Drucker Prager Cap Model Research Articles

OS1727 鉄系圧粉体の材料モデルパラメータの推定

In order to estimate parameters of the simulation model for iron green bodies of press-ready premix consisting of Distaloy AE, 0.5 % graphite and 0.6 % Kenolube, we carried out diametrical compression tests of the iron green bodies. We prepared the iron body with densities of 6.9 g/cm^3, 7.2 g/cm^3, 7.4 g/cm^3. The parameters of failure envelope in the modified Drucker-Prager Cap model were determined using the results of uniaxial compression tests in our previous study and diametrical compression tests.

Prediction of Tablet Characteristics from Residual Stress Distribution Estimated by the Finite Element Method

Tablet characteristics of tensile strength and disintegration time were predicted using residual stress distribution, simulated by the finite element method (FEM). The Drucker-Prager Cap (DPC) model was selected as the method for modeling the mechanical behavior of pharmaceutical powders composed of lactose (LAC), cornstarch (CS), and microcrystalline cellulose (MCC). The DPC model was calibrated using a direct shear test and analysis of the hardening law of the powder. The constructed DPC model was fed into the analysis using the FEM, and the mechanical behavior of pharmaceutical powders during compaction was analyzed using the FEM. The results revealed that the residual stress distribution of the tablets was uniform when the compression force increased. In particular, the residual stress distribution of tablets composed of equal amounts of LAC, CS, and MCC was more uniform than the tablets composed of 67% LAC and 33% CS, with no MCC. The tensile strength and disintegration time were predicted accurately from the residual stress distribution of tablets using multiple linear regression analysis and partial least squares regression analysis. This suggests that the residual stress distribution of tablets is related closely to the tensile strength and disintegration time.

Simulation of the Pressing Process with Combined Forces by Using ABAQUS Software

Actual for machines building is it the problem of finding technological solutions to increase the quality of parts, increase productivity and save resources. Greater interest in it shows the materials that incorporate a range of mechanical proprieties. In this category it is joining metal powder as material, and parts thereof, which occupies a significant share in parts manufacturing having improved and special proprieties. The present work is carried out simulating metal powder pressing process by application of combined forces. To describe properties of metal powder was used Drucker-Prager cap model.

Numerical simulation of residual stress field in green power metallurgy compacts by modified Drucker–Prager Cap model

Compaction process simulation and residual stress prediction of green PM compact were carried out with elasto-plastic 3D FEA based on the modified Drucker–Prager Cap model in Abaqus. The model parameters of the investigated powder Distaloy AE were determined as functions of relative density through typical mechanical property tests of powder. The model was implemented as a user subroutine USDFLD. Single sided compaction of a d20 mm×5 mm disk green compact of Distaloy AE was simulated, and the residual stress of the disk after ejection was predicted with FEA. The FEA results of the compaction process and the residual stress of the disk show good agreement with compaction experiments and X-ray diffraction measurements, which validates the model and its parameters. The results indicate that the compressive residual stresses exist mainly in a thin layer on the side surface, but the residual stresses are very small on the top and bottom surfaces.

FEM simulation of the die compaction of pharmaceutical products: Influence of visco-elastic phenomena and comparison with experiments

This work studies the influence of visco-elastic behavior in the finite element method (FEM) modeling of die compaction of pharmaceutical products and how such a visco-elastic behavior may improve the agreement between experimental and simulated compression curves. The modeling of the process was conducted on a pharmaceutical excipient, microcrystalline cellulose (MCC), by using Drucker-Prager cap model coupled with creep behavior in Abaqus(®) software. The experimental data were obtained on a compaction simulator (STYLCAM 200R). The elastic deformation of the press was determined by performing experimental tests on a calibration disk and was introduced in the simulation. Numerical optimization was performed to characterize creep parameters. The use of creep behavior in the simulations clearly improved the agreement between the numerical and experimental compression curves (stresses, thickness), mainly during the unloading part of the compaction cycle. For the first time, it was possible to reproduce numerically the fact that the minimum tablet thickness is not obtained at the maximum compression stress. This study proves that creep behavior must be taken into account when modeling the compaction of pharmaceutical products using FEM methods.

