A kinematically enhanced constitutive model for progressive damage analysis of unidirectional fiber reinforced composites

The application of fiber reinforced laminated composite structures has been increasing steadily in many engineering disciplines due to their high specific strength and stiffness, corrosion resistance, exceptional durability and many other attractive features over the last few decades. A comprehensive strength and failure assessment of these structures made of composite materials is extremely important for a reliable design of these structures and it has been a major focus of many researchers in this field for a long time. To the best of our knowledge, the majority of the existing studies based on macro based continuum approach are particularly focussed on capturing the effective elastic properties and final failure envelop of the composite material, while the subsequent post-yield inelastic behaviour or the entire nonlinear response is often overlooked. Composite structures with such diverse applications can be subjected to complex loading conditions such as impacts, severe dynamic loads or extreme thermal loads which can lead to a significant damage or complete failure of these structures. It is therefore essential to predict the entire nonlinear response and failure of these structures in many situations for a better design with higher confidence. This problem is quite challenging, specifically with a macro based continuum approach, as the actual failure initiates at the micro scale in the form of matrix cracking, fiber rupture or fiber-matrix interface failure which propagate gradually, accumulate together and finally manifested as macroscale structural failure. Thus tracking the details on the entire failure evolution process from microscale to macroscale is necessary for accurately modelling the structural failure. A detailed micromechanical modelling approach, where all constituents are explicitly modelled, can capture all these microscale failure processes and their evolutions in details but such modelling strategy is not computationally feasible for failure analysis for large structures due to a huge gap between micro/fiber and macro/structural scales. Thus the analysis of these structures requires an innovative modelling approach that can represent and capture the essential features of these microscale failure details, while at the same time, should be computationally efficient like a macro based continuum model for undertaking large scale structural analysis. In this study, a new three-dimensional kinematically enhanced macro-based constitutive model is developed which is applicable at the lamina/ply scale of these laminated composite structures. A novel analytical technique is developed for upscaling the nonlinear response from the fiber/micro scale to the ply scale which is the key for achieving such precise modelling of composites with feasible computational resources. The proposed approach utilized a strategy of strain field enhancements kinematically to account for different rate of deformations in the local fields within a fiber reinforced composite (FRC) ply. Based on these considerations, closed-form analytical expressions are derived which can be used conveniently to express the average macro strain increments of the entire volume element in terms of strain increments in the local fields and vice versa. This modelling strategy provides an opportunity to incorporate both fiber and matrix constitutive responses as well as their interactions into the overall ply response. To this end, a thermodynamics-based continuum model is developed using damage mechanics and plasticity theory to capture the constitutive response of the matrix. This has incorporated two predominant failure mechanisms in the matrix, which are permanent plastic deformation and loss of stiffness. For the fiber-matrix interface that includes interfacial debonding, an anisotropic damage model is developed to account for the directional dependence of the softening response in FRC ply due to fiber debonding failure. The proposed approach and models are developed in incremental forms, allowing the applications in both linear and nonlinear ranges of behaviour. Their verification with available analytical and numerical approaches together with the validation against a wide range of experimental data show both features and good potentials of the proposed approach.Thesis (Ph.D.) (Research by Publication) -- University of Adelaide, School of Civil, Environmental and Mining Engineering, 201

Desenvolvimento de modelos computacionais anisotrópicos baseados em hipoelasticidade e hiperelasticidade incluindo endurecimento cinemático não-linear

