A Fourier‐series‐based Virtual Fields Method for the Identification of 2‐D Stiffness and Traction Distributions

Abstract

The Virtual Fields Method (VFM) allows spatial distributions of material properties to be calculated from experimentally-determined strain fields. A numerically-efficient Fourierseries-based extension to the VFM (the F-VFM) has recently been developed, in which the unknown stiffness distribution is parameterised in the spatial frequency domain rather than in the spatial domain as used in the classical VFM. However, the boundary conditions for the F-VFM are assumed to be well-defined, whereas in practice the traction distributions on the perimeter of the region of interest are rarely known to any degree of accuracy. In the current paper we therefore consider how the F-VFM theory can be extended to deal with the case of unknown boundary conditions. Three different approaches are proposed; their ability to reconstruct normalised stiffness distributions and traction distributions around the perimeter from noisy input strain fields is assessed through simulations based on a forward finite element analysis. Finally a practical example is given involving strain fields of experimental displacements measured from a diametral compression test on an aluminium disc.

A Fourier‐series‐based virtual fields method for the identification of three‐dimensional stiffness distributions and its application to incompressible materials

“…The stiffness distribution of the 3D egg‐box pattern reconstructed by the F‐VFM is presented in Figure c. Even though they are not always clearly seen, ripples at the highest spatial frequency of the Fourier series stiffness expansion exist in the reconstructed result, in a similar way to those observed in the 2D F‐VFM . Also as in the 2D case, these can be filtered out by convolving the recovered stiffness distribution with an appropriate kernel.…”

“…The F‐VFM was developed originally for 2D geometries and extended to the case of incomplete knowledge of the boundary value distributions. In the current paper, it is extended for the first time to volumetric data resulting from, for example, measurements with digital volume correlation or phase contrast MRI.…”

An identification method of mechanical properties of materials based on the full‐field measurement method based on the fringe pattern

“…The VFM, which was proposed by Pierron and Grédiac based on whole deformation fields, is a representative nonupdating method when being applied in a linear material model. Several inverse methods have been developed based on the theory underlying the VFM, including the Fourier series‐based VFM, the sensitivity‐based VFM, the eigenfunction VFM, and several optimisation methods for improving the accuracy of identification results …”

Identification of Local Elastic Parameters in Heterogeneous Materials Using a Parallelized Femu Method

“…In order to identify local mechanical parameters where the homogeneous hypothesis is not verified, some of these methods have been modified to be adapted to heterogeneous materials. The Fourier seriesbased VFM [13] and the constitutive compatibility method (CCM) [14], based on a reformulation of CEGM, are examples of recent developments in this area. As far as we know, there is no work in the literature which has tested the FEMU method in this case.…”