Computing strain fields from discrete displacement fields in 2D-solids

Abstract

Ah&act-The analysis of strain localization and damage evolution in materials requires appropriate experimental techniques to verify the complex material behaviour in the damaging zone. Modern techniques are now available to measure the displacement fields in small zones of a material, and a complementary procedure is needed to derive the accompanying strain fields. The knowledge of the local strain fields gives direct information with respect to the applied constitutive model and serves as initial. input for most parameter estimation procedures, while the tine-tuning of the model parameters should be done by comparing the computed and measured displacement fields. This study presents a theory to compute strains from the displacements in a discrete set of points and is particularly useful in the post-processing of experimentally measured displacement fields. The theory is fully elaborated, and some practical examples are given. A comparison is made with some analytical solutions, and the effect of noise on the input data is evaluated.

A novel method for visualising and quantifying through-plane skin layer deformations

“…To obtain strain information from the experimentally obtained displacement field, a gradient deformation formulation with quadratic interpolation of grid points was used (more details in Geers et al, 1996). The last frame of the second skin deformation cycle (at full 10% skin strain) was analysed (Fig.…”

“…1f). The deformation gradient tensor F was estimated in each data point from the 2D-displacement field (central particle) with a least squares fit through 8 neighbouring points of the displacement field (details on the procedure in Geers et al, 1996).…”

The Diffuse Approximation: a derivative tool dedicated to full-field measurements

“…Therefore, except for the techniques which provide directly the displacement derivatives, it is necessary to differentiate the data. When the gradients of the displacement fields are relatively low, for example when the materials still behave elastically, the small measurement errors may induce large errors on the computed derivative [2]. So the key work is to develop a stable algorithm, in which it is possible to quantify explicitly the effects induced by noise differentiation.…”

Estimation of the strain field from full-field displacement noisy data

“…Therefore, except for the techniques which provide directly the displacement derivatives, it is necessary to differentiate the data. When the gradients of the displacement fields are relatively low, for example when the materials still behave elastically, the small errors for measurement values may induce a large error to the computed derivative (Geers et al, 1996). So the key work is to develop a stable algorithm, in which it is possible to quantify explicitly the effects induced by noise differentiation.…”