Laboratoire de Mécanique Gabriel Lamé

This paper aims to model the effective viscoelastic properties of micro-cracked materials based on the homogenization micro-macro approach. The isotropic case with random orientation and parallel distribution of micro-cracks in Burger and generalized Kelvin non-ageing linear viscoelastic solids was recently considered. To complete these works, this paper develops a model to estimate viscoelastic properties of materials that are constituted of two phases: a non-cracked phase described by Generalized Maxwell model and micro-cracks. The methodology consists in an approximation by using the same Generalized Maxwell model of the non-cracked phase for the overall cracked material. The crucial advantage of this technique is to avoid the complexity of the inverse Laplace–Carson (LC) transform. The approximation is carried out in short- and long-term behaviors in the LC space and validated in transient situation with exact solution obtained from the inverse LC transform in simple loading condition. Useful explicit formulas are provided for calculation of effective viscoelastic properties of isotropic micro-cracked media.

The aim of this paper is to model the effective viscoelastic properties of micro-cracked masonry based on a homogenization approach. The masonry is modeled as a mixture of a micro-cracked viscoelastic mortar matrix and isotropic elastic brick inclusions. Firstly, the effect of micro-cracks on the effective viscoelastic properties of mortar is considered at micro-scale. Secondly, brick inclusions are added in the micro-cracked mortar matrix at mesoscale to simulate effective viscoelastic properties of masonry. The modified Maxwell viscoelastic model is employed for noncracked, micro-cracked mortar matrix and micro-cracked masonry. The use of the same modified Maxwell model of the noncracked mortar to model the viscoelastic properties of the micro-cracked mortar is an approximation. This approximation is carried out in the short- and the long-term behaviors in the Laplace–Carson space. It is validated in transient situation with exact solutions obtained from the inverse Laplace–Carson transform for simple loading conditions. This technique allows avoiding the complexity of the inverse Laplace–Carson transform. The isotropic case with random orientation distribution of open micro-cracks in mortar and with spherical brick inclusions is considered.

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In the past few decades, vibration-based structural damage detection (SDD) has attracted widespread attention. Using the response data of engineering structures, the researchers have developed many methods for damage localization and quantification. Adopting meta-heuristic algorithms, in which particle swarm optimization (PSO) is the most widely used, is a popular approach. Various PSO variants have also been proposed for improving its performance in SDD, and they are generally based on the Global topology. However, in addition to the Global topology, other topologies are also developed in the related literature to enhance the performance of the PSO algorithm. The effects of PSO topologies depend significantly on the studied problems. Therefore, in this article, we conduct a performance investigation of eight PSO topologies in SDD. The success rate and mean iterations that are obtained from the numerical simulations are considered as the evaluation indexes. Furthermore, the average rank and Bonferroni-Dunn’s test are further utilized to perform the statistic analysis. From these analysis results, the Four Clusters are shown to be the more favorable PSO topologies in SDD.

Health surveillance in industries is an important prospect to ensure safety and prevent sudden collapses. Vibration Based Structure Health Monitoring (VBSHM) is being used continuously for structures and machine diagnostics in industry. Changes in natural frequencies are frequently used as an input parameter for VBSHM. In this paper, the frequency shift coefficient (FSC) is used for the assessment of various numerical damaged cases. An FSC-based algorithm is employed in order to estimate the positions and severity of damages using only the natural frequencies of healthy and unknown (damaged) structures. The study focuses on cantilever beams. By considering the minimization of FSC, damage positions and severity are obtained. Artificially damaged cases are assessed by changes in its positions, the number of damages and the size of damages along with the various parts of the cantilever beam. The study is further investigated by considering the effect of uncertainty on natural frequencies (0.1%, 0.2% and 0.3%) in damaged cases, and the algorithm is used to estimate the position and severity of the damage. The outcomes and efficiency of the proposed FSC based method are evaluated in order to locate and quantify damages. The efficiency of the algorithm is demonstrated by locating and quantifying double damages in a real cantilever steel beam using vibration measurements.