Doutoramento em Engenharia MecânicaIn the present work, finite strain elastoplastic constitutive formulations suitable for advanced metallic materials are developed. The main goals are the correct description of the elastoplastic behaviour, including strong plastic anisotropy and cyclic hardening phenomena, in the large strain regime, as well as the development of numerically efficient algorithmic procedures for numerical implementation of the constitutive models into codes of numerical simulation by the Finite Element Method. Two different approaches are used in the derivation of the finite strain constitutive formulations, namely, hypoelasticity and hyperelasticity. On the one hand, regarding the hypoelastic-based model, particular attention is given to the development of computationally effcient forward- and backward-Euler algorithms considering distinct techniques. On the other hand, concerning the hyperelastic-based model, the focus is on the possibility of using any (quadratic or nonquadratic) yield criteria and on a new procedure that ensures that the anisotropy is correctly described in the finite strain regime. Moreover, the constitutive relations are solely expressed in the reference configuration, hence yielding symmetric tensor-valued quantities only. This symmetry, allied to an algorithm that preserves it, is crucial for the computational efficiency of the model's implementation since it reduces the storage effort and the required solver capacities when compared to the model's standard counterparts. For a better description of cyclic hardening phenomena, the developed models and corresponding algorithms, are extended to include several back stresses. This extension is carried out by considering a modified rheological model of nonlinear kinematic hardening and using additional state variables. The capabilities of the developed models for accurate reproduction of the plastic anisotropy and cyclic hardening phenomena are assessed by means of their implementation into material user subroutines of the commercial code Abaqus. The accuracy and computational efficiency of the models and numerical algorithms are compared by means of simulations of benchmarks. These benchmarks allow the models' assessment in the description of, e.g., metal forming defects such as earing and springback, as well as the comparison of the stability and precision of the numerical algorithms.No presente trabalho, são desenvolvidas formulações constitutivas elastoplásticas para grandes deformações, adequadas a materiais metálicos avançados. Os principais objectivos deste estudo consistem na correcta descrição do comportamento elastoplástico, incluindo anisotropia plástica acentuada e fenómenos de endurecimento cíclico, no regime de grandes deformações, bem como o desenvolvimento de procedimentos algorítmicos eficientes para a implementação numérica dos modelos constitutivos em códigos de simulação numérica pelo Método dos Elementos Finitos. São usadas duas metodologias diferentes na derivação das formulações constitutivas de grandes deformações, nomeadamente, hipoelasticidade e hiperelasticidade. Por um lado, relativamente ao modelo baseado em hipoelasticidade, é dada particular atenção ao desenvolvimento de algoritmos eficientes do ponto de vista computacional, considerando técnicas particulares. Por outro lado, em relação ao modelo baseado em hiperelasticidade, a possibilidade de usar qualquer critério de cedência (quadrático ou não-quadrático) e a apresentação de um procedimento inovador, que garante a correcta descrição da anisotropia na presença de grandes deformaçães, são destacadas. Além disso, as relações constitutivas são expressas unicamente na configuração de referência, resultando no uso de apenas variáveis simétricas de segunda ordem. Esta simetria e o uso de um algoritmo que a preserva são cruciais no que diz respeito à eficiência numérica da implementação do modelo, uma vez que reduz significativamente o espaço de armazenamento e o custo computacional de cálculo, relativamente aos modelos hiperelásticos convencionais. Os modelos, e respectivos algoritmos de integração, são posteriormente alargados ao uso de múltiplos tensores das tensões inversas de modo a permitir uma melhor descrição dos fenómenos de endurecimento cíclico. Para tal, foi considerado um modelo reológico modificado de endurecimento cinemático e usadas variáveis de estado adicionais. O desempenho dos modelos desenvolvidos na reprodução precisa de anisotropia plástica e fenómenos de endurecimento cíclico é avaliado através da sua implementação no código comercial Abaqus usando subrotinas de utilizador. A precisão e eficiência computacional dos modelos e algoritmos desenvolvidos são comparados entre si através de simulações de benchmarks. Estes benchmarks permitem a avaliação dos modelos na descrição de, por exemplo, defeitos na conformação de chapas metálicas, tais como a formação de orelhas e o retorno elástico, bem como a comparação da estabilidade e precisão dos algoritmos numéricos

Machine Learning Aided Stochastic Elastoplastic and Damage Analysis of Functionally Graded Structures

The elastoplastic and damage analyses, which serve as key indicators for the nonlinear performances of engineering structures, have been extensively investigated during the past decades. However, with the development of advanced composite material, such as the functionally graded material (FGM), the nonlinear behaviour evaluations of such advantageous materials still remain tough challenges. Moreover, despite of the assumption that structural system parameters are widely adopted as deterministic, it is already illustrated that the inevitable and mercurial uncertainties of these system properties inherently associate with the concerned structural models and nonlinear analysis process. The existence of such fluctuations potentially affects the actual elastoplastic and damage behaviours of the FGM structures, which leads to the inadequacy between the approximation results with the actual structural safety conditions. Consequently, it is requisite to establish a robust stochastic nonlinear analysis framework complied with the requirements of modern composite engineering practices. In this dissertation, a novel uncertain nonlinear analysis framework, namely the machine leaning aided stochastic elastoplastic and damage analysis framework, is presented herein for FGM structures. The proposed approach is a favorable alternative to determine structural reliability when full-scale testing is not achievable, thus leading to significant eliminations of manpower and computational efforts spent in practical engineering applications. Within the developed framework, a novel extended support vector regression (X-SVR) with Dirichlet feature mapping approach is introduced and then incorporated for the subsequent uncertainty quantification. By successfully establishing the governing relationship between the uncertain system parameters and any concerned structural output, a comprehensive probabilistic profile including means, standard deviations, probability density functions (PDFs), and cumulative distribution functions (CDFs) of the structural output can be effectively established through a sampling scheme. Consequently, by adopting the machine learning aided stochastic elastoplastic and damage analysis framework into real-life engineering application, the advantages of the next generation uncertainty quantification analysis can be highlighted, and appreciable contributions can be delivered to both structural safety evaluation and structural design fields

