Amélie Fau

École normale supérieure Paris-Saclay

Temporally and spatially dependent uncertain parameters are regularly encountered in engineering applications. Commonly these uncertainties are accounted for using random fields and processes which require knowledge about the appearing probability distributions functions which is not readily available. In these cases non-probabilistic approaches su...

Some areas of mechanical and system engineering such as dynamic systems commonly exhibit highly fluctuating responses over given parametric domains. Therefore, classifying some quantities of interest over the parametric domain for designing new systems turns out to be a highly challenging task. In this context, an innovative adaptive sampling algor...

Metamodels aim to approximate characteristics of functions or systems from the knowledge extracted on only a finite number of samples. In recent years kriging has emerged as a widely applied metamodeling technique for resource-intensive com-putational experiments. However its prediction quality is highly dependent on the size and distribution of th...

Imprecise random fields consider both, aleatory and epistemic uncertainties. In this paper, spatially varying material parameters representing the constitutive parameters of a damage model for concrete are defined as imprecise random fields by assuming an interval valued correlation length. For each correlation length value, the corresponding rando...

In-situ (tomography) experiments are generally based on scans reconstructed from a large number of projections acquired under constant deformation of samples. Standard digital volume correlation (DVC) methods are based on a limited number of scans due to acquisition duration. They thus prevent analyses of time-dependent phenomena. In this paper, a...

In this work, we apply reduced-order modeling to the parametrized, time-dependent, incompressible, laminar Navier-Stokes equations. The major goal is to reduce the computational costs by replacing the high-fidelity system by a low-rank approximation, which preserves the solution behavior. We utilize projection-based reduced basis methods and carry...

Solving dynamics problem in the frequency domain gives significant advantages compared with solutions fully computed in the temporal domain, but history-dependent nonlinear behaviour is an obstacle to employ that strategy. A hybrid approach is proposed to solve the nonlinear behaviour in the temporal domain, while the mechanical equilibrium is solv...

The formulation of history-dependent material laws has been a significant research and industrial activity in solid mechanics for over a century. A large variety of models has been developed, tailored for the description of different families of materials. However, model selection for a specific problem is a delicate issue and there still remain op...

In this work, the dual-weighted residual (DWR) method is applied to obtain a certified incremental proper orthogonal decomposition (POD) based reduced order model. A novel approach called MORe DWR (Model Order Rduction with Dual-Weighted Residual error estimates) is being introduced. It marries tensor-product space-time reduced-order modeling with...

Compositionśproperty correlations are fundamental to understand cement-based materials' behavior and optimize their formulation. Modeling based on fundamental material components constitutes a reliable tool to establish these correlations with the advantage of better exploring the formulation space when compared to the often adopted experimental tr...

This work presents an hp-adaptive variant of multi-element polynomial chaos expansion (ME-gPCE), referred to as anisotropic multi-element polynomial chaos expansion (AME-gPCE). The main advantage of the proposed framework is that the basis functions of the local gPCE are selected adaptively within each local element. The p-adaptivity allows the ord...

This work presents an hp-adaptive variant of multi-element polynomial chaos expansion (ME-gPCE), referred to as anisotropic multi-element polynomial chaos expansion (AME-gPCE). The main advantage of the proposed framework is that the basis functions of the local gPCE are selected adaptively within each local element. The p-adaptivity allows the ord...

The quantification of debonding was performed for additively manufactured “fractal” fibers embedded within two brittle matrices. Three pull-out tests were carried out inside of an X-ray tomograph allowing for Digital Volume Correlation analyses. Relative motions at the interfaces were measured thanks to adapted meshes with split nodes. Profiles of...

Composition-property correlations are fundamental to understand cement-based materials behavior and optimize their formulation. Modelling based on fundamental material component constitutes a reliable tool to establish these correlations with the advantage of better exploring formulation space when compared with the often adopted experimental trial...

Sophisticated sampling techniques used for solving stochastic partial differential equations efficiently and robustly are still in a state of development. It is known in the scientific community that global stochastic collocation methods using isotropic sparse grids are very efficient for simple problems but can become computationally expensive or...

