A Computational Method for the Determination of the Elastic Displacement Field using Measured Elastic Deformation Field.

A novel approach to compute the elastic displacement field from a measured elastic deformation field (i.e. deformation gradient or strain) is presented in this paper. The method is based on the integration of the deformation field using Finite Element discretisation. Space and displacement fields are approximated using similar piece-wise interpolation functions. Hence, the full elastic deformation field can be expressed in terms of the nodal displacements which are the unknowns. The nodal displacements are then obtained using a least square method, i.e. minimising the sum of the squares of the differences between the measured and predicted deformation field components. The method is validated against the two-dimensional mode-I stationary crack problem in elastic solid. The method is able to accurately predict Westergaard solution of the displacement field.