About this Abstract |
Meeting |
6th International Congress on 3D Materials Science (3DMS 2022)
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Symposium
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6th International Congress on 3D Materials Science (3DMS 2022)
|
Presentation Title |
Imposing Equilibrium on Measured 3-D Stress Fields Using Helmholtz Decomposition and FFT-based Optimization |
Author(s) |
Ricardo A. Lebensohn, Hao Zhou, Peter Reischig, Wolfgang Ludwig, Kaushik Bhattacharya |
On-Site Speaker (Planned) |
Ricardo A. Lebensohn |
Abstract Scope |
We present a methodology to impose micromechanical constraints to arbitrary voxelized stress fields obtained, e.g. by x-ray diffraction. The method consists in finding the equilibrated stress field closest to the measured field, posed as an optimization problem. The extraction of the divergence-free (equilibrated) stress is performed using the Hodge/Helmholtz decomposition of a symmetric matrix field. The combination of the latter with the Euler-Lagrange equations of the optimization gives an expression that contains the bi-harmonic operator and the curl operator acting twice on the measured stress field. These high-order derivatives are efficiently performed in Fourier space. The method is applied to filter: a) synthetic piecewise constant stress fields, b) synthetic equilibrated fields perturbed with noise, c) measured stress fields in Gum Metal, a beta-Ti alloy. In cases a) and c), the largest corrections were obtained near grain boundaries. In case b), the filter was able to partially de-noise the perturbed field. |
Proceedings Inclusion? |
Definite: Other |