Usually, within stochastic framework, a testing dataset is used to evaluate the approximation error between a surrogate model (e.g., a polynomial chaos expansion) and the exact model. We propose here another method to estimate the quality of an approximated solution of a stochastic process, within the context of structural dynamics. We demonstrate that the approximation error is governed by an equation based on the residue of the approximate solution. This problem can be solved numerically using an approximated solution, here a coarse Monte Carlo simulation. The developed estimate is compared to a reference solution on a simple case. The study of this comparison makes it possible to validate the efficiency of the proposed method. This validation has been observed using different sets of simulations. To illustrate the applicability of the proposed approach to a more challenging problem, we also present a problem with a large number of random parameters. This illustration shows the interest of the method compared to classical estimates.

The main aim of this paper was to reproduce the frictional behaviour that occurred in milling with a pin-on-cylinder system. Three different tribological tests were conducted reproducing friction phenomenon that happened in three machining conditions: (i) dry rubbing, representing the dry machining condition, (ii) MQL applied to front face rubbing which was similar to milling with MQL applied on the insert rake face and (iii) MQL applied to rear end rubbing which was similar to milling with MQL applied on flank face. Tribological tests were carried out with coated tungsten carbide pins rubbing on X100CrMoV5 steel cylinder. Apparent coefficient of friction, adhesion area and heat flux transmitted to the pin were analysed. It has been shown that MQL rear end rubbing provided a lower adhesion area and lower apparent coefficient of friction than with MQL front face rubbing. Furthermore, MQL rear end rubbing resulted in a greater cooling ability. These findings helped to explain why better results were obtained with MQL flank face lubrication in milling compared to MQL rake face lubrication.

DYNAMIC ANALYSIS OF PERIODIC STRUCTURES AND METAMATERIALS VIA WAVE APPROACHES AND FINITE ELEMENT PROCEDURES - 8th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering - 28-30 June 2021, Streamed from Athens, Greece

Composite materials can be produced by several technologies, such as Liquid Composite Manufacturing (LCM). In this technology, a fabric can be formed by highly double curved punch geometries. During its forming, the fabric is submitted to several deformations and mechanical stresses, like biaxial tensile stress, shear, bending, compaction and friction. The cumulative effect of these stresses leads to the appearance of different types of defects such as wrinkles, buckles, sliding, etc. These defects may have a significant influence on the mechanical properties of the final composite materials. In order to understand the forming mechanisms of these defects, as well as their effect on the behavior of composite materials, an experimental machine was designed and built. The aim of this machine is to generate different types of defects with controlled and adjusted amplitudes (calibrated defects), in samples of a fabric. These samples are then used to manufacture composite samples with calibrated defects, by an LCM process. The defected composite samples are then tested and compared with composite samples without defects. The obtained results have identified the experimental parameters corresponding to the appearance of different types of defects.

Abstract The spatio-temporal evolution of the shock wave generated by a laser induced breakdown is often investigated and interpreted in the framework of the theory of shock similarity solutions. This work is a discussion about the choice of the most relevant geometry (spherical or cylindrical) to be used in the Jones modelling to track the intermediate-strength shockwave trajectory coming from a laser-induced non-resonant breakdown in argon. Laser incident energies ranging from 10 to 200 mJ with initial pressure of argon from 250 to 2500 mbar are investigated using a Q-switched Nd:YAG laser operating at a wavelength of 532 nm with a 6 ns pulse duration. Experimental results show that using the radial component <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>r</mml:mi> <mml:mi>b</mml:mi> </mml:msub> </mml:mrow> </mml:math> of the ellipsoidal shape of the shockwave with a cylindrical geometry best describes the shockwave trajectory over time. Moreover, the deduced characteristic length <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>r</mml:mi> <mml:mn>0</mml:mn> </mml:msub> </mml:mrow> </mml:math> allows us to observe a shockwave shape similarity for all tested laser energies at a given pressure.

Interest in the design of products that link performance and comfort is rapidly growing in the field of sport. To this end, the equipment industry is progressively shifting towards customization and it is focusing on man-machine interaction. The notion itself remains insufficiently studied by the scientific community. With regard to golf, several works conclude that vibrations that are perceived in the handle may be harmful and they have significant influence on comfort as well as performance. In that respect, the present paper investigates the effects of grip strength on three indicators of club dynamics: modal characteristics, overall vibratory levels, and vibration dose perceived by the club user, according to ISO 5349 standard. The study can be broken down into three steps. First, the experimental modal characteristics of a golf club are identified while using free-free, fixed-free, and grip-free (with three levels of grip strength) boundary conditions. Subsequently, a numerical model is developed and updated using experimental results. Finally, the root mean squared values and vibration dose transmitted to the hand-arm system after ball contact are extracted from the validated numerical model.

