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Simple Flow Rules for Three-Phase Viscoplastic Materials
No full textEditeur : Trans Tech Publications LtdInternational audienceNoting that there is very little literature on the topic, a first analytical approach is proposed in this work for estimating the viscosity-like parameter of three-phase viscoplastic materials. In a first part, the conditions of application and the consequences of the three classical averaging equations involving the strain rates, the stresses and the power are reviewed for 2-phase mixtures and extended to three phases. The classical static and Taylor bounds as well as the heuristic "Iso-strain rate" assumption are analyzed. An extension of the Mori-Tanaka estimation to the three-phase case is then proposed for viscoplastic linear constituents. If the volume fraction of one of the phases (inclusions) is very low, in particular when its viscosity tends towards zero or infinity, fully analytical results are presented, which provides an extension of the classical dilute model
Microstructural dependence and reduction of the size of the representative volume element in polycrystals: Case of cubic and hexagonal elasticity
No full textInternational audienceClosed-form expressions of the size of the representative volume element are determined for computing the elastic moduli of polycrystalline materials with cubic and hexagonal crystal symmetries. The size of the representative volume element corresponds to the number of grains needed in a polycrystal, N, to compute a property of the material (an elastic modulus) with a given error, e. The elastic moduli are computed using periodic polycrystals and finite element simulations. A typical, experimental grain-growth microstructure is considered as a reference case, and the microstructure properties are then modified. This allows us to determine the effect of the different microstructural properties on the error (e). The relationship between the error (e) and the size of the representative volume element (N) is shown to be e=a/√N, where a depends on both the crystal anisotropy of the material and the variability of the effective orientation distribution of the microstructure. This variability in turn arises from the cumulative effects of two main sources: the random sampling of the orientation distribution and the grain size distribution. Then, general expressions of a applying to all cubic and hexagonal-symmetry materials are determined. It is demonstrated that reducing the microstructural variability does not affect the computed elastic modulus values, thereby enabling the use of polycrystals with significantly fewer grains. For copper, the error in the computed shear modulus (e) can be reduced by a factor of 9.4 (for a given number of grains in a polycrystal, N), or equivalently, the number of grains needed in a polycrystal (N) can be reduced by a factor of about 90 (for a given error, e). Similar results are obtained for (hexagonal-symmetry) titanium and zinc, for which N can be reduced by factors of 140 and 45, respectively. The results also indicate that the size of the representative volume element (N) is smaller for hexagonal-symmetry materials than for cubic-symmetry materials, and smaller for the bulk modulus than for the shear modulus
An innovative setup to study the breakage of SiO2 agglomerates under shear stress
No full textInternational audienceGranular materials are involved in many industrial processes such as mixing, compaction, etc. When the granular material is in the form of agglomerates, i.e. an assembly of aggregates, particle fragmentation might occur under shear stress. This can either be a benefit for the process and should be controlled, or an issue which must be avoided. This paper focuses on the study of agglomerate breakage under shear stress, presenting a new experimental set-up designed for industrial contexts. The stress range selected lead to two distinct regimes: at low stresses, agglomerates break into individualized fragments, while high stresses fines agglomeration leads to the formation of flakes. These observations contribute to quantify the breakage stress of initial agglomerates, showing agreement with findings in the existing literature
Enhancing scalable reconfigurable manufacturing systems through robust optimisation: energy efficiency and cost minimisation under uncertainty
No full textInternational audienceReconfigurable manufacturing systems are dynamic systems designed with scalable and flexible production capabilities to address changing market demands. This paper presents a novel multi-objective integer programming model aimed at optimising the configuration and capacity scalability of reconfigurable machine tools in uncertain environments. The model focuses on minimising three key objectives: total energy consumption, unused capacity, and total cost. It incorporates critical manufacturing constraints such as peak power thresholds and limited tool availability. To effectively manage uncertainty, particularly in demand fluctuations, a scenario-based robust optimisation approach is applied, striking a balance between solution robustness and model adaptability. A comprehensive case study demonstrates the model's effectiveness, comparing deterministic and uncertain solutions. Additionally, sensitivity analyses are performed on parameters such as peak power thresholds, risk coefficients, and infeasibility weights, highlighting their impact on system performance. The results provide insights into the efficient design and operation of scalable reconfigurable manufacturing systems under uncertainty, with recommendations for future research directions
Large-scale constrained Gaussian processes for shape-restricted function estimation
