Rayleigh-Taylor Instability in Elastoplastic Solids: A Local Catastrophic Process

International audienceWe show that the Rayleigh-Taylor instability in elastoplastic solids takes the form of local perturbations penetrating the material independently of the interface size, in contrast with the theory for simple elastic materials. Then, even just beyond the stable domain, the instability abruptly develops as bursts rapidly moving through the other medium. We show that this is due to the resistance to penetration of a finger which is minimal for a specific finger size and drops to a much lower value beyond a small depth (a few millimeters). The Rayleigh-Taylor instability (RTI) is a well-known instability which occurs when a denser fluid rests on top of a lighter one [1]. As it develops, the two fluids penetrate one another, in the form of fingers. Instability is driven by the density difference and the acceleration to which the fluids are submitted, while surface tension provides a stabilizing effect. In contrast, RTI in solids is much less studied and understood, even though it relates to many application fields and can cause irreversible damage to structures. Examples include metal plates submitted to strong pressure or acceleration in high-energy density physics experiments [2], magnetic implosion of impactor liners [3,4], assessment of solid strength under high strain rate [5], slowly accreting neutron stars [6]. Other applications are found in geology: volcanic island formation [7], salt dome formation [8], and more generally, magmatic diapirism in Earth's mantle and continental crust [9,10], correspond to situations where a liquid opens its way through a layer of denser solid material above it. In most approaches to this problem [7–9,11], the upper material was considered as a highly viscous fluid, which allowed simple simulations of the process, but could also be misleading. Another situation concerns oil well cementing operations, in which yield stress fluids of different densities (drilling muds and cement, e.g.), which behave as solids at rest, may be pumped into the well in an ill-favored density order [12]. The basic approach to RTI for solids assumes linear elastic materials. The problem appears similar to that for simple fluids, except that the role of surface tension effects, neglected for solids, is played by elasticity. For a single solid above a liquid with a (positive) density difference Δρ, the instability criterion (A) is given by gΔρ > 4απG=L, where G and L are the shear modulus and length of the sample, respectively, and g denotes the gravitational acceleration. Depending on boundary conditions, factor α was found to be 1 [3,13], 1.6 [14], or 2 [15]. A couple of experiments on metal plates [16] and with a yogurt [17] provided some support to this theory. From a more complete study [18] using soft elastic solids, the overall validity of this approach was proved but the wavelength was shown to be smaller than expected from theory and dependent on uncontrollable, slight disturbances of the surface [19]. RTI for solids is further complicated by the fact that yielding may occur beyond a critical deformation. So far, this aspect has been considered separately, leading to the conclusion that instability results from a sufficiently large initial perturbation amplitude ε 0 (penetration depth). The instability criterion (B) then reads gΔρ > βτ c =ε 0 , where τ c denotes the material's yield stress (in simple shear), and where 0.5 ≤ β ≤ 2 depending on the sample aspect ratio [13–15,18,24,25]. Some tests with a single material were apparently in agreement with this criterion [17] but the plastic regime for this material was not so well-defined [19]. Finally, it was suggested [2] that elastic and plastic stability criteria should be taken into account successively, and deep theoretical analysis [26] predicted that for plastic materials, once the threshold is reached somewhere, the perturbation grows unlimitedly. These approaches have the advantage of considering independently the elasticity and the yielding effects. However, one cannot exclude that the interplay of both mechanisms could play a crucial role in the early stage of the perturbation growth. Here we aim at clarifying this problem through experiments on well-characterized materials, linearly elastic below a critical deformation and elastoplastic beyond this deformation. We show that the RTI in solids does not develop as predicted by the theory for simple elastic materials, but results from the ability of local perturbations to penetrate the material by involving, from the start, both elastic and plastic effects. At some point during the process, resistance to penetration drops, causing an abrup