Improvement in robustness and computational efficiency of material models for finite element analysis of metal powder compaction and experimental validation

In metal powder compaction, density nonuniformity can be a source of flaws. Material models in finite element analysis for the prediction of density distribution still lack robustness and are computationally expensive. In this work, the Drucker–Prager cap (DPC) material model is implemented into the commercial finite element (FE) software ABAQUS/Explicit using the user-subroutine VUMAT. Yield functions in this material model are pressure-dependent and the curvature of the cap yield surface is high. This can cause numerical instability. We implemented a sub-increment technique to address this instability problem in a previous paper (Kashani et al., Trans North Am Manuf Res Inst SME 38:623–631, 2010). The DPC model is also a non-smooth, multi-yield surface material model which has instability problems at the intersection of the yield surfaces; we adopted the corner region in the DPC material models for soils in order to remove instability and the results of which were presented in (Kashani et al., Trans North Am Manuf Res Inst SME 38:623–631, 2010). The computational efficiency of the DPC material model was improved using a novel technique to solve the constitutive equations analytically which was shown in a previous paper by the authors (Kashani et al., Trans North Am Manuf Res Inst SME 38:623–631, 2010). In this paper, experimental tests were conducted where cylindrically shaped parts were compacted from Distaloy AE iron-based powder to 7.0 g/cm3 using 592 MPa of pressure. To measure local density, metallography and image processing were used to find the void area fraction of the surface. The FE results were compared to experimental results and it was shown that the FE analysis predicted local relative density within 3 % of the actual experimental measurements.

The effect of punch's shape on die compaction of pharmaceutical powders

This paper investigates the compaction of pharmaceutical powders using different shapes of punches. We introduce a model of mechanical behaviour Drucker–Prager Cap (DPC), using the approach of compressible continuous media. The model parameters that are depending on the material density, were identified from experimental data and a calibration process was applied on Microcrystalline Cellulose (MCC) powder. In addition, the mathematical formulation of the boundary problem of compaction in rigid tools brings back to an optimization problem with constraint, which is solved by finite element method. The Drucker–Prager Cap model, which is implemented in Abaqus/Standard software, was employed using a user subroutine, USDFLD. Three kinds of typical pharmaceutical tablets are considered: flat-face tablet and concave face tablet with two different depths. Results of simulations of die compaction cycle as compression, decompression and ejection, reproduce the powder compaction process for the studied shaped punches. The effects of the punch's shape on the compaction process were observed on the distribution and the maximum of stress and density in the compact. Examination of the density gradient according to the shape, suggests a capping tendency, which increases with the punch depth. This study illustrates the potentiality of the FEM method, which could be used as an efficient tool to predict the density and the stress distributions into shaped compacts and to provide a diagnostic of the capping problems.

Modelling of the break force of tablets under diametrical compression

A numerical method to predict the break force of curved faced tablets is proposed. The constitutive model and the failure criteria necessary to obtain predictions consistent with experimental data are identified. A modified Drucker-Prager cap model together with a maximum principal stress based failure criteria was found sufficient to predict the break force of tablets under diametrical compression loading. The conditions for the validity of the method were identified with reference to practical tablet shapes and failure patterns. Under these conditions the numerical procedures can be used as a practical tool to predict tablet breakage as an alternative to the empirical methods currently used in pharmaceutical product design and process development.

Modeling and Simulation of Pharmaceutical Powder Compaction

The finite element method was conducted to simulate the pharmaceutical powder compression process by using Drucker–Prager Cap model and elastic-plastic deformation theory. The effects of different friction coefficient on tablet property were systematically studied. The results show that the pressure-density curves shift towards right-hand side with slight decrease at smaller friction coefficient. The fluidity of powder remains the inverse decrease with the friction coefficient, and the density distribution changed more uniform. The maximum Mises stress becomes larger with the friction coefficient increased. The powder displacement decreases near die as the friction coefficient increasing. The research can both predict the tablet property and provide the theory reference for tablet practice production through the finite element analysis of pharmaceutical powder compaction.

Finite Element Analysis of Pharmaceutical Tablet Compaction

A finite element simulation of convex tablet compaction was present in this paper with Drucker–Prager Cap model of lactose material. The effects of different compression speed on tablet property were analysis. The results show that the maximum stress appears the top and bottom near the die and the mises stress distribution become more uniform with the speed decreased. The density distribution change little with the variation of compression speed and the maximum density locate the top and bottom near the die rim. The compression speeds have little affected on the powder displacement. The research can contribute to save cost for tablet production test through the simulation analyze the tablet property of compression process.

