École normale supérieure de Cachan

About: École normale supérieure de Cachan is a education organization based out in Cachan, Île-de-France, France. It is known for research contribution in the topics: Decidability & Nonlinear system. The organization has 2717 authors who have published 5585 publications receiving 175925 citations.

Integrated XFEM-CE analysis of delamination migration in multi-directional composite laminates

Abstract: Progressive damage and failure in composites are generally complex and involve multiple interacting failure modes. Depending on factors such as lay-up sequence, loading and specimen configurations, failure may be dominated by extensive matrix crack-delamination interactions, which are very difficult to model accurately. The present study further develops an integrated extended finite element method (XFEM) and cohesive element (CE) method for three-dimensional (3D) delamination migration in multi-directional composite laminates, and validates the results with experiment performed on a double-cantilever beam (DCB). The plies are modeled by using XFEM brick elements, while the interfaces are modeled using CEs. The interaction between matrix crack and delamination is achieved by enriching the nodes of cohesive element. The mechanisms of matrix fracture and delamination migration are explained and discussed. Matrix crack initiation and propagation can be predicted and delamination migration is also observed in the results. The algorithm provides for the prediction of matrix crack angles through the ply thickness. The proposed method provides a platform for the realistic simulation of progressive failure of composite laminates.

The linear boltzmann equation for long-range forces: a derivation from particle systems

Abstract: In this paper we consider a particle moving in a random distribution of obstacles. Each obstacle generates an inverse power law potential es/|x|s, where e is a small parameter and s>2. Such a rescaled potential is truncated at distance eγ-1, where γ∈] 0, 1[ is suitably large. We also assume that the scatterer density is diverging as e-d+1, where d is the dimension of the physical space. We prove that, as e→0 (the Boltzmann–Grad limit), the probability density of a test particle converges to a solution of the linear (uncutoff) Boltzmann equation with the cross-section relative to the potential V(x)=|x|-s.

Numerical simulations for nodal domains and spectral minimal partitions

Abstract: We recall here some theoretical results of B. Helffer, T. Hoffmann-Ostenhof and S. Terracini about minimal partitions and propose numerical computations to illustrate some of their published or unpublished conjectures.

Thermocapillary actuation by optimized resistor pattern: bubbles and droplets displacing, switching and trapping

Abstract: We report a novel method for bubble or droplet displacement, capture and switching within a bifurcation channel for applications in digital microfluidics based on the Marangoni effect, i.e. the appearance of thermocapillary tangential interface stresses stemming from local surface tension variations. The specificity of the reported actuation is that heating is provided by an optimized resistor pattern (B. Selva, J. Marchalot and M.-C. Jullien, An optimized resistor pattern for temperature gradient control in microfluidics, J. Micromech. Microeng., 2009, 19, 065002) leading to a constant temperature gradient along a microfluidic cavity. In this context, bubbles or droplets to be actuated entail a surface force originating from the thermal Marangoni effect. This actuator has been characterized (B. Selva, I. Cantat, and M.-C. Jullien, Migration of a bubble towards a higher surface tension under the effect of thermocapillary stress, preprint, 2009) and it was found that the bubble/droplet (called further element) is driven toward a high surface tension region, i.e. toward cold region, and the element velocity increases while decreasing the cavity thickness. Taking advantage of these properties three applications are presented: (1) element displacement, (2) element switching, detailed in a given range of working, in which elements are redirected towards a specific evacuation, (3) a system able to trap, and consequently stop on demand, the elements on an alveolus structure while the continuous phase is still flowing. The strength of this method lies in its simplicity: single layer system, in situ heating leading to a high level of integration, low power consumption (P < 0.4 W), low applied voltage (about 10 V), and finally this system is able to manipulate elements within a flow velocity up to 1 cm s−1.