A Computational Method for the Determination of the Elastic Displacement Field using Measured Elastic Deformation Field
Abstract
A novel approach was derived to compute the elastic displacement field from a measured elastic deformation field (i.e., deformation gradient or strain). The method is based on integrating the deformation field using Finite Element discretisation. Space and displacement fields are approximated using piece-wise interpolation functions. Hence, the full elastic deformation field can be expressed as nodal displacements, the unknowns. The nodal displacements are then obtained using a least square method. The proposed method was applied to the symmetrical (residual) elastic deformation field measured using high (angular) resolution electron backscatter diffraction around a Vickers micro-indenting impression on a (001) mono-Si crystal sample with the integrated out-of-plane surface displacements matched with the impression topography measured using. The (residual) displacement field was used as the boundary conditions to calculate the three-dimensional stress intensity factors (K_(I,II,III)) at the cracks emanating from the indentation.
Keywords
Cite
@article{arxiv.2107.10330,
title = {A Computational Method for the Determination of the Elastic Displacement Field using Measured Elastic Deformation Field},
author = {Abdalrhaman Koko and James Marrow and Elsiddig Elmukashfi},
journal= {arXiv preprint arXiv:2107.10330},
year = {2025}
}