Finite Element Method (FEM) modeling of the powder compaction of cosmetic products: Comparison between simulated and experimental results

The numerical modeling of the die compaction process using the Finite Element Method (FEM) and the Drucker Prager Cap (DPC) Model has been widely developed in recent years. The advantage of this approach is to provide access to the distribution of variables in the powder bed (local values of stresses, strains and density) which permit to understand better the process, but also to predict the influence of the tools geometry.In the field of pharmaceuticals and cosmetics only a few kinds of powder have been studied, that do not represent the variety of the powder used in this industries. In this work, we present for the first time the simulation of the compression of a cosmetic powder corresponding to an eye shadow. Moreover, one of the aims of this article was to compare the experimental results and the simulations, which was not for now widely done in the existing literature.The first step was the determination of the parameters of the powder in order to implement the DPC model for the simulation. The image of the distribution of the density and stress inside the compact during the compaction obtained by the modeling were totally consistent with the existing literature.The comparison between experimental and simulation results showed that some of the parameters were well simulated, such as the axial transmission, the radial transmission during the loading, the hardening and the final plastic deformation of the compact. Nevertheless it was also shown that there was a disagreement between experiment and simulation for the thickness under compression and the stress evolution during the unloading phase. It was proved that these disagreements came from the linear elastic model used for the simulation.This work emphasizes the importance of the comparison between experiment and simulation to improve the simulation results and prediction abilities.

Calibration of a Density-Dependent Modified Drucker-Prager Cap Model for AZO Powder

AZO (Aluminum doped Zinc Oxide) is widely used to produce transparent conductive coatings for liquid crystal displays, flat panel displays, plasma displays, touch panels, and electronic ink applications. The densification behavior of AZO powder is a critical factor related to the design of the compaction process. In this study, the densification behavior of AZO powder during cold compaction has been investigated in order to calibrate the modified Drucker-Prager Cap (DPC) model for FE simulations. A compaction test with a cylindrical die was carried out, and two failure tests were performed: the diameteral compression test and the uniaxial compression test. AZO compacts with various densities from the compact tests were used as specimens for the failure tests. Based on the experimental results, the parameters of the modified DPC model were determined through simple manipulations.

Analysis of strain stress state in roller compaction process

The process of drawing and densification of powdered microcrystalline cellulose by roller press in a steady state operation is analyzed using a 2D modeling with the finite element method and the modified Drucker–Prager Cap model as material behavior. Distributions of process variables in contact surface between powder and roller such as pressure, shear stress and relative speed were predicted and used to analyze the basic mechanisms of the transport and the densification of powder between rolls. The results show clearly the existence of three contiguous zones: a phase where the powder is drawn between rolls by a sliding mechanism, a sticking phase where the powder is transported with the same velocity as the roll and where the densification by deforming the powder bed is achieved under the increase of roll pressure that reaches its peak before the neutral angle. The formed compact is then expulsed out of the gap by a slip mechanism resulting from the change of the sign of the shear stress. The predicted density distribution between the rolls, shows a gradual increase. The density reaches its maximum before the neutral point and shows values in agreement with the density of strips prepared with an instrumented roll press. The effect of varying the material parameters on the maximum pressure and the nip angle is also investigated. Beyond the description of the basic mechanisms of roller compaction, this modeling shows a real potential of the optimization of the roller compaction process.

Experimental calibration of density-dependent modified Drucker-Prager/Cap model using an instrumented cubic die for powder compact

Theory and experimental calibration of density dependent modified Drucker-Prager/Cap (DPC) model are presented by using a novel instrumented cubic die in powder compaction tests. The cubic die is designed for directly determining the loading and unloading forces and displacements of powder compact inside the die in compaction and transverse directions without any additional calibration. The cap surface parameters and elastic properties are characterized by fitting stress and strain curves recorded during loading and unloading at different green density values and the plastic material parameters for failure surface are obtained by additional radial and axial compressive tests. The experimental data is subsequently used in the simulation of cubic die compaction to verify the results from the density dependent modified DPC model.

Finite element analysis of pharmaceutical tablet compaction using a density dependent material plasticity model

Finite element method (FEM) simulations of pharmaceutical tablet compaction using a Drucker–Prager Cap (DPC) model are presented in which material properties are relative density (solid fraction) dependent. Results from the solid fraction dependent model are compared to those from a constant property model. Predictions from the solid fraction dependent model more closely match experimental measurements of surface hardness, punch force, and material displacement than the constant property model. These results suggest that FEM simulations using the DPC model should account for material property dependence on local solid fraction.