No full textInternational audienceIn this paper, we revisit the problem of Bayesian shape-restricted function estimation. The finite-dimensional Gaussian process (GP) approximation proposed in Maatouk and Bay (2017) is considered, which admits an equivalent formulation of the shape constraints in terms of basis coefficients. This approximation satisfies a wide variety of shape constraints everywhere, whether applied alone, in combination, or sequentially. We propose a new, efficient, and fast algorithm for sampling from a large Gaussian vector extracted from a stationary GP. The proposed approach significantly improves the novel circulant embedding technique proposed in Ray et al (2020) for efficiently sampling from the resulting posterior constrained distribution. The main idea of the algorithm developed in the present paper is to divide the input domain into smaller subdomains and apply a cross-correlated technique to address the correlation structure in the entire domain. As the number of subdomains increases, the computational complexity is drastically reduced. The developed algorithm is accurate and efficient, as demonstrated through comparisons with competing approaches. The performance of the proposed approach has been evaluated within the context of shape-restricted function estimation
Une infrastructure multi-agents pour coupler des environnements robotiques physiques et numériques
No full textInternational audienceThis paper presents a multi-agent based infrastructure achieving a seamless coupling between physical and digital environments, enabling effective synchronization and control of robotic systems. The proposed infrastructure introduces agents to act on behalf of physical and digital robots, facilitating real-time interaction and coordination between both environments. The infrastructure is validated through a motivating scenario using a programming framework for hypermedia multi-agent systems, that offers a solid framework for controlling and deploying agents on a robotic platform.Cet article présente une infrastructure multi-agents pour un couplage transparent entre des environnements physiques et numériques pour la conception de systèmes robotiques. Notre objectif est de mettre à disposition une infrastructure unique pour la synchronisation et le contrôle de robots exécutés sur des plateformes existantes qu’ils soient réels ou numériques. L’infrastructure proposée introduit des agents pour agir au nom des robots physiques et numériques à des fins de conception d’un nouveau système robotique. Déployés dans la plateforme de programmation multi-agents Hypermedea, ces agents simplifient la tâche du concepteur en facilitant la mise en place de mécanismes pour l’interaction et la coordination en temps réel entre lesdeux environnements sans avoir à considérer les spécificités techniques de chacun d’eux. Le fonctionnement de l’infrastructure est illustré par unscénario de synchronisation entre un robot numérique et un robot physique dans le domaine de l’industrie 4.
Bayesian optimization with derivatives acceleration
No full textGuillaume Perrin, first author. Rodolphe Le Riche, second author, invited speaker of the workshop.National audienceBayesian optimization algorithms form an important class of methods to minimize functions that are costly to evaluate, which is a very common situation. These algorithms iteratively infer Gaussian processes from past observations of the function and decide where new observations should be made through the maximization of an acquisition criterion. Often, in particular in engineering practice, the objective function is defined on a compact set such as in a hyper-rectangle of a d-dimensional real space, and the bounds are chosen wide enough so that the optimum is inside the search domain. In this situation, this work provides a way to integrate in the acquisition criterion the a priori information that these functions, once modeled as GP trajectories, should be evaluated at their minima, and not at any point as usual acquisition criteria do. We propose an adaptation of the widely used Expected Improvement acquisition criterion that accounts only for GP trajectories where the first order partial derivatives are zero and the Hessian matrix is positive definite. The new acquisition criterion keeps an analytical, computationally efficient, expression. This new acquisition criterion is found to improve Bayesian optimization on a test bed of functions made of Gaussian process trajectories in dimensions 2, 3 and 5. The addition of first and second order derivative information is particularly useful for multimodal functions
Multiscale micromechanical study of polymer core solder ball for BGA interconnections reliability
No full textInternational audiencePolymer core solder balls (PCSB) are among the most promising lead-free solder solutions for the optimization of assembly reliability. This type of solder ball is produced through electroless plating processes, which result in specific deposit microstructures as well as unique mechanical properties. However, the properties of bulk materials are often attributed to them, leading to inaccurate predictive modeling of interconnection lifespan. This study focuses on the mechanical characterization of PCSB across representative scales. First, at the microscopic scale, the characterization of the mechanical properties (Young’s modulus (Ε) and yield strength (σ)) of two coatings (Cu, Ni-P) is conducted by in-situ micro-mechanical tests (micropillar compression and nanoindentation). Then, at the mesoscopic scale, the aforementioned properties are validated by applying a compressive load to a PCSB solder ball. All these mechanical data were then used to feed predictive models of assembly service life. Finally, a comparison was made between PCSBs and standard SAC balls in terms of interconnection fatigue life
