This article is a review regarding recently developed inverse strategies coupled with finite element simulations for the identification of the parameters of constitutive laws that describe the plastic behaviour of metal sheets. It highlights that the identification procedure is dictated by the loading conditions, the geometry of the sample, the type of experimental results selected for the analysis, the cost function, and optimization algorithm used. Also, the type of constitutive law (isotropic and/or kinematic hardening laws and/or anisotropic yield criterion), whose parameters are intended to be identified, affects the whole identification procedure.

This work aims to compare the performance of various parametric and non-parametric metamodeling techniques when applied to sheet metal forming processes. For this, the U-Channel and the Square Cup forming processes were studied. In both cases, three steel grades were considered, and numerical simulations were performed, in order to establish a database for each combination of forming process and material. Each database was used to train and test the various metamodels, and their predictive performances were evaluated. The best performing metamodeling techniques were Gaussian processes, multi-layer perceptron, support vector machines, kernel ridge regression and polynomial chaos expansion.

The elastic properties of armchair and zigzag multiwalled carbon nanotubes were investigated under tensile, bending, and torsion loading conditions. A simplified finite element model of the multiwalled carbon nanotubes, without taking into account the van der Waals interactions between layers, was used to assess their tensile, bending, and torsional rigidities and, subsequently, Young’s and shear moduli. Relationships between the tensile rigidity and the squares of the diameters of the outer and inner layers in multiwalled carbon nanotubes, and between the bending and torsional rigidities with the fourth powers of the diameters of the outer and inner layers, were established. These relationships result in two consistent methods, one for assessment to the Young’s modulus of armchair and zigzag multiwalled carbon nanotubes, based on tensile and bending rigidities, and the other to evaluate shear modulus using tensile, bending, and torsional rigidities. This study provides a benchmark regarding the determination of the mechanical properties of nonchiral multiwalled carbon nanotubes by nanoscale continuum modeling approach.