Vibro-impact of a plate on rigid obstacles: existence theorem, convergence of a scheme and numerical simulations

The purpose of this paper is to describe a fully discrete approximation and its convergence to the continuum dynamical impact problem for the fourth-order Kirchhoff–Love plate model with nonpenetration Signorini contact condition. We extend to the case of plates the theoretical results of weak convergence due to Y. Dumont and L. Paoli, which was stated for Euler–Bernouilli beams. In particular, this provides an existence result for the solution of this problem. Finally, we discuss the numerical results we obtain

Study of some optimal XFEM type methods

The XFEM method in fracture mechanics is revisited. A first improvement is considered using an enlarged fixed enrichment subdomain aroud the crack tip and a bonding condition for the corresponding degree of freedom. An efficient numerical integration rule is introduced for the nonsmooth enrichment functions. The lack of accuracy due to the transition layer between the enrichment aera and the rest of the domain leads to consider a pointwise matching condition at the boundary of the subdomain. An optimal numerical rate of convergence is then obtained using such a nonconformal method

Mitochondria Retrograde Signaling and the UPR mt: Where Are We in Mammals?

Mitochondrial unfolded protein response is a form of retrograde signaling that contributes to ensuring the maintenance of quality control of mitochondria, allowing functional integrity of the mitochondrial proteome. When misfolded proteins or unassembled complexes accumulate beyond the folding capacity, it leads to alteration of proteostasis, damages, and organelle/cell dysfunction. Extensively studied for the ER, it was recently reported that this kind of signaling for mitochondrion would also be able to communicate with the nucleus in response to impaired proteostasis. The mitochondrial unfolded protein response (UPR(mt)) is activated in response to different types and levels of stress, especially in conditions where unfolded or misfolded mitochondrial proteins accumulate and aggregate. A specific UPR(mt) could thus be initiated to boost folding and degradation capacity in response to unfolded and aggregated protein accumulation. Although first described in mammals, the UPR(mt) was mainly studied in Caenorhabditis elegans, and accumulating evidence suggests that mechanisms triggered in response to a UPR(mt) might be different in C. elegans and mammals. In this review, we discuss and integrate recent data from the literature to address whether the UPR(mt) is relevant to mitochondrial homeostasis in mammals and to analyze the putative role of integrated stress response (ISR) activation in response to the inhibition of mtDNA expression and/or accumulation of mitochondrial mis/unfolded proteins

Schémas numériques conservatifs pour des problèmes de vibro-impacts de poutres et de plaques

Nous proposons une adaptation de la méthode de Dynamique Singulière pour certains schémas numériques modélisant les vibro-impacts d’une poutre ou d’une plaque sur des obstacles rigides. Elle est appliquée sur deux problèmes pour lesquels on a démontré l’existence d’une solution, mais sans avoir d’information sur le bilan énergétique. Par cette nouvelle méthode d’approximation par éléments finis les semi-discrétisations en espace sont stables et bien posées à la différence des approximations classiques

The singular dynamic method for dynamic contact of thin elastic structures

This paper adresses the approximation of the dynamic impact of thin elastic structures. The principle of the presented method is the use of a singular mass matrix obtained by different discretizations of the deflection and velocity. The obtained semi-discretized problem is proved to be well-posed and energy conserving. The method is applied on some membrane, beam and plate models and associated numerical experiments are discussed

Energy conservative finite element semi-discretization for vibro-impacts of plates on rigid obstacles

Our purpose is to describe and compare some families of fully discretized approximations and their properties, in the case of vibro-impact of plates between rigid obstacles with non-penetration Signorini’s conditions. To this aim, the dynamical Kirchhoff–Love plate model is considered and an extension to plates of the singular dynamic method, introduced by Renard and previously adapted to beams by Pozzolini and Salaün, is described. A particular emphasis is given in the use of an adapted Newmark scheme in which intervene a discrete restitution coefficient. Finally, various numerical results are presented and energy conservation capabilities of several numerical schemes are investigated and discussed

Schémas asymptotiquement conservatifs en énergie dans un problème de vibro-impact de plaques

Le mouvement d'une plaque entre des obstacles rigides est étudié. Plusieurs familles de schémas totalement discrétisés sont comparées et l'intérêt de la méthode de la Dynamique Singulière pour obtenir des schémas conservatifs en énergie est illustré. Enfin, l'influence du coefficient de restitution lors du choc est mise en évidence

A numerical approach for modelling thin cracked plates with XFEM

The modelization of bending plates with through the thickness cracks is investigated. We consider the Kirchhoff-Love plate model which is valid for very thin plates. We apply the eXtended Finite Element Method (XFEM) strategy: enrichment of the finite element space with the asymptotic bending and with the discontinuity across the crack. We present two variants and their numerical validations and also a numerical computation of the stress intensity factors