Validation of material models for the numerical simulation of aluminium foams

In the last years a lot of studies dealt with the material modeling of metallic foams, especially for the Aluminium ones. All these activities were performed especially for automotive field applications because the high energy-absorbing property of such foams fits very well the requirement to carry impacting loads efficiently. In spite of this, the industrial applications are not yet so widespread both for manufacturing costs and for a lack of knowledge regarding a whole mechanical characterization. The anisotropic properties of the foams induced mainly by the manufacturing processes, like the continuous casting procedure [1,2] is the reason due until now it has not been possible to assess in a well-known way the foams mechanical performances. In function of the wide spectrum of loading configurations, foaming direction, open and closed cells typology, cells morphology, density, thickness, etc., the output data regarding the mechanical tests are largely scattered (e.g. the stress/strain curves change according to the direction along the experimental test is performed), so a numerical model designed to reproduce accurately the foam behavior needs to take into account the parameters affecting the foam response. Different FE approaches are being developed at this aim: apart from the micro-structural approach and the macro-structural one [3, 4], from an engineeristic point of view, the material models available in the explicit, non-linear finite element code LS-DYNA represent a more efficient way to handle and to investigate the foam behavior. The efficiency feature is strictly connected with the CPU time required to perform the numerical analyses for calibration and/or validation purpose: its reduction can be achieved by selecting a simple material model within reasonable accuracy. The easy utilization of material model can be expressed in terms of number of material parameters, or in terms to exploit directly the data coming from material testing, like for example the stress/strain curves. Several material models for foams are available in the LS-DYNA database and further in the last years different enhancements have been performed with the aim to include the physical phenomenons able to increase the accuracy of the models [5,6]. At the aim to evaluate the behavior of suitable LS-DYNA material models when applied to reproduce in numerical way the experimental behavior of Aluminium foams, an extended study has been set. The current activity represents the first step of such study because it is focused on the assessment of a procedure able to calibrate and validate in a sharp way the constitutive parameters of advanced material models, especially for the most challenging ones. Therefore, the procedure must accomplish an efficient set-up of numerical models, integrate in a unique workflow all the different experimental tests (so that the same material model could be managed contemporaneously in respect of them), point out which data analysis tools are more suitable to elaborate multivariate data. The above requirements imply, first of all, to develop an as accurate as possible numerical models vs. the corresponding experimental ones, keeping low at the same time the computational effort. A preliminary calibration of the numerical models representing just the experimental equipments has been performed to be sure about the goodness of such stand-alone equipment set-ups (i.e. the equipment set up has been assessed for known material properties). Starting from this baseline, the whole FE models (i.e. with the unknown material properties) have been tested under several FE configurations. Following, every material model taken into account requires to be calibrated, that is the free parameters embedded in its constitutive relations have to be tuned so that a good fitting between the numerical and experimental data can be reached. As a general rule, to get a good and robust numerical-experimental correlation, we need to handle at the same time the objective functions representing the performance we are interested. For example, if a material model has to be arranged for tension and compression load conditions, but it is adjusted against only uniaxial tests, then a mismatch will come out since Aluminium foam exhibits quite different behavior in tension than in compression: elastic, plastic and compaction phases in compression, while elastic deformation phase followed by fracture in uniaxial tests [5]. For these reasons, the calibration process requires to optimize the free parameters according to different goals, which are usually in conflicting between them. At this purpose, the code LS-DYNA has to be coupled with modeFRONTIER, Process Integration and Design Optimization software. Once all the numerical models related to the corresponding experimental tests have been integrated, an efficient optimization strategy can explore the design space (i.e. the free parameters dominions) in order to get the configurations satisfying the different goals (i.e. specimen response in different loading conditions). Eventually, efficient and intuitive post-processing tools have been selected to establish some good practices to apply for the data analysis. The experimental tests supporting the planned investigations are focused to characterize the compression, flexural, shear and dynamic behavior of open and closed cells Aluminium foams, different in terms of morphology (open and closed kind), density and panel thickness. Moreover, loadings in the foaming direction and in the perpendicular one were taken into account