Pierre Feissel

Estimation of the strain field from full-field displacement noisy data

In this study, the issue of reconstructing strain fields from corrupted full-field displacement data is addressed. Two approaches are proposed, a global one based on Finite Element Approximation (FEA) and a local one based on Diffuse Approximation (DA). Both approaches are compared on a case study which is supposed difficult (open-hole tensile test). DA provides more stable results, but is more CPU time consuming. Eventually, it is proposed to monitor locally the filtering effect of both approaches, the prospects being an impending improvement of the reconstruction for both approaches.

Comparison of two approaches for differentiating full-field data in solid mechanics

In this study, the issue of reconstructing the gradients of noisy full-field data is addressed within the framework of solid mechanics. Two approaches are considered, a global one based on finite element approximation (FEA) and a local one based on diffuse approximation (DA). For both approaches, it is proposed to monitor locally the filtering effect in order to adapt the uncertainty to the local signal to noise ratio. Both approaches are applied to a case study which is commonly considered as difficult in solid mechanics (open-hole tensile test on a composite laminate). Both DA and FEA are successful for detecting local subsurface damage from the measured noisy displacement fields. Indications are also provided about the compared performances of DA and FEA. It is shown that DA is more robust, but the downside is that it is also more CPU time consuming.

Identification strategy in the presence of corrupted measurements

– To propose and develop an identification method of material parameters from dynamics test in the presence of extensively corrupted measurements., – The method we propose, which is based on the use of the error in constitutive relation for identification problems in the framework of transient dynamics, leads to nonstandard wave propagation problems. For solving this numerical difficulty, we used the transition matrix method for short‐duration tests and the combined Riccati constant/transition matrix approach for long‐duration tests., – A numerical strategy adapted to the problem. Results obtained appears to be insensitive to perturbation of measurements up to a very high level of perturbation., – Only simple case of elastic bar have been treated so far., – Without any a priori information on the level of perturbation, this method is robust with respect to the perturbation. A coupling of two resolution methods allows to deal with problem of arbitrary duration.

A robust identification strategy for rate-dependent models in dynamics

The motivation of the paper is to develop a method allowing us to make use, in the context of identification, of highly perturbed tests leading to non-reliable measurements. Such tests are not seldom especially when dealing with structural fracture in dynamics. We follow here the concept of the modified constitutive relation error (MCRE) [1] where error on the model and error on the experimental data are both introduced. A first paper was devoted to the extension of the MCRE method to transient elasticity [2]. This paper is devoted to the extension to nonlinear constitutive relations, in particular viscoplasticity and damage. The MCRE formulation in transient dynamics leads to the solving of a coupled direct and adjoint nonlinear problem, which implies dedicated methods, which is the core of this paper. This has led us to define a particular MCRE formulation well suited for numerical treatment and to develop an extension of the LATIN method [3] to ill-posed problems. Once the difficulties have been resolved and the formulation implemented in the one-dimensional case, the proposed identification strategy appears to be very robust with respect to perturbed measurements in the absence of a priori knowledge, even in the case of localization and rupture.

Development of an Inverse Approach for the Characterization of In Vivo Mechanical Properties of the Lower Limb Muscles

The purpose of this study was to develop an inverse method, coupling imaging techniques with numerical methods, to identify the muscle mechanical behavior. A finite element model updating (FEMU) was developed in three main interdependent steps. First, a 2D FE modeling, parameterized by a Neo-Hookean behavior (C10 and D), was developed from a segmented thigh muscle 1.5T MRI (magnetic resonance imaging). Thus, a displacement field was simulated for different static loadings (contention, compression, and indentation). Subsequently, the optimal mechanical test was determined from a sensitivity analysis. Second, ultrasound parameters (gain, dynamic, and frequency) were optimized on the thigh muscles in order to apply the digital image correlation (DIC), allowing the measurement of an experimental displacement field. Third, an inverse method was developed to identify the Neo-Hookean parameters (C10 and D) by performing a minimization of the distance between the simulated and measured displacement fields. To replace the experimental data and to quantify the identification error, a numerical example was developed. The result of the sensitivity analysis showed that the compression test was more adapted to identify the Neo-Hookean parameters. Ultrasound images were recorded with a frequency, gain, and dynamic of 9 MHz, 34 dB, 42 dB, respectively. In addition, the experimental noise on displacement field measurement was estimated to be 0.2 mm. The identification performed on the numerical example revealed a low error for the C10 (<3%) and D (<7%) parameters with the experimental noise. This methodology could have an impact in the scientific and medical fields. A better knowledge of the muscle behavior will help to follow treatment and to ensure accurate medical procedures during the use of robotic devices.