AGATHE: A tool for personalized rehabilitation of cognitive functions

Stroke, traumatic brain injury, multiple sclerosis, Parkinson's disease, Alzheimer's... Every year in France, tens of thousands of people fall victim to one of those neurological pathologies. Acquired brain injury leads to cognitive impairment and heavy loss of autonomy. Rehabilitation interventions are needed to enable people to recover capacity and return to Activities of Daily Living (ADL), such as grocery shopping. Unfortunately, the resources made available in cognitive rehabilitation are insufficient for the growing needs of victims of brain damage. The assets of virtual reality to address this big problem of public health are today scientifically recognized [Rizzo and Kim 2005; Klinger, et al. 2010]. In this context, we designed the AGATHE tool (Adaptable, configurable and upgradable tool for the generation of personalized therapeutic applications in cognitive rehabilitation) (AGATHE project, ANR-09-TECS-002).French National Research Agency (ANR) Laval Agglomération et Conseil Général de la Mayenn

AGATHE: A tool for personalized rehabilitation of cognitive functions

Stroke, traumatic brain injury, multiple sclerosis, Parkinson's disease, Alzheimer's... Every year in France, tens of thousands of people fall victim to one of those neurological pathologies. Acquired brain injury leads to cognitive impairment and heavy loss of autonomy. Rehabilitation interventions are needed to enable people to recover capacity and return to Activities of Daily Living (ADL), such as grocery shopping. Unfortunately, the resources made available in cognitive rehabilitation are insufficient for the growing needs of victims of brain damage. The assets of virtual reality to address this big problem of public health are today scientifically recognized [Rizzo and Kim 2005; Klinger, et al. 2010]. In this context, we designed the AGATHE tool (Adaptable, configurable and upgradable tool for the generation of personalized therapeutic applications in cognitive rehabilitation) (AGATHE project, ANR-09-TECS-002).French National Research Agency (ANR) Laval Agglomération et Conseil Général de la Mayenn

Resilient Computing Curriculum

This Deliverable presents the MSc Curriculum in Resilient Computing suggested by ReSIST. It includes the description of the syllabi for all the courses in the two semesters of the first year, those for the common courses in semester 3 in the second year together with an exemplification of possible application tracks with the related courses. This MSc curriculum has been updated and completed taking advantage of a large open discussion inside and outside ReSIST. This MSc Curriculum is on-line on the official ReSIST web site, where all information is available together with all the support material generated by ReSIST and all other relevant freely available support material.European Commission through NoE IST-4-026764-NOE (ReSIST

Resilient Computing Courseware

This Deliverable describes the courseware in support to teaching Resilient Computing in a Curriculum for an MSc track following the scheme of the Bologna process. The development of the supporting material for such a curriculum has required a rather intensive activity that involved not only the partners in ReSIST but also a much larger worldwide community with the aim of identifying available updated support material that can be used to build a progressive and methodical line of teaching to accompany students and interested persons in a profitable learning process. All this material is on-line on the official ReSIST web site http://www.resistnoe.org/, can be viewed and downloaded for use in a class and constitutes, at our knowledge, the first, almost comprehensive attempt, to build a database of support material related to Dependable and Resilient Computing.European Commission through NoE IST-4-026764-NOE (ReSIST

Modelling the biochemical behaviour of growing trees at the forest stand scale. Part I: Development of an incremental transfer matrix method and application to simplified tree structures

Stem straightness defects are often associated with heterogeneities in wood structure in relation to tree tropisms. This paper presents a numerical model which is dedicated to simulate the biomechanical behaviour of growing trees. A simplified description of tree structure, separating trunk and crown, has been used in order to perform future calculations at the stand level. The model is based on the Transfer Matrix Method, which was adjusted under an incremental form to compute the evolution of trunk biomechanics during growth. Deflections due to self-weight distribution and straightening up reactions, which are associated with maturation strains of reaction wood cells, were considered. This model has been implemented in the CAPSIS software. Numerical results were compared to those obtained by the software AMAPpara, which is more applicable to the whole tree architecture level. Limits of the simplified description, which will be useful for studies at stand level, are discussed. (Résumé d'auteur

Utility of the Conconi's Heart Rate Deflection to Monitor the Intensity of Aerobic Training

International audienc