A material model for warm forming of aluminium sheet

A material model has been developed to simulate the warm forming of Al–Mg\ud sheet. Both the hardening behaviour, including temperature and strain rate effects, and the\ud biaxial stress–strain response of the sheet are considered. A physically-based hardening model\ud according to Bergström is used. This model incorporates the influence of the temperature\ud and strain rate on the flow stress and on the hardening rate based on dynamic recovery. For\ud deformations at constant temperature and strain rate, the Bergström model reduces to the well\ud known Voce hardening model. The Bergström/Voce models can be fitted quite well to the results\ud of monotonic tensile tests of an AA 5754-O alloy.\ud The biaxial stress–strain response of the material is experimentally determined by uniaxial,\ud plane strain, simple shear and equi-biaxial stress tests. It is demonstrated that the widely used\ud Hill ’48 yield locus is inappropriate for simulation of deformation of aluminium. The low Rvalues\ud for aluminium lead to a significant underestimation of the equi-biaxial yield stress. In\ud the simulation of the deep drawing of a cylindrical cup this results in a much too thin bottom of\ud the cup. The Vegter yield criterion is sufficiently flexible to accurately represent the shape of the\ud yield locus and the anisotropy.\ud

Recent developments in finite element simulations of the deep drawing process

Some new developments in a finite element code for the deep drawing process are presented\ud in this paper. First the phenomenon of friction is treated. A Stribeck friction model has been\ud developed which accounts for the dependency of the friction coefficient on the local contact\ud conditions. Secondly a new yield criterion has been developed by Vegter. This Vegter yield\ud criterion is based on multi-axial stress states. Finally attention will be paid to reduce the CPUtime\ud of a simulation when drawbeads are used. An equivalent drawbead model has been\ud developed to avoid an enormous increase in calculation time

Effect of temperature on anisotropy in forming simulations of aluminum alloys

A combined experimental and numerical study of the effect of temperature on anisotropy in warm forming of AA 6016-T4 aluminum was performed. The anisotropy coefficients of the Vegter yield function were calculated from crystal plasticity models with an adequate combination of extra slip systems. Curve fitting was used to fit the anisotropy coefficients calculated at discrete temperatures. This temperature dependent constitutive model was successfully applied to the coupled thermo-mechanical analysis of deep drawing of aluminum sheet and results were compared with experiments

STiC -- A multi-atom non-LTE PRD inversion code for full-Stokes solar observations

The inference of the underlying state of the plasma in the solar chromosphere remains extremely challenging because of the nonlocal character of the observed radiation and plasma conditions in this layer. Inversion methods allow us to derive a model atmosphere that can reproduce the observed spectra by undertaking several physical assumptions. The most advanced approaches involve a depth-stratified model atmosphere described by temperature, line-of-sight velocity, turbulent velocity, the three components of the magnetic field vector, and gas and electron pressure. The parameters of the radiative transfer equation are computed from a solid ground of physical principles. To apply these techniques to spectral lines that sample the chromosphere, NLTE effects must be included in the calculations. We developed a new inversion code STiC to study spectral lines that sample the upper chromosphere. The code is based the RH synthetis code, which we modified to make the inversions faster and more stable. For the first time, STiC facilitates the processing of lines from multiple atoms in non-LTE, also including partial redistribution effects. Furthermore, we include a regularization strategy that allows for model atmospheres with a complex stratification, without introducing artifacts in the reconstructed physical parameters, which are usually manifested in the form of oscillatory behavior. This approach takes steps toward a node-less inversion, in which the value of the physical parameters at each grid point can be considered a free parameter. In this paper we discuss the implementation of the aforementioned techniques, the description of the model atmosphere, and the optimizations that we applied to the code. We carry out some numerical experiments to show the performance of the code and the regularization techniques that we implemented. We made STiC publicly available to the community.Comment: Accepted for publication in Astronomy & Astrophysic

Statistical Methods for the Qualitative Assessment of Dynamic Models with Time Delay (R Package qualV)

Results of ecological models differ, to some extent, more from measured data than from empirical knowledge. Existing techniques for validation based on quantitative assessments sometimes cause an underestimation of the performance of models due to time shifts, accelerations and delays or systematic differences between measurement and simulation. However, for the application of such models it is often more important to reproduce essential patterns instead of seemingly exact numerical values. This paper presents techniques to identify patterns and numerical methods to measure the consistency of patterns between observations and model results. An orthogonal set of deviance measures for absolute, relative and ordinal scale was compiled to provide informations about the type of difference. Furthermore, two different approaches accounting for time shifts were presented. The first one transforms the time to take time delays and speed differences into account. The second one describes known qualitative criteria dividing time series into interval units in accordance to their main features. The methods differ in their basic concepts and in the form of the resulting criteria. Both approaches and the deviance measures discussed are implemented in an R package. All methods are demonstrated by means of water quality measurements and simulation data. The proposed quality criteria allow to recognize systematic differences and time shifts between time series and to conclude about the quantitative and qualitative similarity of patterns.

MODELING OF BOND YIELD CURVE USING CUBIC BEZIER CURVE

Investors attracted to Bond have to analyze the Bond yield curve. In this study, the bond yield curve is modeled using a cubic bezier curve. The cubic bezier curve is flexible, precise, and simple to use and evaluate. The bonds used in this study are Surat Berharga Negara (Government Paper) Fix Rate type dated August, 2nd–6th 2021. Bond data is obtained from the Indonesia Stock Exchange https://www.idx.co.id. The results show that the bond yield curve that is formed varies because bond yields change every time following market developments. The cubic bezier curve is able to model the bond yield curve well. Cubic bezier curves have 4 control values ​​that help guide the curve well. The MSE value obtained by the bezier curve is small in general. The MSE values of the cubic bezier curve for the Bond yield data, sequentially from the least to the greatest, are 0,098 on August 4th, 2021; 0,1719 on August 5th, 2021; 0,2161 on August 3rd, 2021; 0,2498 on August 6th, 2021; and 0,2906 on August 2nd, 2021