Identification of elastic properties from full-field measurements: a numerical study of the effect of filtering on the identification results

The use of full-field displacement measurements in mechanical testing has increased dramatically over the last two decades. This is a result of the very rich information they provide, which is enabling new possibilities for the characterization of material constitutive parameters for inhomogeneous tests often based upon inverse approaches. Nonetheless, the measurement errors limit the accuracy of the identification of the constitutive parameters and their possible spatial resolution. The question addressed by this work is the following: can a filtering of the displacement measurement improve the results of the identification of elastic properties? The discussion is based on the study of a numerical example where the elastic parameters of an elastic structure with inhomogeneous properties are sought from synthetic data representative of in-plane full-field data. The displacement data are first filtered through a diffuse approximation algorithm, based on a moving least-squares approximation. Then, the identification of the elastic parameters is performed by an inverse approach based on the minimization of a cost function, defined as the least-squares gap between the experimental data and their numerical counterpart (finite element model updating). Within this framework, a first-order analysis is proposed in order to characterize the errors in the identified parameters, the measurement error characteristics being known. Results from raw and filtered displacement data are compared and discussed, filtering improving the identification for lower spatial resolution. The choice of the norm to define the gap between the experiment and the calculation is also discussed. For practical use and to take advantage of the proposed first-order methodology, two different ways can be considered: applying the methodology to a numerical example, representative of the experimental setup, to determine whether or not a filtering is valuable, and estimating the uncertainties of the identified parameters at the end of the identification process of an experimental characterization.

Use of digital image correlation and ultrasound: analysis of thigh muscle displacement fields

The understanding of the mechanical behavior of the muscle tissue is an important field of investigation with different applications in medicine, car crash and sport. Currently, few in vivo imaging techniques are able to characterize the mechanical properties of muscle. Thus, the development of an in vivo identification method is a current thematic where the displacement field measurements could be used for further interpretations. This study aims at presenting the displacement fields measured in the anterior, posterior, lateral and medial parts of the thigh muscles using ultrasound and Digital Image Correlation (DIC) techniques. The results of the displacement field measurements confirmed and are correlated with the ultrasound observations.

Identification of hyperelastic properties of passive thigh muscle under compression with an inverse method from a displacement field measurement

The mechanical behavior of muscle tissue is an important field of investigation with different applications in medicine, car crash and sport, for example. Currently, few in vivo imaging techniques are able to characterize the mechanical properties of muscle. Thus, this study presents an in vivo method to identify a hyperelatic behavior from a displacement field measured with ultrasound and Digital Image Correlation (DIC) techniques. This identification approach was composed of 3 inter-dependent steps. The first step was to perform a 2D MRI acquisition of the thigh in order to obtain a manual segmentation of muscles (quadriceps, ischio, gracilis and sartorius) and fat tissue, and then develop a Finite Element model. In addition, a Neo-Hookean model was chosen to characterize the hyperelastic behavior (C10, D) in order to simulate a displacement field. Secondly, an experimental compression device was developed in order to measure the in vivo displacement fields in several areas of the thigh. Finally, an inverse method was performed to identify the C10 and D parameters of each soft tissue. The identification procedure was validated with a comparison with the literature. The relevance of this study was to identify the mechanical properties of each investigated soft tissues.

Modified Constitutive Relation Error Strategy for Elastic Properties Identification

The aim of this paper is to present an inverse approach dedicated to the exploitation of full-field measurements, to identify elastic properties of heterogeneous materials, such as composites. The method is based on the modified constitutive relation error principle and could be split in two steps. The first one consists in defining mechanical fields from the available theoretical and experimental data, for a fixed set of mechanical parameters, by the minimization of a criterion allowing a compromise between constitutive equation and measurements adequacy. The second step takes the form of minimizing a cost function defined by using these fields, to identify the sought material properties. Moreover, the robustness of the method was tested on some numerical examples where white Gaussian perturbations were added to displacement values to simulate an experimental errors.

Identification of elastic properties in the belief function framework

Abstract Handling the uncertainty of information sources is a key issue in parameter identification. In this work, we address this issue using the theory of belief functions. First, measurement information is described through likelihood-based belief functions, and prior information is represented by an arbitrary belief function. Second, both belief functions are combined by Dempsters rule using point-cloud representation of focal sets and Monte Carlo simulation. Lastly, to summarize the combined belief function, we propose to find the minimal-area region in the parameter space, whose belief and plausibility values exceed given thresholds. As compared to Bayesian inference, this approach is more flexible, as it allows us to specify weak prior information. Experimental results show that it is also more robust than Bayesian inference to unreliable prior information.