7th through 9th, 2021 at Universitat Politècnica de València, Spain. The main objective is to bring together in a relaxed environment young students, researchers and professors from all areas related with computational science and engineering, as in the previous YIC conferences series organized under the auspices of the European Community on Computational Methods in Applied Sciences (ECCOMAS). Participation of senior scientists sharing their knowledge and experience is thus critical for this event.YIC 2021 is organized at Universitat Politécnica de València by the Sociedad Española de Métodos Numéricos en Ingeniería (SEMNI) and the Sociedad Española de Matemática Aplicada (SEMA). It is promoted by the ECCOMAS.The main goal of the YIC 2021 conference is to provide a forum for presenting and discussing the current state-of-the-art achievements on Computational Methods and Applied Sciences,including theoretical models, numerical methods, algorithmic strategies and challenging engineering applications.Nadal Soriano, E.; Rodrigo Cardiel, C.; Martínez Casas, J. (2022). Proceedings of the YIC 2021 - VI ECCOMAS Young Investigators Conference. Editorial Universitat Politècnica de València. https://doi.org/10.4995/YIC2021.2021.15320EDITORIA

Parallel computations based on domain decompositions and integrated radial basis functions for fluid flow problems

The thesis reports a contribution to the development of parallel algorithms based on Domain Decomposition (DD) method and Compact Local Integrated Radial Basis Function (CLIRBF) method. This development aims to solve large scale fluid flow problems more efficiently by using parallel high performance computing (HPC). With the help of the DD method, one big problem can be separated into sub-problems and solved on parallel machines. In terms of numerical analysis, for each sub-problem, the overall condition number of the system matrix is significantly reduced. This is one of the main reasons for the stability, high accuracy and efficiency of parallel algorithms. The developed methods have been successfully applied to solve several benchmark problems with both rectangular and non-rectangular boundaries. In parallel computation, there is a challenge called Distributed Termination Detection (DTD) problem. DTD concerns the discovery whether all processes in a distributed system have finished their job. In a distributed system, this problem is not a trivial problem because there is neither a global synchronised clock nor a shared memory. Taking into account the specific requirement of parallel algorithms, a new algorithm is proposed and called the Bitmap DTD. This algorithm is designed to work with DD method for solving Partial Differential Equations (PDEs). The Bitmap DTD algorithm is inspired by the Credit/Recovery DTD class (or weight-throw). The distinguishing feature of this algorithm is the use of a bitmap to carry the snapshot of the system from process to process. The proposed algorithm possesses characteristics as follows. (i) It allows any process to detect termination (symmetry); (ii) it does not require any central control agent (decentralisation); (iii) termination detection delay is of the order of the diameter of the network; and (iv) the message complexity of the proposed algorithm is optimal. In the first attempt, the combination of the DD method and CLIRBF based collocation approach yields an effective parallel algorithm to solve PDEs. This approach has enabled not only the problem to be solved separately in each subdomain by a Central Processing Unit (CPU) but also compact local stencils to be independently treated. The present algorithm has achieved high throughput in solving large scale problems. The procedure is illustrated by several numerical examples including the benchmark lid-driven cavity flow problem. A new parallel algorithm is developed using the Control Volume Method (CVM) for the solution of PDEs. The goal is to develop an efficient parallel algorithm especially for problems with non-rectangular domains. When combined with CLIRBF approach, the resultant method can produce high-order accuracy and economical solution for problems with complex boundary. The algorithm is verified by solving two benchmark problems including the square lid-driven cavity flow and the triangular lid-driven cavity flow. In both cases, the accuracy is in great agreement with benchmark values. In terms of efficiency, the results show that the method has a very high efficiency profile and for some specific cases a super-linear speed-up is achieved. Although overlapping method yields a straightforward implementation and stable convergence, overlapping of sub-domains makes it less applicable for complex domains. The method even generates more computing overhead for each subdomain as the overlapping area grows. Hence, a parallel algorithm based on non-overlapping DD and CLIRBF has been developed for solving Navier-Stokes equations where a CLIRBF scheme is used to solve the problem in each subdomain. A relaxation factor is employed for the transmission conditions at the interface of sub-domains to ensure the convergence of the iterative method while the Bitmap DTD algorithm is used to achieve the global termination. The parallel algorithm is demonstrated through two fluid flow problems, namely the natural convection in concentric annuli (Boussinesq fluids) and the lid-driven cavity flow (viscous fluids). The results confirm the high efficiency of the present method in comparison with a sequential algorithm. A super-linear efficiency is also observed for a range of numbers of CPUs. Finally, when comparing the overlapping and non-overlapping parallel algorithms, it is found that the non-overlapping one is less stable. The numerical results show that the non-overlapping method is not able to converge for high Reynolds number while overlapping method reaches the same convergence profile as the sequential CLIRBF method. Thus, in this research when dealing with non-Newtonian fluids and large scale problems, the overlapping method is preferred to the nonoverlapping one. The flow of Oldroyd-B fluid through a planar contraction was considered as a benchmark problem. In this problem, the singularity of stress at the re-entrant corners always poses difficulty to numerical methods in obtaining stable solutions at high Weissenberg numbers. In this work, a high resolution simulation of the flow is obtained and the contour of streamline is shown to be in great agreement with other results