Mines ParisTech

About: Mines ParisTech is a education organization based out in Paris, France. It is known for research contribution in the topics: Finite element method & Microstructure. The organization has 6564 authors who have published 11676 publications receiving 359898 citations. The organization is also known as: École nationale supérieure des mines de Paris & École des mines de Paris.

A three-dimensional cellular automation-finite element model for the prediction of solidification grain structures

Abstract: A three-dimensional (3-D) model for the prediction of dendritic grain structures formed during solidification is presented. This model is built on the basis of a 3-D cellular automaton (CA) algorithm. The simulation domain is subdivided into a regular lattice of cubic cells. Using physically based rules for the simulation of nucleation and growth phenomena, a state index associated with each cell is switched from zero (liquid state) to a positive value (mushy and solid state) as solidification proceeds. Because these physical phenomena are related to the temperature field, the cell grid is superimposed to a coarser finite element (FE) mesh used for the solution of the heat flow equation. Two coupling modes between the microscopic CA and macroscopic FE calculations have been designed. In a so-called “weak” coupling mode, the temperature of each cell is simply interpolated from the temperature of the FE nodes using a unique solidification path at the macroscopic scale. In a “full” coupling mode, the enthalpy field is also interpolated from the FE nodes to the CA cells and a fraction of solid increment is computed for each mushy cell using a truncated Scheil microsegregation model. These fractions of solid increments are then fed back to the FE nodes in order to update the new temperature field, thus accounting for a more realistic release of the latent heat (i.e., the solidification path is no longer unique). Special dynamic allocation techniques have been designed in order to minimize the computation costs and memory size associated with a very large number of cells (typically 107 to 108). The potentiality of the CAFE model is demonstrated through the predictions of typical grain structures formed during the investment casting and continuous casting processes.

Asymptotic stabilization via output feedback for lower triangular systems with output dependent incremental rate

Abstract: We study the global asymptotic stabilization by output feedback for systems whose dynamics are in a feedback form and where the nonlinear terms admit an incremental rate depending only on the measured output. The output feedback we consider is of the observer-controller type where the design of the controller follows from standard robust backstepping. The novelty is in the observer which is high-gain such as with a gain coming from a Riccati equation.

Stabilization in Spite of Matched Unmodeled Dynamics and an Equivalent Definition of Input-to-State Stability*

Abstract: We consider nonlinear systems with input-to-output stable (IOS) un- modeled dynamics which are in the "range" of the input. Assuming the nominal system is globally asymptotically stabilizable and a nonlinear small-gain condi- tion is satisfied, we propose a first control law such that all solutions of the perturbed system are bounded and the state of the nominal system is captured by an arbitrarily small neighborhood of the origin. The design of this controller is based on a gain assignment result which allows us to prove our statement via a Small-Gain Theorem (JTP, Theorem 2.1). However, this control law exhibits a high-gain feature for all values. Since this may be undesirable, in a second stage we propose another controller with different characteristics in this respect. This con- troller requires more a priori knowledge on the unmodeled dynamics, as it is dynamic and incorporates a signal bounding the unmodeled effects. However, this is only possible by restraining the IOS property into the exp-IOS property. Never- theless, we show that, in the case of input-to-state stability (ISS)--the output is the state itself--ISS and exp-ISS are in fact equivalent properties.

Adaptive Designs of Experiments for Accurate Approximation of a Target Region

Abstract: This paper addresses the issue of designing experiments for a metamodel that needs to be accurate for a certain level of the response value. Such situation is encountered in particular in constrained optimization and reliability analysis. Here, we propose an iterative strategy to build designs of experiments, which is based on an explicit trade-off between reduction of global uncertainty and exploration of the regions of interest. The method is illustrated on several test-problems. It is shown that a substantial reduction of error can be achieved in the crucial regions, with reasonable loss on the global accuracy. The method is finally applied to a reliability analysis problem; it is found that the adaptive designs significantly outperform classical space-filling designs.

Microstructural and mechanical approaches of the selective laser melting process applied to a nickel-base superalloy

Abstract: This article aims at presenting the Nimonic 263 as-processed microstructure of the selective laser melting which is an innovative process. Because the melting pool is small and the scanning speed of the laser beam is relatively high, the as-processed microstructure is out-of-equilibrium and very typical to additive manufacturing processes. To match the industrial requirement, the microstructures are modified through heat treatments in order to either produce precipitation hardening or relieve the thermal stresses. Tensile tests at room temperature give rise to high mechanical properties close or above those presented by Wang et al. [1]. However, it is noted a strong anisotropy as a function of the building direction of the samples because of the columnar grain growth.