Florent Pled

Bio: Florent Pled is an academic researcher from École normale supérieure de Cachan. The author has contributed to research in topics: Finite element method & Stochastic partial differential equation. The author has an hindex of 8, co-authored 35 publications receiving 234 citations. Previous affiliations of Florent Pled include University of Paris.

On the techniques for constructing admissible stress fields in model verification: Performances on engineering examples

Abstract: Robust global/goal-oriented error estimation is used nowadays to control the approximate finite element solutions obtained from simulation. In the context of Computational Mechanics, the construction of admissible stress fields (\ie stress tensors which verify the equilibrium equations) is required to set up strict and guaranteed error bounds (using residual based error estimators) and plays an important role in the quality of the error estimates. This work focuses on the different procedures used in the calculation of admissible stress fields, which is a crucial and technically complicated point. The three main techniques that currently exist, called the element equilibration technique (EET), the star-patch equilibration technique (SPET), and the element equilibration + star-patch technique (EESPT), are investigated and compared with respect to three different criteria, namely the quality of associated error estimators, computational cost and easiness of practical implementation into commercial finite element codes. The numerical results which are presented focus on industrial problems; they highlight the main advantages and drawbacks of the different methods and show that the behavior of the three estimators, which have the same convergence rate as the exact global error, is consistent. Two- and three-dimensional experiments have been carried out in order to compare the performance and the computational cost of the three different approaches. The analysis of the results reveals that the SPET is more accurate than EET and EESPT methods, but the corresponding computational cost is higher. Overall, the numerical tests prove the interest of the hybrid method EESPT and show that it is a correct compromise between quality of the error estimate, practical implementation and computational cost. Furthermore, the influence of the cost function involved in the EET and the EESPT is studied in order to optimize the estimators.

Toward 4D mechanical correlation

Abstract: The goal of the present study is to illustrate the full integration of sensor and imaging data into numerical procedures for the purpose of identification of constitutive laws and their validation. The feasibility of such approaches is proven in the context of in situ tests monitored by tomography. The bridging tool consists of spatiotemporal (i.e., 4D) analyses with dedicated (integrated) correlation algorithms. A tensile test on nodular graphite cast iron sample is performed within a lab tomograph. The reconstructed volumes are registered via integrated digital volume correlation (DVC) that incorporates a finite element modeling of the test, thereby performing a mechanical integration in 4D registration of a series of 3D images. In the present case a non-intrusive procedure is developed in which the 4D sensitivity fields are obtained with a commercial finite element code, allowing for a large versatility in meshing and incorporation of complex constitutive laws. Convergence studies can thus be performed in which the quality of the discretization is controlled both for the simulation and the registration. Incremental DVC analyses are carried out with the scans acquired during the in situ mechanical test. For DVC, the mesh size results from a compromise between measurement uncertainties and its spatial resolution. Conversely, a numerically good mesh may reveal too fine for the considered material microstructure. With the integrated framework proposed herein, 4D registrations can be performed and missing boundary conditions of the reference state as well as mechanical parameters of an elastoplastic constitutive law are determined in fair condition both for DVC and simulation.

New bounding techniques for goal-oriented error estimation applied to linear problems

Abstract: The paper deals with the accuracy of guaranteed error bounds on outputs of interest computed from approximate methods such as the finite element method. A considerable improvement is introduced for linear problems thanks to new bounding techniques based on Saint-Venant's principle. The main breakthrough of these optimized bounding techniques is the use of properties of homothetic domains which enables to cleverly derive guaranteed and accurate boundings of contributions to the global error estimate over a local region of the domain. Performances of these techniques are illustrated through several numerical experiments.