Recent advances and applications of machine learning in metal forming processes

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Recent Advances and Applications of Machine Learning in Metal Forming Processes

Machine learning (ML) technologies are emerging in Mechanical Engineering, driven by the increasing availability of datasets, coupled with the exponential growth in computer performance. In fact, there has been a growing interest in evaluating the capabilities of ML algorithms to approach topics related to metal forming processes, such as: Classification, detection and prediction of forming defects; Material parameters identification; Material modelling; Process classification and selection; Process design and optimization. The purpose of this Special Issue is to disseminate state-of-the-art ML applications in metal forming processes, covering 10 papers about the abovementioned and related topics

Numerical modelling of additive manufacturing process for stainless steel tension testing samples

Nowadays additive manufacturing (AM) technologies including 3D printing grow rapidly and they are expected to replace conventional subtractive manufacturing technologies to some extents. During a selective laser melting (SLM) process as one of popular AM technologies for metals, large amount of heats is required to melt metal powders, and this leads to distortions and/or shrinkages of additively manufactured parts. It is useful to predict the 3D printed parts to control unwanted distortions and shrinkages before their 3D printing. This study develops a two-phase numerical modelling and simulation process of AM process for 17-4PH stainless steel and it considers the importance of post-processing and the need for calibration to achieve a high-quality printing at the end. By using this proposed AM modelling and simulation process, optimal process parameters, material properties, and topology can be obtained to ensure a part 3D printed successfully

Modélisation et simulation du couplage changement de phases-mécanique par la méthode des champs de phases

A general constitutive framework is proposed to incorporate linear and nonlinear mechanical behaviour laws (i.g. elastoviscoplasticity) into a standard phase field model. A finite element formulation of a coupled phase field/diffusion/mechanical problem for alloys is proposed within the general framework of continuum thermodynamics. This formulation is based on the concept of generalized stresses as proposed by Gurtin, where an additional balance equation for generalized stresses, called microforces, associated with the order parameter and its first gradient, is postulated. The formulation is used to simulate the complex morphological evolutions of the heterogeneous microstructures and to describe the diffuse interface between two phases in the presence of the stresses induced by phase transformation. Using the principles of the thermodynamics of irreversible processes, the balance and constitutive equations are clearly separated in the formulation. Also, boundary and initial conditions for the displacement, concentration and order parameter and their dual quantities are clearly stated within the formulation. The theory is shown to be well-suited for a finite element formulation of the initial boundary value problems on nite size specimens with arbitrary geometries and for very general non-periodic or periodic boundary conditions. In the diffuse interface region where both phases coexist, mixture rules taken from homogenization theory are introduced into the formulation. The consequences of the choice of a specific interface behaviour is investigated, with regard to the mechanical effect on phase equilibria (equilibrium compositions and volume fractions of the coexisting phases), as well as on the transformation kinetics. The set of coupled evolution equations, which are the local static equilibrium, the balance of generalized stresses and the balance of mass, is solved using a finite element method for the space discretization and a finite difference method for the temporal discretization. To validate the numerical finite element implementation and to illustrate the ability of the proposed model to handle precipitation together with mechanical contribution effect, some elementary initial boundary value problem in coupled diusion-elasto-plasticity on finite size specimens has been solved and validated against corresponding sharp interface analytical solutions.Nous proposons un cadre générique, permettant l'incorporation des différentes lois de comportement de mécanique linéaires ou non-linéaires (i.e. elastoviscoplastique) dans les approches des champs de phases utilisées pour la modélisation et la simulation de la mobilité d'interfaces diffuses. Dans ce cadre, une formulation par éléments finis des modèles couplés champ de phases-élastoplasticité pour les alliages binaires est développée dans le formalisme général de la thermodynamique des milieux continus. Cette formulation est basée sur la théorie d'équilibre des microforces, proposée par Gurtin, où une équation supplémentaire, fonction du paramètre d'ordre et de son gradient, est introduite. La formulation est employée pour simuler les évolutions morphologiques complexes des microstructures hétérogènes et décrire l'interface diffuse entre deux phases en présence des contraintes induites par transformation de phase. En utilisant les principes de la thermodynamique des processus irréversibles, les lois de comportement et les équations d'évolution sont clairement exposées et séparées dans la formulation de sorte que des modèles non-linéaires et fortement couplés puissent être implantés plus facilement dans un code par éléments finis. Cette formulation peut être appliquée aux corps finis périodiques et non périodiques, aux microstructures hétérogènes. Les conditions initiales et les conditions aux limites en paramètre d'ordre et en concentration ainsi que leurs quantités duales sont clairement énoncées. Des techniques d'homogénéisation ont été utilisées pour décrire le comportement dans les interfaces diffuses. Les conséquences de ces choix de modélisation ont été déterminées en ce qui concerne les effets des contraintes mécaniques sur les équilibres de phases et la cinétique de transformation. L'ensemble des équations d'évolution couplées, à savoir l'équation d'équilibre statique local, l'équation de champ de phases et l'équation de conservation de la masse, est résolu en utilisant la méthode des éléments finis pour la discrétisation spatiale et un schéma implicite des différences finies pour la discrétisation temporelle. Afin d'illustrer l'intérêt de l'approche proposée, des calculs par éléments finis ont été effectués sur des situations élémentaires telles que le calcul des concentrations d'équilibre des phases en présence de contraintes et la croissance de précipités dans une matrice élastique ou élasto-plastique, situations pour lesquelles des solutions analytiques pour des interfaces parfaites sont disponibles