Abstract A modelling of the laser-induced breakdown spatial location is presented and compared to experiments where the considered variables are the incident laser energy and the initial pressure of argon in the vessel. The proposed modelling is based on the assumption that the conservation of the threshold laser energy per unit surface needs to produce a breakdown. The experiment consists in 100 consecutive laser shots for eight laser energies from 4.48 to 147.81 mJ at λ = 532 nm and four initial pressures, from 0.25 to 1 bar. A dimensionless number, E / E th , is also proposed to compare all obtained data to each other with E the incident energy and E th the threshold energy below the one no breakdown appears. The proposed modelling is in good agreement with observed values (&lt;10% in most experiments) and is particularly interesting for laser-induced breakdown spectroscopy in gas where the location of the plasma is of great importance.

Based on the association of finite elements homogenization method and a rigorous homogenization scheme accounting for crack interactions, this paper provides rigorous predictions for the local and effective properties of microcracked viscoelastic masonry with or without creep of bricks. For the sake of simplicity, viscoelastic brick and mortar are assumed to follow the Generalized Maxwell rheological model and to be respectively safe and microcracked. In the mortar, the distribution of microcracks orientations is assumed to be random. Two steps are followed. The first one is based on the identification at the short and long terms of an approximate analytical creep function for the mortar. This step relies on the coupling between the Griffith’s brittle fracture theory and a rigorous homogenization scheme - the Ponte Castañeda &amp; Willis model - accounting for crack interaction instead of the dilute scheme adopted previously in Rekik et al. Two cases are considered: open and closed cracks. The first step allows to avoid recourse to 'heavy' numerical inversion of the Laplace-Carson transform. The second one provides overall creep coefficients of masonry by means of periodic homogenization carried out by finite elements method. For open cracks state, time-dependent crack density is investigated. The proposed model is validated by comparison with an analytical one available for a compressed masonry wall with "standard" viscoelastic mortar joints. Effect induced by microcracks is also highlighted by comparison with uncracked masonry. At last, results provided by the proposed model can be considered to be rigorous solution improving on dilute estimates for the creep behavior of microcracked mortar and demonstrating the interest to not neglect both cracks interactions and creep of bricks units.

The study of the nonlinear dynamic behaviour of friction systems in general and of clutch systems in particular remains an open problem. Noise and vibrations induced by friction in the sliding phase of a clutch are very sensitive to design parameters. The latter have significant dispersions. In the study of the system stability, the problem is not only to know if the parameter values lead to the appearance of unstable equilibrium points; the real challenge lies in estimating the vibration levels when such unstable equilibrium points occur. This estimation is analyzed using the limit cycles. This article aims to study the ability of robust approaches based on developments in nonintrusive generalized polynomial chaos and a constrained harmonic balance method to estimate the vibration levels through the limit cycles of a clutch system in the presence of uncertainty. The purpose is to provide a low-cost, high precision approach, compared to the classic Monte Carlo method.

This study deals with the experimental investigation and the modelling of the behaviour of an aggregate composite material used as a simulant for Plastic-Bonded Explosives (PBX). At first, a large experimental campaign was conducted using some original experimental protocols. These tests include: tension, compression, alternated tension/compression, triaxial compression, compression 0°-90°-0°, channel-die, torsion and confined torsion. The experimental results highlighted different aspects of behaviour: damage induced anisotropy, effectivity, viscoelasticity, hysteresis cycles, sensitivity to hydrostatic pressure and presence of irreversible strains. At second, a damageable viscoelastic plastic model was proposed using microplane formulation. This model was implemented in finite element software (Abaqus/Standard). The tests were then simulated and the results compared to the experimental data, and then discussed. Finally, two failure criteria that govern the failure of the studied materials were identified. These criteria were initially developed in the literature for concrete materials that present a microstructure and behaviour similar to those of aggregate materials.

