The main goal of this work is to present a three-dimensional mechanical model for the numerical simulation of the deep-drawing process. The model takes into account the large elastoplastic strains and rotations that occur in the deep-drawing process. Hill's orthotropic yield criteria with isotropic and kinematics hardening describes the anisotropic plastic properties of the sheet. Coulomb's classical law models the frictional contact problem treated with an augmented Lagrangian approach. This method yields a mixed system where the ®nal unknowns of the problem are static (frictional contact forces) and kinematic (displacements) variables. To solve this problem use is made of a fully implicit algorithm of Newton±Raphson type. Three-dimensional isoparametric ®nite elements with a selective reduced integration are used for the spatial discretization of the deformed body. The geometry of the forming tools is modelled by Be Âzier surfaces. The numerical results of the deep-drawing of a square cup are presented to focus their good agreement with the results of experiment.

The development of depth sensing indentation equipment has allowed easy and reliable determination of two of the most popular measured mechanical properties of materials: the hardness and the YoungÕs modulus. However, some difficulties emerge in the experimental procedure to calculate accurate values of these properties. This is related to, for example, the tip geometrical imperfections of the diamond pyramidal indenter and the definition of the contact area at the maximum load. Being so, numerical simulation of ultramicrohardness tests can be a helpful tool for better understanding of the influence of these parameters on procedures for determining the hardness and the YoungÕs modulus. For this purpose, specific finite element simulation software, HAFILM, was developed to simulate the ultramicrohardness tests. Different mesh refinements were tested because of the dependence between the values of the mechanical properties and the size of the finite element mesh. Another parameter studied in this work is the value of the friction coefficient between the indenter and the sample in the numerical simulation. In order to obtain numerical results close to reality, a common geometry and size of the imperfection of the tip of Vickers indenter was taken into account for the numerical description of the indenter.

a b s t r a c tThis paper presents two procedures for the identification of material parameters, a genetic algorithm and a gradient-based algorithm. These algorithms enable both the yield criterion and the work hardening parameters to be identified. A hybrid algorithm is also used, which is a combination of the former two, in such a way that the result of the genetic algorithm is considered as the initial values for the gradient-based algorithm. The objective of this approach is to improve the performance of the gradient-based algorithm, which is strongly dependent on the initial set of results. The constitutive model used to compare the three different optimization schemes uses the Barlat'91 yield criterion, an isotropic Voce type law and a kinematic Lemaitre and Chaboche law, which is suitable for the case of aluminium alloys. In order to analyse the effectiveness of this optimization procedure, numerical and experimental results for an EN AW-5754 aluminium alloy are compared.

Depth-sensing indentation equipment is widely used for evaluation of the hardness and Young's modulus of materials. The depth resolution of this technique allows the use of ultra-low loads. However, aspects related to the determination of the contact area under indentation should be cautiously considered when using this equipment. These are related to the geometrical imperfections of the tip, the diamond pyramidal punch and the formation of pileup or the presence of sink-in, which alter the shape and size of the indent. These and other aspects, such as the thermal drift of the equipment and the scattering at the zero indentation depth position related to surface finishing, are discussed in this work. A study concerning the hardness and the Young's modulus results determined by Vickers indentation on different materials was performed. Samples of fused silica, BK7 glass, aluminium, copper and mild steel (for which the values of Young's modulus were previously known) were tested using indentation loads in the range 10-1000 mN. Moreover, two methods are proposed for performing the indentation geometrical calibration of the contact area; these are compared with a former method proposed by Oliver and Pharr (OP). The present methods are based on: (i) analysis of the punch profile using atomic force microscopy (AFM); and (ii) a linear penetration-depth function correction (LM), based on knowledge of the values of the Young's modulus of several materials. By applying these methods to the indentation loadyindentation depth results, it was possible to draw some conclusions about the benefit of the AFM and LM methods now under proposal.

The main difficulty with the characterization of thin coatings using depth-sensing indentation tests is related to the determination of the contributions of the substrate and the film to the measured properties. In this study, three-dimensional numerical simulations of the Vickers hardness test are used in order to examine the influence of the elastic and plastic properties of the substrate and the film on the composite's Young's modulus results. The hardness of the film is equal to or higher than the substrate hardness. A study of the stress distributions and the indentation geometry of composites, film/ substrate, was performed, taking into account the relative mechanical properties of the film and substrate. In addition, stress evolution during indentation was studied, in order to quantify the critical indentation depth under which the substrate is not elastically deformed. The accurate evaluation of the Young's modulus of the films using weight functions is also examined: some of these have previously been proposed and one was introduced for this study. Two different fitting procedures were used to compare the results obtained from eight fictive film/substrate combinations using six weight functions. The first procedure, commonly used, considers the substrate's modulus as a known parameter in the fitting process. In the second, the film and the substrate's modulus are considered as unknown variables that are calculated simultaneously during the fitting process. The validity of the conclusions obtained using the fictive materials was checked by applying the weight functions to four real composites.