An enhanced method with local energy minimization for the robust a posteriori construction of equilibrated stress fields in finite element analyses

Abstract: In the context of global/goal-oriented error estimation applied to computational mechanics, the need to obtain reliable and guaranteed bounds on the discretization error has motivated the use of residual error estimators. These estimators require the construction of admissible stress fields verifying the equilibrium exactly. This article focuses on a recent method, based on a flux-equilibration procedure and called the element equilibration + star-patch technique (EESPT), that provides for such stress fields. The standard version relies on a strong prolongation condition in order to calculate equilibrated tractions along finite element boundaries. Here, we propose an enhanced version, which is based on a weak prolongation condition resulting in a local minimization of the complementary energy and leads to optimal tractions in selected regions. Geometric and error estimate criteria are introduced to select the relevant zones for optimizing the tractions. We demonstrate how this optimization procedure is important and relevant to produce sharper estimators at affordable computational cost, especially when the error estimate criterion is used. Two- and three-dimensional numerical experiments demonstrate the efficiency of the improved technique.

Digital Volume Correlation: Review of Progress and Challenges

Abstract: 3D imaging has become popular for analyzing material microstructures. When time lapse series of 3D pictures are acquired during a single experiment, it is possible to measure displacement fields via digital volume correlation (DVC), thereby leading to 4D results. Such 4D analyses have been performed for almost two decades. The present paper aims at reviewing the achievements of and challenges faced by such measurement technique. Ex-situ and in-situ experiments are discussed. A general and unified DVC framework is introduced. Various sources of measurement bias and uncertainties are analyzed. The current challenges are studied and some propositions are given to address them.

Iterative Global/Local Finite Element Analysis

Abstract: In spite of the advances in computer technology, there is still a need for more computationally efficient methods for performing stress analysis. One approach which is receiving increasing attention is global/local analysis. Such analyses can take a variety of forms. The form described herein uses two distinct meshes (one global and one local), but retains the same level of accuracy as one would obtain if one was to use a single refined global mesh. The accuracy is retained by using an iterative procedure to enforce equilibrium between the global and local regions. The procedure was tested for two configurations. The good performance observed indicates that the iterative global/local procedure warrants further examination.

Toward 4D mechanical correlation

Abstract: The goal of the present study is to illustrate the full integration of sensor and imaging data into numerical procedures for the purpose of identification of constitutive laws and their validation. The feasibility of such approaches is proven in the context of in situ tests monitored by tomography. The bridging tool consists of spatiotemporal (i.e., 4D) analyses with dedicated (integrated) correlation algorithms. A tensile test on nodular graphite cast iron sample is performed within a lab tomograph. The reconstructed volumes are registered via integrated digital volume correlation (DVC) that incorporates a finite element modeling of the test, thereby performing a mechanical integration in 4D registration of a series of 3D images. In the present case a non-intrusive procedure is developed in which the 4D sensitivity fields are obtained with a commercial finite element code, allowing for a large versatility in meshing and incorporation of complex constitutive laws. Convergence studies can thus be performed in which the quality of the discretization is controlled both for the simulation and the registration. Incremental DVC analyses are carried out with the scans acquired during the in situ mechanical test. For DVC, the mesh size results from a compromise between measurement uncertainties and its spatial resolution. Conversely, a numerically good mesh may reveal too fine for the considered material microstructure. With the integrated framework proposed herein, 4D registrations can be performed and missing boundary conditions of the reference state as well as mechanical parameters of an elastoplastic constitutive law are determined in fair condition both for DVC and simulation.

Big Data in Experimental Mechanics and Model Order Reduction: Today’s Challenges and Tomorrow’s Opportunities

Abstract: Since the turn of the century experimental solid mechanics has undergone major changes with the generalized use of images. The number of acquired data has literally exploded and one of today’s challenges is related to the saturation of mining procedures through such big data sets. With respect to digital image/volume correlation one of tomorrow’s pathways is to better control and master this data flow with procedures that are optimized for extracting the sought information with minimum uncertainties and maximum robustness. In this paper emphasis is put on various hierarchical identification procedures. Based on such structures a posteriori model/data reductions are performed in order to ease and make the exploitation of the experimental information far more efficient. Some possibilities related to other model order reduction techniques like the proper generalized decomposition are discussed and new opportunities are sketched.