ABSTRACT The transition from normal (surface) to abnormal (convective) burning modes of explosives is still a difficult phenomenon to model. This transition, which yields the acceleration of the combustion propagation, could result in a violent reaction. Nowadays, abnormal burning is interpreted as an increase in burning surface area. The latter depends on the initial state of the microstructure and therefore of the mechanical history. This paper considers the coupling between the combustion of HMX‐based polymer‐bonded explosives and its previous mechanical loadings. The experimental set‐ups used to (1) apply a triaxial compression (that mimics the mechanical fields experienced by the explosive composition when submitted to a Steven test) and (2) burn the samples in a closed vessel will be described. Experiments show a strong dependence on the critical pressure leading to abnormal combustion on a previous mechanical loading. An analytical model is proposed to determine the real‐time burning surface area during combustion. It enables modelling of the increase in surface area increase when the critical pressure is reached. Experimental results and surface determinations are presented in this paper. Future works will be discussed.

The objectives of the thesis are to characterize and model the piezoresistive behavior of carbon nanotubes elastomeric composites under quasi-static and dynamic compression. This work was supported by the CLEBER project partners: the Gabriel Lamé laboratory and ATCOM Télémétrie. In particular, we have sought the microstructural mechanisms at the origin of the piezoresistive behavior of such composites. An increase of the electrical resistance was observed under quasi-static compression forces. This behavior is attributed to reorientations of the CNT network during the test, leading to an increase of the distances between CNT. Furthermore, the carbon nanotube weight fraction was related to the electrical sensitivity of the composites. Dynamic compression tests were carried out on a Split Hopkinson Pressure Bars apparatus. High strain rates in these tests cause damage of the composites, characterized by a dramatic increase in the electrical resistance and a loss in the elastic modulus. To model the piezoresistive behavior, the carbon nanotube network is described by a resistor network representation. The change of the conductive network, i.e. movements of carbon nanotubes, is determined using simulations on the LS-Dyna finite element code. A decoupling hypothesis between the matrix and the carbon nanotubes is used to compute the displacements of the carbon nanotubes.

The material parameters identification procedure usually takes benefit of measured kinematicfield obtained by non intrusive techniques. In dynamics, such a procedure can be challengingbecause of the important flow of information to take into account. By the way, the reliability of thosemeasured information is likely to define the quality of the parameters identified. In this work, we developtwo new numerical tools in order to simplify the identification procedure in term of numericaland experimental implementation. The first tool, based on the virtual fields method, leads to a smallsystem inversion. This method allows one to significantly decrease the cost of one identification. Thismethod is compared to the finite element model updating method in linear elasticity. The second toolis a geometrical approach of the finite element model updating method. This new method aim atovercoming the deposit of a random speckle and of simplifying image processing associated with thedigital image correlation technique. Results demonstrate that the method is adapted to the frameworkof dynamics in large transformations. Both numerical tools are assessed in term of robustness andaccuracy when different kind of uncertainties are considered.

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This thesis presents a probabilistic approach to modelling the mechanics of materials and structures where the modelled performance is influenced by uncertainty in the input parameters. The work is interdisciplinary and the methods described are applied to medical and civil engineering problems. The motivation for this work was the necessity of mechanics-based approaches in the modelling and simulation of implants used in the repair of ventral hernias. Many uncertainties appear in the modelling of the implant-abdominal wall system. The probabilistic approach proposed in this thesis enables these uncertainties to be propagated to the output of the model and the investigation of their respective influences. The regression-based polynomial chaos expansion method is used here. However, the accuracy of such non-intrusive methods depends on the number and location of sampling points. Finding a universal method to achieve a good balance between accuracy and computational cost is still an open question so different approaches are investigated in this thesis in order to choose an efficient method. Global sensitivity analysis is used to investigate the respective influences of input uncertainties on the variation of the outputs of different models. The uncertainties are propagated to the implant-abdominal wall models in order to draw some conclusions important for further research. Using the expertise acquired from biomechanical models, modelling of historic timber joints and simulations of their mechanical behaviour is undertaken. Such an investigation is important owing to the need for efficient planning of repairs and renovation of buildings of historical value.