Ce travail présente une stratégie de construction de surfaces de réponse incluant une technique de réduction de modèle permettant de prédire la défaillance de structures en dynamique basse fréquence non linéaire. Les défis, la fiabilité et les potentialités de l’approche sont discutés.

The formulation of history-dependent material laws has been a significant challenge in solid mechanics for over a century. Recently, data-driven techniques have generated accurate and reliable surrogates for elasto-plastic constitutive laws. However, most of these methods are deeply rooted in the big data domain and fail when only a few physically...

Temporally and spatially dependent uncertain parameters are regularly encountered in engineering applications. Commonly these uncertainties are accounted for using random fields and processes, which require knowledge about the appearing probability distributions functions that is not readily available. In these cases non-probabilistic approaches su...

An innovative sampling strategy called MiVor coupled with kriging metamodeling is employed for detecting stick-slip instabilities within a parametric domain based on very few simulations. The interest of the approach is here exposed on an oscillator of Duffing's type in combination with an elasto-plastic friction force model, more details can be fo...

Computational multiscale methods for analyzing and deriving constitutive responses have been used as a tool in engineering problems because of their ability to combine information at different length scales. However, their application in a nonlinear framework can be limited by high computational costs, numerical difficulties, and/or inaccuracies. I...

Fragility curves are one of the main tools used to characterize the resistance to seismic hazard ofcivil engineering structures, such as nuclear facilities. These curves describe the probability thatthe response of a structure exceeds a given criterion, called failure criterion, as a function of theexpected seismic loading level. The numerical cons...

Closed forms of stabilizing sets are generally only available for linearized systems. An innovative numerical strategy to estimate stabilizing sets of PI or PID controllers tackling (uncertain) nonlinear systems is proposed. The stability of the closed-loop system is characterized by the sign of the largest Lyapunov exponent (LLE). In this framewor...

Precise prediction of the elastic response is crucial to model cracking at early and late ages of cement-based materials and structures. Here, we use Machine Learning (ML) techniques to predict the elastic properties of Ordinary Portland Cement (OPC) pastes. A database with 365 observations is built on experimental studies from in the literature. W...

Some areas of mechanical and system engineering such as dynamic systems commonly exhibit highly fluctuating responses over given parametric domains. Therefore, classifying some quantities of interest over the parametric domain for designing new systems turns out to be a highly challenging task. In this context, an innovative adaptive sampling algor...

Precise prediction of the elastic response is crucial to model cracking at early and late ages of cement-based materials and structures. Here, we use Machine Learning (ML) techniques to predict the elastic properties of Ordi-nary Portland Cement (OPC) pastes. A database with 365 observations is built on experimental studies from in the literature....

Computational multiscale methods for analyzing and deriving constitutive responses have been used as a tool in engineering problems because of their ability to combine information at different length scales. However, their application in a nonlinear framework can be limited by high computational costs, numerical difficulties, and/or inaccuracies. I...

Closed-forms of stabilizing sets are generally only available for linearized systems. An innovative numerical strategy to estimate stabilizing sets of PI or PID controllers tackling (uncertain) nonlinear systems is proposed. The stability of the closed-loop system is characterized by the sign of the largest Lyapunov exponent (LLE). In this framewor...

Metamodels aim to approximate characteristics of functions or systems from the knowledge extracted on only a finite number of samples. In recent years kriging has emerged as a widely applied metamodeling technique for resource-intensive computational experiments. However its prediction quality is highly dependent on the size and distribution of th...

Engineering simulation provides better designed products by allowing many options to be quickly explored and tested. In that context, the computational time is a strong issue because using high-fidelity direct resolution solvers is not always suitable. Metamodels are commonly considered to explore design options without computing every possible com...

High fidelity structural problems that involve nonlinear material behaviour, when subjected to cyclic loading, usually demand infeasible computational resources; this demonstrates the need for efficient model order reduction (MOR) techniques in order to shrink these demands to fit into the available means. The solution of cyclic damage problems in...

Experimental observation of the evolution of a structure under fatigue loading has shown in the literature largely scattered results. To represent these uncertainties, a stochastic damage model based on random process is proposed. The kinetic continuum damage model is compared with some experimental data and other modelling approaches. The original...

