Seminar Team APLI by Stéphane BERBENNI

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Date | Time
04/11/2014 | 2 h 00 min - 6 h 00 min

Salle Klepaczko


« A FFT approach for solving elasto-static field dislocation and g-disclination mechanics: applications to twin tips and grain boundaries »

Abstract :
Recently, a small-distortion theory of coupled plasticity and phase transformation accounting for the kinematics and dynamics of generalized defects, i.e., dislocations and generalized (g-) disclinations, has been proposed [1]. In the present contribution, a numerical spectral approach is developed to solve the elasto-static equations of field dislocation and g-disclination mechanics set out in this theory for periodic media. Given the spatial distribution of Nye’s dislocation density and/or g-disclination density tensors in heterogeneous or homogenous linear elastic media, the incompatible and compatible elastic distortions are obtained from the solution of Poisson and Navier-type equations in the Fourier space by using a Fast Fourier Transform method (FFT) based on intrinsic Discrete Fourier Transforms well adapted to the discrete grid. The elastic strain/rotation and Cauchy stress tensors are calculated using the inverse FFT. In order to validate the present spectral approach, comparisons are made with analytical solutions and with Finite Element results for linear isotropic elastic solids. The numerical examples include the stress and elastic rotation fields of single screw and edge dislocations, standard wedge disclinations and associated dipoles, grain boundaries, as well as twin tips seen as g-disclinations. The details on the technique can be found in [2]. 

Références :
[1] Acharya, A., Fressengeas, C., 2012. Int. J. Fract. 174, 8794.
[2] Berbenni, S., Taupin, V., Djaka, K.S., Fressengeas, C., 2014. Int. J. Solids Struct. 51, 4157-4175.