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

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 fine-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