Recent Developments in Gradient Plasticity—Part II: Plastic Heterogeneity and Wavelets

Abstract

Wavelet analysis is used for describing heterogeneous deformation in different scales. Slip step height experimental measurements of monocrystalline alloy specimens subjected to compression are considered. The experimental data are subjected to discrete wavelet transform and the spatial distribution of deformation in different scales (resolutions) is calculated. At the finer scale the wavelet analyzed data are identical to the experimental measurements, while at the coarser scale the profile predicted by the wavelet analysis resembles the shear band solution profile provided by gradient theory in agreement with experimental observations. The different data sets provided by wavelet analysis are used to train a neural network in order to predict the spatial distribution of strain at resolutions higher than those possible by the available experimental probes. In addition, applications of wavelet analysis to interpret size effect data in torsion and bending at the micron scale are examined by deriving scale-dependent constitutive equations which are used for this purpose.