Écoulements de solides amorphes : modélisation élastoplastique et théorie de couplage de modes

Contrary to the case of simple fluids, a finite stress is required to initiate the flow of amorphous solids, a broad class of materials ranging from bulk metallic glasses to dense emulsions. The objective of this thesis is to model the flow of these materials in a general framework, with an emphasis on heterogeneities.In a first approach, using the liquid regime as a starting point, I have investigated to what extent inhomogeneities can be accommodated in the framework of the mode-coupling theory of rheology. A generic equation for the evolution of density inhomogeneities has been derived.At low temperatures, the flow is indeed quite heterogeneous: it consists of periods of elastic deformation interspersed with swift localised rearrangements of particles, that induce long-range elastic deformations and can thereby spark off new rearrangements. In a second approach, a model rooted in this scenario has been refined so as to reflect the interplay between the external drive and the localised rearrangements, which is at the origin of the flow curve of athermal solids. The latter has been reproduced satisfactorily.Turning to spatial correlations in the flow, we have shown that there exists no universal scaling for these correlations in elastoplastic models, although a broad class of correlation lengths scale with \dot{\gamma}^{\nicefrac{-1}{d}} in the shear-dominated regime in d dimensions.Besides, shear localisation has been observed in diverse variants of the model, whenever blocks are durably weakened following a plastic event.Finally, we have directly compared model predictions to experimental results on the flow of dense emulsions through microchannels and to athermal molecular dynamics simulations. Spurred on by the observation of some discrepancies, we have developed and implemented a more flexible code, based on a simplified Finite Element routine, which notably provides a better account of structural disorder and inertial effects.À la différence des liquides simples, les solides amorphes, une vaste catégorie de matériaux allant des verres métalliques aux émulsions concentrées, ne se mettent à s'écouler qu'au-delà d'une contrainte finie. Notre thèse a pour objet la modélisation de cet écoulement, dans un cadre général et avec un accent mis sur les hétérogénéités.En premier lieu, notre travail a porté sur l'inclusion d'inhomogénéités dans le cadre de la théorie de couplage de modes appliquée à la rhéologie et nous avons notamment obtenu une équation générale d'évolution des inhomogénéités de densité.À basse température, l'écoulement est en effet fortement hétérogène : des phases de déformation élastique sont entrecoupées de réarrangements de particules, brusques et localisés, qui interagissent par le biais des déformations élastiques qu'ils génèrent. En second lieu, nous avons donc considéré un modèle calqué sur ce scénario et affiné ses éléments constitutifs pour rendre compte de la compétition entre cisaillement appliqué et réarrangements locaux, à l'origine de la courbe d'écoulement des matériaux athermiques. Cette dernière a été reproduite de manière satisfaisante.Pour ce qui est des corrélations spatiales dans l'écoulement, nous avons montré qu'il n'existe pas de loi d'échelle universelle dans les modèles élasto-plastiques, malgré la présence d'une classe de longueurs de corrélation décroissant comme \dot{\gamma}^{\nicefrac{-1}{d}} en d dimensions, dans le régime dominé par le cisaillement.Par ailleurs, dans diverses variantes du modèle, le cisaillement se trouve localisé dans une région du matériau. Ce phénomène apparaît dès lors que les blocs élasto-plastiques sont durablement fragilisés à la suite d'un événement plastique.Enfin, les prédictions du modèle ont été directement mises en regard avec des expériences sur l'écoulement en microcanal d'émulsions concentrées et des simulations de dynamique moléculaire à température nulle. Les écarts observés nous ont poussé à développer et implémenter un code plus flexible, qui s'appuie sur une routine simplifiée d'Éléments Finis et rend mieux compte du désordre structurel et des effets inertiels