Nonlinear numerical modelling for the effects of surface explosions on buried reinforced concrete structures

The analysis of structure response and design of buried structures subjected to dynamic destructive loads have been receiving increasing interest due to recent severe damage caused by strong earthquakes and terrorist attacks. For a comprehensive design of buried structures subjected to blast loads to be conducted, the whole system behaviour including simulation of the explosion, propagation of shock waves through the soil medium, the interaction of the soil with the buried structure and the structure response needs to be simulated in a single model. Such a model will enable more realistic simulation of the fundamental physical behaviour. This paper presents a complete model simulating the whole system using the finite element package ABAQUS/Explicit. The Arbitrary Lagrange Euler Coupling formulation is used to model the explosive charge and the soil region near the explosion to eliminate the distortion of the mesh under high deformation, while the conventional finite element method is used to model the rest of the system. The elasto-plastic Drucker-Prager Cap model is used to model the soil behaviour. The explosion process is simulated using the Jones-Wilkens-Lee equation of state. The Concrete Damage Plasticity model is used to simulate the behaviour of concrete with the reinforcement considered as an elasto-plastic material. The contact interface between soil and structure is simulated using the general Mohr-Coulomb friction concept, which allows for sliding, separation and rebound between the buried structure surface and the surrounding soil. The behaviour of the whole system is evaluated using a numerical example which shows that the proposed model is capable of producing a realistic simulation of the physical system behaviour in a smooth numerical process.

A study on the sensitivity of Drucker–Prager Cap model parameters during the decompression phase of powder compaction simulations

The compaction of pharmaceutical powders can be simulated using phenomenological elasto-plastic continuum models adopted from soil mechanics. These models are typically implemented in finite element codes and have been used recently to investigate the macroscopic property distributions in powders during compaction. The present study demonstrates the importance of obtaining accurate yield surface parameters for use in such models. A commercial finite element code implementing the Drucker–Prager Cap (DPC) model was used to model the compression and decompression stages of powder compaction in a tabletting operation. The parameters used in the DPC model were obtained from the literature. Although the compression stage of the process gave expected behavior, the decompression response was unrealistic for at least one set of published data. Small values for the friction and cohesion parameters resulted in a significant elastic recovery during decompression. This study demonstrates the need to obtain accurate parameter data in order to model the decompression stage of powder compaction.

Temperature Evolution during Compaction of Pharmaceutical Powders

A numerical approach to the prediction of temperature evolution in tablet compaction is presented here. It is based on a coupled thermomechanical finite element analysis and a calibrated Drucker-Prager Cap model. This approach is capable of predicting transient temperatures during compaction, which cannot be assessed by experimental techniques due to inherent test limitations. Model predictions are validated with infrared (IR) temperature measurements of the top tablet surface after ejection and match well with experiments. The dependence of temperature fields on speed and degree of compaction are naturally captured. The estimated transient temperatures are maximum at the end of compaction at the center of the tablet and close to the die wall next to the powder/die interface.

A modified Drucker-Prager Cap model for die compaction simulation of pharmaceutical powders

In this paper, we present a modified density-dependent Drucker-Prager Cap (DPC) model to simulate the compaction behaviour of pharmaceutical powders. In particular, a nonlinear elasticity law is proposed to describe the observed nonlinear unloading behaviour following compaction. To extract the material parameters for the modified DPC model, a novel experimental calibration procedure is used, based on uniaxial single-ended compaction tests using an instrumented cylindrical die. The model is implemented in ABAQUS by writing a user subroutine, and a calibration process on microcrystalline cellulose (MCC) Avicel PH101 powders is detailed. The calibrated parameters are used for the manufacturing process simulation of two kinds of typical pharmaceutical tablets: the flat-face tablet and the concave tablet with single or double radius curvatures. The model developed can describe not only the compression and decompression phases, but also the ejection phase. The model is validated by comparing finite element simulations with experimental loading–unloading curves during the manufacture of 8 and 11 mm round tablets with flat-face (FF), single radius concave (SRC) and double radius concave (DRC) profiles. Moreover, the density and stress distributions during tabletting are used to analyse and explain the failure mechanism of tablets. The results show that the proposed model can quantitatively reproduce the compaction behaviour of pharmaceutical powders and can be used to obtain the stress and density distributions during compression, decompression and ejection.

Analysis of pharmaceutical powder compaction using multiplicative hyperelasto-plastic theory

Single-ended compaction of lactose powder is investigated numerically within the framework of multiplicative hyperelasto-plastic theory. In keeping with previous work in the pharmaceutical field, a slightly modified Drucker–Prager Cap model is described and used in the simulations. Coulomb friction is included on all interfaces. Our results indicate that simulations of this type may be useful not only to determine density and stress distributions within tablets, as has been done hitherto, but also may provide indications of circumstances under which the tableting operation fails due to capping.