Parametric studies are required to detect instability regimes of dynamic systems. This prediction can be computationally demanding as it requires a fine exploration of large parametric space due to the disrupted mechanical behavior. In this paper, an efficient surrogate strategy is proposed to investigate the behavior of an oscillator of Duffing’s...

Kriging is an efficient machine-learning tool, which allows to obtain an approximate response of an investigated phenomenon on the whole parametric space. Adaptive schemes provide a the ability to guide the experiment yielding new sample point positions to enrich the metamodel. Herein a novel adaptive scheme called Monte Carlo-intersite Voronoi (Mi...

Parametric studies for dynamic systems are of high interest to detect instability domains. This prediction can be demanding as it requires a refined exploration of the parametric space due to the disrupted mechanical behavior. In this paper, an efficient surrogate strategy is proposed to investigate the behavior of an oscillator of Duffing's type i...

The goal of this paper is to introduce a model order reduction method for high-cycle fatigue simulations using a kinetic damage model, i.e. a constitutive model in which the damage evolution law is defined as a rate form for the damage variable. In the framework of continuum mechanics, high-cycle fatigue simulation involves a two-scale damage model...

Considering an uncertain correlation length of the input random fields described by a Karhunen-Loève expansion leads to a probability-box approach for the stochastic finite element computation. But, these computations are highly costly. Then, a stochastic collocation method using sparse grids within a Smolyak algorithm is proposed to reduce the com...

The solution of structural problems with nonlinear material behaviour in a model order reduction framework is investigated in this paper. In such a framework, greedy algorithms or adaptive strategies are interesting as they adjust the reduced order basis (ROB) to the problem of interest. However, these greedy strategies may lead to an excessive inc...

In structural analysis with multivariate random fields, the underlying distribution functions, the autocorrelations, and the crosscorrelations require an extensive quantification. While those parameters are difficult to measure in experiments, a lack of knowledge is included. Therefore, polymorphic uncertainty models are attained by involving uncer...

The solution of structural problems with nonlinear material behaviour in a model order reduction framework is investigated in this paper. In such a framework, greedy algorithms or adaptive strategies are interesting as they adjust the reduced order basis (ROB) to the problem of interest. However, these greedy strategies may lead to an excessive inc...

In order to regard mixed aleatory and epistemically uncertain random fields within stochastic finite element method, a probability box approach using stochastic collocation method is introduced. The influence of an interval‐valued correlation length on the output is investigated.

The objective of this article is to introduce a new method including model order reduction for the life prediction of structures subjected to cycling damage. Contrary to classical incremental schemes for damage computation, a non-incremental technique, the LATIN method, is used herein as a solution framework. This approach allows to introduce a PGD...

One of the challenges of fatigue simulation using continuum damage mechanics framework over the years has been reduction of numerical cost while maintaining acceptable accuracy. The extremely high numerical expense is due to the temporal part of the quantities of interest which must reflect the state of a structure that is subjected to exorbitant n...

The simulation of mechanical responses of structures subjected to cyclic loadings for a large number of cycles remains a challenge. The goal herein is to develop an innovative computational scheme for fatigue computations involving non-linear mechanical behaviour of materials, described by internal variables. The focus is on the Large Time Incremen...

This contribution focuses on the use of a new method to reduce the computational demands of fatigue damage computations using continuum damage mechanics. The LArge Time INcrement (LATIN) method incorporates a model order reduction approach namely the proper generalised decomposition (PGD). LATIN has been extended to tackle damage problems. (© 2017...

Different numerical tests for fatigue damage in metals using non-incremental approach

Different numerical tests for fatigue damage in metals using non-incremental approach

Non incremental approach for simulating fatigue damage in metals.

LATIN-PGD approach for cyclic viscoplasticity involving large number of cycles

Since performances of experimental and numerical tools have been largely improved, mechanics of materials can explore smaller and smaller scales. Thus, a better comprehension, or even a prediction, of local phenomena associated with macroscopic deformations are hoped. This dissertation focuses on the smallest scale involved in mechanical behavior o...