Concurrent multiscale modelling for heterogeneous materials with CutFEM

Computational modelling of heterogeneous materials with complex microstructures is challenging due to their multiscale nature. While direct numerical simulations lead to accurate results, it is not tractable for large-scale models. Therefore, in this thesis, two novel concurrent multiscale frameworks have been developed for tractable simulation of 2D/3D highly heterogeneous materials, including composites and trabecular bone materials. The difficulty of discretising such materials with complex microstructure is circumvented by using the cut finite element method (CutFEM). Then, two efficient zooming techniques are proposed for coupling micro and acroscale models. In our multiscale frameworks, the CutFEM technique is utilised to discretise the corresponding micro/macro interface besides the microstructure. In the first framework, the smooth transition concurrent multiscale method, the two models are blended in a transition region and discretised over a single fixed computational mesh. While in the second framework, the two models have different meshes and are coupled over a sharp interface using Nitsche’s method. In both frameworks, the CutFEM technology has been used for discretisation purposes that permits representing the microstructure and micro/macro interfaces in a mesh-independent fashion. This feature of CutFEM allows to (re)locate the zooming region(s) (the region(s) we require microscopic analysis) over a fixed background mesh arbitrarily, thus improving the robustness of multiscale modelling and analysis. In chapter 3, the efficiency and robustness of the smoothed concurrent multiscale method is demonstrated for 2D and 3D linear elasticity problems. Then, in chapter 5, the performance of the second concurrent multiscale framework with a sharp interface is tested for 2D linear elasticity and plasticity materials. In chapter 4, the smoothed concurrent multiscale method developed in Chapter 3 is extended for brittle fracture problems, which are a prevalent example of multiscale phenomena. According to the literature, fracture initiation starts in microscopic length scales by an accumulation of micro cracks in a process zone that eventually leads to the creation of macro cracks. In this thesis, the phase field model has been adopted for the fracture problem, which considers the fracture in a diffusive way. Since phase field models suffer from demanding extremely refined meshes to represent cracks, an efficient numerical framework is essential to balance accuracy and computational costs. In chapter 4, we show that our smoothed concurrent multiscale framework is a suitable choice for such problems

Stress Transmission in a Granular System

A sample of soil under external loads shows nonlinear behaviour. These external loads are propagated through grain-to-grain contacts. Consequently, the grains are being subjected to both tensile and compressive stresses according to their shape, position, and number of contacts. Thus, the nonlinear mechanical behaviour of soil may be described by investigating inter-particle stress transmission. The direct measurement of stress is a challenging task, both experimentally and numerically. In this study, stress-transmitting grains in a sand specimen are identified using an image-based approach. The methodology consists of measuring the geometrical data of the individual grains and following their evolution. On the numerical side, a more realistic description of soil behaviour is provided by developing a computational approach that quantifies internal stresses in each individual grain, termed micro Finite Element (μFE) model. The fabric of a natural sand obtained from the micro computed tomography (μCT) is virtualised to simulate the mechanical response of the material. The grain-to-grain interactions under loading are modelled in a framework of combined discrete-finite element method. Each individual grain is represented by a collection of nodes and elements and modelled as a continuum body that can deform according to a prescribed constitutive properties with appropriate friction contact conditions. The insights that can be gained into the stress transmission mechanisms and yield initiation within the grains are shown in a case study of an intact sand subjected to 1D compression. This includes stress and displacement field, inertia tensor, and active contact area. The contact behaviour used in the model is validated against existing theories for a single sphere and an assembly of spheres under triaxial loading. Then, single grain tests are conducted experimentally and numerically in order to better understand the influence of grain morphology on stress transmission. This study shows the strong dependency of contact behaviour on grain morphology. In addition, the effect of surface roughness is investigated showing the role of asperity abrasion under low normal loading. The evaluation of the μFE model has yielded results that compare well to experimental data obtained from a triaxial test in a μCT scanner. The stress field within each grain in the granular media is studied, contributing new insights beyond the commonly reported force chains. The ‘stress chain’ concept is considered as an alternative way to reflect grain breakage that may initiate on the weak force network and compromise the stability of the assembly. It is thus suggested that the ‘stress chain’ concept can be richer than ‘force chain’ and contains information about grain shape, mechanical properties and local fabric