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.

Plastic potentials for anisotropic porous solids

Abstract: The aim of this paper is to incorporate plastic anisotropy into constitutive equations of porous ductile metals. It is shown that plastic anisotropy of the matrix surrounding the voids in a ductile material could have an influence on both effective stress–strain relation and damage evolution. Two theoretical frameworks are envisageable to study the influence of plastic flow anisotropy: continuum thermodynamics and micromechanics. By going through the Rousselier thermodynamical formulation, one can account for the overall plastic anisotropy, in a very simple manner. However, since this model is based on a weak coupling between plasticity and damage dissipative processes, it does not predict any influence of plastic anisotropy on cavity growth, unless a more suitable choice of the thermodynamical force associated with the damage parameter is made. Micromechanically-based models are then proposed. They consist of extending the famous Gurson model for spherical and cylindrical voids to the case of an orthotropic material. We derive an upper bound of the yield surface of a hollow sphere, or a hollow cylinder, made of a perfectly plastic matrix obeying the Hill criterion. The main findings are related to the so-called ‘scalar effect’ and ‘directional effect’. First, the effect of plastic flow anisotropy on the spherical term of the plastic potential is quantified. This allows a classification of sheet materials with regard to the anisotropy factor h ; this is the scalar effect. A second feature of the model is the plasticity-induced damage anisotropy. This results in directionality of fracture properties (‘directional effect’). The latter is mainly due to the principal Hill coefficients whilst the scalar effect is enhanced by ‘shear’ Hill coefficients. Results are compared to some micromechanical calculations using the finite element method.

Antileakage Fourier transform for seismic data regularization

Abstract: Seismic data regularization, which spatially transforms irregularly sampled acquired data to regularly sampled data, is a long-standing problem in seismic data processing. Data regularization can be implemented using Fourier theory by using a method that estimates the spatial frequency content on an irregularly sampled grid. The data can then be reconstructed on any desired grid. Difficulties arise from the nonorthogonality of the global Fourier basis functions on an irregular grid, which results in the problem of “spectral leakage”: energy from one Fourier coefficient leaks onto others. We investigate the nonorthogonality of the Fourier basis on an irregularly sampled grid and propose a technique called “antileakage Fourier transform” to overcome the spectral leakage. In the antileakage Fourier transform, we first solve for the most energetic Fourier coefficient, assuming that it causes the most severe leakage. To attenuate all aliases and the leakage of this component onto other Fourier coefficients, the data component corresponding to this most energetic Fourier coefficient is subtracted from the original input on the irregular grid. We then use this new input to solve for the next Fourier coefficient, repeating the procedure until all Fourier coefficients are estimated. This procedure is equivalent to “reorthogonalizing” the global Fourier basis on an irregularly sampled grid. We demonstrate the robustness and effectiveness of this technique with successful applications to both synthetic and real data examples.