Modèle de Gurson à matrice de Coulomb et Drucker-Prager : solutions exactes sous chargement isotrope

Alors que la solution du problème d'analyse limite du modèle sphérique de Gurson - à matrice de von Mises et en symétrie sphérique - est bien connue, elle n'est pas, à notre connaissance, disponible dans les deux cas de chargement isotrope (traction, compression) pour les matrices de Coulomb et Drucker-Prager. Dans la présente note, nous établissons les solutions exactes en traction-compression isotropes pour une sphère creuse soumise à une traction ou compression isotrope externe. On fournit une comparaison avec des approches 3D par éléments finis du problème d'analyse limite. Il convient de mentionner que les solutions analytiques établies sont utiles non seulement en tant que solutions de référence mais qu'elles peuvent aussi servir comme partie de la solution générale en vitesses du modèle de la sphère creuse soumise à des sollicitations arbitraires

Human oocyte-derived methylation differences persist in the placenta revealing widespread transient imprinting

Thousands of regions in gametes have opposing methylation profiles that are largely resolved during the post-fertilization epigenetic reprogramming. However some specific sequences associated with imprinted loci survive this demethylation process. Here we present the data describing the fate of germline-derived methylation in humans. With the exception of a few known paternally methylated germline differentially methylated regions (DMRs) associated with known imprinted domains, we demonstrate that sperm-derived methylation is reprogrammed by the blastocyst stage of development. In contrast a large number of oocyte-derived methylation differences survive to the blastocyst stage and uniquely persist as transiently methylated DMRs only in the placenta. Furthermore, we demonstrate that this phenomenon is exclusive to primates, since no placenta-specific maternal methylation was observed in mouse. Utilizing single cell RNA-seq datasets from human preimplantation embryos we show that following embryonic genome activation the maternally methylated transient DMRs can orchestrate imprinted expression. However despite showing widespread imprinted expression of genes in placenta, allele-specific transcriptional profiling revealed that not all placenta-specific DMRs coordinate imprinted expression and that this maternal methylation may be absent in a minority of samples, suggestive of polymorphic imprinted methylation

Limit analysis and convex programming: A decomposition approach of the kinematic mixed method

This paper proposes an original decomposition approach to the upper bound method of limit analysis. It is based on a mixed finite element approach and on a convex interior point solver using linear or quadratic discontinuous velocity fields. Presented in plane strain, this method appears to be rapidly convergent, as verified in the Tresca compressed bar problem in the linear velocity case. Then, using discontinuous quadratic velocity fields, the method is applied to the celebrated problem of the stability factor of a Tresca vertical slope: the upper bound is lowered to 3.7776-value to be compared with the best published lower bound 3.772-by succeeding in solving non-linear optimization problems with millions of variables and constraints. Copyright (C) 2008 John Wiley & Sons, Ltd

Numerical limit analysis bounds for ductile porous media with oblate voids

International audienceThe paper is devoted to a numerical limit analysis of a hollow spheroidal model with a von Mises solid matrix. To this purpose, existing kinematic and static 3D-FEM codes for the case of spherical cavities have been modified and improved to account for the model of a spheroidal cavity confocal with the external spheroidal boundary. The optimized conic programming formulations and the resulting codes appear to be very efficient. This framework is then applied to the derivation of numerical upper and lower anisotropic bounds in the case of an oblate void. The numerical results obtained from a series of tests are presented and allow to assess the accuracy of closed-form expressions of the macroscopic criteria proposed by (Gologanu et al., 1994) and (Gologanu et al., 1997) for porous media with oblate voids

Hollow sphere models, conic programming and third stress invariant

International audienceIn this paper the hollow sphere model is investigated within the framework of limit analysis (LA), using the classical two-part velocity field, i.e., the exact solution for hydrostatic loading plus a linear solution, in both cases of von Mises and Drucker–Prager matrices. We use the kinematic LA approach in a quasi-analytical approach by imposing the plastic admissibility (PA) condition (Drucker–Prager matrix) or upper bounding the dissipated power (von Mises matrix) in a sufficiently high number of distributed points, thanks to conic programming formulations. Then we analyze the “porous Drucker–Prager” case to confirm that the so-called UBM (Upper Bound Model) approach of Guo et al. (2008) is only an estimate, although a good one in fact. Moreover, it is shown that the mean stress axis should not be a strict axis of symmetry for the macroscopic criterion. Then, considering the “Porous von Mises” case, we obtain that the real criterion is not only lower than the Gurson criterion, but probably non-symmetric with respect to the mean stress axis, more than in the Drucker–Prager case. We finally use ad hoc updated 3D-FEM LA codes to confirm the previous results and to evaluate the entire influence of the third stress invariant: the classical (Σm, Σeqv) formulation of the Gurson criterion clearly overestimates the real, non-symmetric solution of the hollow sphere model, at least for porosities of the same order of magnitude as the value used in this work

Limit analysis of hollow spheres or spheroids with Hill orthotropic matrix

International audienceRecent theoretical studies of the literature are concerned by the hollow sphere or spheroid (confocal) problems with orthotropic Hill type matrix. They have been developed in the framework of the limit analysis kinematical approach by using very simple trial velocity fields. The present Note provides, through numerical upper and lower bounds, a rigorous assessment of the approximate criteria derived in these theoretical works. To this end, existing static 3D codes for a von Mises matrix have been easily extended to the orthotropic case. Conversely, instead of the non-obvious extension of the existing kinematic codes, a new original mixed approach has been elaborated on the basis of the plane strain structure formulation earlier developed by F. Pastor (2007). Indeed, such a formulation does not need the expressions of the unit dissipated powers. Interestingly, it delivers a numerical code better conditioned and notably more rapid than the previous one, while preserving the rigorous upper bound character of the corresponding numerical results. The efficiency of the whole approach is first demonstrated through comparisons of the results to the analytical upper bounds of Benzerga and Besson (2001) or Monchiet et al. (2008) in the case of spherical voids in the Hill matrix. Moreover, we provide upper and lower bounds results for the hollow spheroid with the Hill matrix which are compared to those of Monchiet et al. (2008)

Méthodes de l'analyse limite et matériaux sensibles à la contrainte moyenne poreux

International audienceLe premier objectif de cet article est la formulation numérique des trois méthodes générales de l'Analyse Limite, les méthode statique, cinématiques classique et mixte, pour les problèmes dont les matériaux obéissent aux critères de plasticité de Drucker-Prager et Mises-Schleicher. Dans chaque cas, les deux algorithmes de l'optimisation conique sont utilisées pour résoudre le problème final et ainsi aboutir à des formulations numériques efficaces. Les codes résultants sont tout d'abord comparés sur le problème de la sphère creuse sous chargement isotrope dont la solution exacte est connue pour chacun des matériaux précédents. Ensuite, second objectif, les codes statiques et mixtes sont retenus pour contrôler les critère approchés disponibles dans la littérature pour les matériaux poreux à matrice de Drucker-Prager et Mises-Schleicher