Theoretical and numerical comparison of hyperelastic and hypoelastic formulations for Eulerian non-linear elastoplasticity

The aim of this paper is to compare a hyperelastic with a hypoelastic model describing the Eulerian dynamics of solids in the context of non-linear elastoplastic deformations. Specifically, we consider the well-known hypoelastic Wilkins model, which is compared against a hyperelastic model based on the work of Godunov and Romenski. First, we discuss some general conceptual differences between the two approaches. Second, a detailed study of both models is proposed, where differences are made evident at the aid of deriving a hypoelastic-type model corresponding to the hyperelastic model and a particular equation of state used in this paper. Third, using the same high order ADER Finite Volume and Discontinuous Galerkin methods on fixed and moving unstructured meshes for both models, a wide range of numerical benchmark test problems has been solved. The numerical solutions obtained for the two different models are directly compared with each other. For small elastic deformations, the two models produce very similar solutions that are close to each other. However, if large elastic or elastoplastic deformations occur, the solutions present larger differences.Comment: 14 figure

Convergence and Sensitivity Analysis of Repair Algorithms in 1D

International audienceWe prove the convergence of some repair algorithms for linear advection in dimension one. The convergence depends on the size of the box where the distribution of the mass excess is performed. Various numerical examples illustrate the theoretical results. Applications to gas dynamics in dimension one is also discussed

Scholarly Communication and Documentary Fragmentations in the Public Space: a Functional Citation Study

This paper studies how academic content published in Open Edition.org, an online publication platform in the Social Sciences and Humanities is re-appropriated by members of the public. Our research is therefore concerned with the public appropriation of science and Open science. After extracting the contexts of citation of these content and mapping them, we propose a typology of citation functions as well as of citers (their origins and types). Our preliminary results indicated that academic literature is repurposed and cited by members of the public mainly as scientific warrant (support for their argumentation). We also found that academic content is cited in all types of web documents including blogs, press releases, book reviews, newspaper articles, scientific articles, discussion forums, library catalogs, government agencies or ministries. Finally, we looked at that the elapsed time between the publication of an academic content and its citation in the public arena and found that this follows the already observed citations patterns within the scientific community (sleeping beauties, long tail, unexpected reader, silent conversation)

Multi-dimensional Optimal Order Detection (MOOD) — A very high-order Finite Volume Scheme for conservation laws on unstructured meshes.

Preprint for Finite Volume for Complex Applications 6 (FVCA6)The Multi-dimensional Optimal Order Detection (MOOD) method is an original Very High-Order Finite Volume (FV) method for conservation laws on unstructured meshes. The method is based on an a posteriori degree reduction of local polynomial reconstructions on cells where prescribed stability conditions are not fulfilled. Numerical experiments on advection and Euler equations problems are drawn to prove the efficiency and competitiveness of the MOOD method

« Musa levis gloria magna » : la recusatio chez les poètes élégiaques des Lumières

Les cheveux flottants, l’élégie a traversé les siècles de sa démarche inégale, et fait résonner ses chants déliés sans jamais se fixer en un lieu. Comme son inspiration, ses inflexions sont vagabondes mais reconnaissables à leur étrange façon d’imposer leur légèreté avec une morgue discrète. Peu de formes poétiques ont poussé aussi loin l’art de cultiver l’indécision sur l’ambition qu’elles poursuivent : à l’âge classique, l’élégie reste le genre insaisissable apparu lorsque les poètes antiques ont brigué une gloire en dehors de la grande tradition héroïque et donné au roman du cœur ses lettres de noblesse poétiques. Ses diverses métamorphoses et les débats qui ont accompagné sa survie littéraire n’ont jamais effacé cette ambiguïté constitutive, qui fait d’elle un genre en quête de reconnaissance dans un système de hiérarchie qu’elle contribue, de par son existence même, à renverser. C’est ainsi qu’au xviiie siècle, l’élégie a participé de près à l’effervescence problématique de la poésie, en un siècle dont la métromanie peut se comprendre à la fois comme signe d’une vigueur et comme symptôme d’un déclin. Dans ce contexte, l’élégie a focalisé un certain nombre de questions qui renvoient plus ou moins directement à la « crise de la poésie » qui affecte le siècle.Hair unbound, the elegy has crossed the centuries with an uneven step, its nimble melodies reverberating but never confining themselves to a single place. Its inflections, like its inspiration, are erratic but discernible for their odd way of imposing their gracefulness with a discrete hauteur. In few poetic forms has the art of cultivating indecision about the objective pursued been taken so far: in the Enlightenment, the elegy remains the elusive genre that appeared when the poets of Antiquity sought glory outside the great heroic tradition and accorded the romance a poetic status. Its various metamorphoses and the debates accompanying its literary survival have never erased that constitutive ambiguity, making the elegy a genre seeking recognition in a system of hierarchy that its very existence helped overthrow. Thus, the elegy was an important factor in the problematic effervescence of poetry in the eighteenth century, a time when metromania was understood as both a sign of vigor and a symptom of decline. In this context, the elegy focused on a certain number of questions that refer, more or less directly, to the “crisis of poetry” that marked the century

A high-order finite volume method for hyperbolic systems: Multi-dimensional Optimal Order Detection (MOOD).

International audienceIn this paper, we investigate an original way to deal with the problems generated by the limitation process of high-order finite volume methods based on polynomial reconstructions. Multi-dimensional Optimal Order Detection (MOOD) breaks away from classical limitations employed in high-order methods. The proposed method consists of detecting problematic situations after each time update of the solution and of reducing the local polynomial degree before recomputing the solution. As multi-dimensional MUSCL methods, the concept is simple and independent of mesh structure. Moreover MOOD is able to take physical constraints such as density and pressure positivity into account through an “a posteriori” detection. Numer- ical results on classical and demanding test cases for advection and Euler system are presented on quadrangular meshes to support the promising potential of this approach

The MOOD method in the three-dimensional case: Very-High-Order Finite Volume Method for Hyperbolic Systems.

The Multi-dimensional Optimal Order Detection (MOOD) method for two-dimensional geometries has been introduced in "A high-order finite volume method for hyperbolic systems: Multi-dimensional Optimal Order Detection (MOOD)", J. Comput. Phys. 230 (2011), and enhanced in "Improved Detection Criteria for the Multi-dimensional Optimal Order Detection (MOOD) on unstructured meshes with very high-order polynomials", Comput. & Fluids 64 (2012). We present in this paper the extension to 3D mixed meshes composed of tetrahedra, hexahedra, pyramids and prisms. In addition, we simplify the u2 detection process previously developed and show on a relevant set of numerical tests for both the convection equation and the Euler system that the optimal high-order of accuracy is reached on smooth solutions while spurious oscillations near singularities are prevented. At last, the intrinsic positivity-preserving property of the MOOD method is confirmed in 3D and we provide simple optimizations to reduce the computational cost such that the MOOD method is very competitive compared to existing high-order Finite Volume methods

Three-dimensional preliminary results of the MOOD method: A Very High-Order Finite Volume method for Conservation Laws.

The Multi-dimensional Optimal Order Detection (MOOD) method has been designed by authors in [5] and extended in [7] to reach Very-High-Order of accuracy for systems of Conservation Laws in a Finite Volume (FV) framework on 2D unstructured meshes. In this paper we focus on the extension of this method to 3D unstructured meshes. We present preliminary results for the three-dimensional advection equation which confirm the good behaviour of the MOOD method. More precisely, we show that the scheme yields up to sixth-order accuracy on smooth solutions while preventing oscillations from appearing on discontinuous profiles