Drucker Prager Cap Research Articles

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.

Density and plastic strain evaluations using small-angle X-ray scattering and finite element simulations for powder compacts of complex shape

Previous work suggested that two-dimensional small-angle X-ray scattering (2D-SAXS) could offer a new method for evaluating the local variations of density, strain and principal strain direction within powder compacts, which arise due to the effects of friction and die shape. In order to test this method further, this work compared results from 2D-SAXS with finite element (FE) simulations using a modified density-dependent Drucker–Prager Cap (DPC) model, for compacts of complex shape, prepared using a cylindrical die, a flat-faced upper punch and shaped lower punches with three different central protrusions. Variations in compaction behaviour were observed, which were due to friction against the die walls and the punch shape. Good agreement was obtained between SAXS measurements and FE simulation, supporting previous indications. Hence, this combination of experimental and computational techniques appeared particularly powerful for investigating powder compaction behaviour, in considerable accuracy and detail. Moreover, observations of the compaction behaviour in the vicinity of the central protrusion may be relevant to tablets with embossed features or compacted artefacts of more complex shape.

Finite element modeling of interfacial forces and contact stresses of pneumatic tire on fresh snow for combined longitudinal and lateral slips

Significant challenges exist in the prediction of interaction forces generated from the interface between pneumatic tires and snow-covered terrains due to the highly non-linear nature of the properties of flexible tires, deformable snow cover and the contact mechanics at the interface of tire and snow. Operational conditions of tire–snow interaction are affected by many factors, especially interfacial slips, including longitudinal slip during braking or driving, lateral slip (slip angle) due to turning, and combined slip (longitudinal and lateral slips) due to brake-and-turn and drive-and-turn maneuvers, normal load applied on the wheel, friction coefficient at the interface and snow depth. This paper presents comprehensive three-dimensional finite element simulations of tire–snow interaction for low-strength snow under the full-range of controlled longitudinal and lateral slips for three vertical loads to gain significant mechanistic insight. The pneumatic tire was modeled using elastic, viscoelastic and hyperelastic material models; the snow was modeled using the modified Drucker–Prager Cap material model (MDPC). The traction, motion resistance, drawbar pull, tire sinkage, tire deflection, snow density, contact pressure and contact shear stresses were obtained as a function of longitudinal slip and lateral slip. Wheel states – braked, towed, driven, self-propelled, and driving – have been identified and serve as key classifiers of discernable patterns in tire–snow interaction such as zones of contact shear stresses. The predicted results can be applied to analytical deterministic and stochastic modeling of tire–snow interaction.

얼음의 재료 모델 적용 타당성 연구

To define ice as a solid material, mathematical and physical characteristics and their application examples are investigated for several materials' yield functions which include isotropic elastic, isotropic elastic-plastic, classical Drucker-Prager, Drucker-Prager Cap, Heinonen's elliptic, Derradji-Aouat's elliptic, and crushable foam models. Taking into account brittle failure mode of ice subject to high loading rate or extremely low temperature, isotropic elastic model can be better practicable than isotropic elastic-plastic model. If a failure criterion can be properly determined, the elastic model will provide relatively practicable impact force history from ice-hull interactions. On the other hand, it is thought that the soil models can better predict the ice spalling mechanism, since they contain both terms of shear stress-induced and hydrostatic stress-induced failures in the yield function.

Numerical Investigation of Stress Distribution during Die Compaction of Food Powders

A numerical method is presented to determine the internal stress distribution in powder compacts during uniaxial die compaction using the finite element method. A continuum-based analysis was carried out considering the powder body forming a tablet as an elastic-plastic continuum. Compaction behavior and mechanical material properties were defined using a modified density-dependent Drucker-Prager cap (DPC) material model. In addition, a nonlinear elasticity law was adopted to describe the nonlinear unloading behavior observed for the tested amorphous and crystalline food powders. The constitutive model was calibrated using an experimental procedure based on uniaxial die compaction experiments. All material-dependent parameters were determined experimentally using a fully instrumented hydraulic tablet press with a single-ended compaction profile. Numerical simulations of the compaction process were carried out by the commercial finite element software package ABAQUS using the calibrated material model and experimental friction data. The simulation results were in good agreement with experimental data, which demonstrated the suitability of this method to investigate internal processes during tableting.

Material Data for Modelling Density Distributions in Green Parts

Die compaction of powders is a process which involves filling a die with powder, compaction using rigid punches to form a dense compact and ejection from the die. The process can be treated as a large deformation plasticity problem. The challenge is to develop and implement appropriate constitutive models that capture the evolution of the powder from a loose state into a dense compact. In this paper we describe data analysis procedures and calibrate classic incremental plasticity models, such as Cam-Clay, Drucker-Prager cap models. The complexity of the models is increased from models with a hardening law to more complex constitutive models using density as state variable. The compaction behaviour of a range of powder materials is characterized experimentally. Numerical simulation of the compaction of simple parts and complex parts is demonstrated. The merits of various models are evaluated in terms of the balance between complexity and practicality. The discussion is illustrated with case studies exploring the applicability of the models specific to various powder pressing scenarios.

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.

Temperature and density evolution during compaction of a capsule shaped tablet

This paper continues the effort to validate the finite element based analysis of tableting. A three-dimensional capsule shaped tablet is studied using a Drucker–Prager cap constitutive model and a coupled thermomechanical analysis. Predictions of the model for the internal distribution of porosity and temperature are found to be in agreement with X-ray microtomography measurements of relative density and infrared camera measurements of surface temperatures of the ejected tablet. The fact that the model is calibrated using data from a cylindrical flat-faced tablet which can predict the compaction of a completely different shape proves the capability offered by finite element analysis. In addition, this method demonstrates the role it can play in the optimization of tableting operations in the spirit of quality by design principles.

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.

A combined experimental–numerical study of the compaction behavior of NaCl

The compaction behavior of NaCl as a model substance is investigated by an integrated experimental and computational approach. The method for characterization of this granular material employs convenient experiments: load–displacement measurements of compaction; measurements of strain on outer circumference of an elastic tubular die; load on bottom and top of the powder compact, as well as compressive strength tests. Related equations for identification of material parameters are derived and are used to characterize powder behavior and powder–die friction. Subsequently, these material parameters are used in simulations with the Drucker–Prager-Cap (DPC) model. For the verification of the computations density distributions are determined based on micro X-ray computer tomography. Good agreement between the spatial density distributions from measurements and simulations is obtained. Restrictions of computer tomography in powder compaction applications are specified. While the study employs NaCl as a model substance, the approach is applicable to a wider array of granular substances.

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.

Numerical Simulation on Pharmaceutical Powder Compaction

In this paper, we present a modified density-dependent Drucker-Prager Cap (DPC) model with a nonlinear elasticity law developed to describe the compaction behavior of pharmaceutical powders. The model is implemented in ABAQUS with a user subroutine. Using microcrystalline cellulose (MCC) Avicel PH101 as an example, the modified DPC model is calibrated and used for finite element simulations of uniaxial single-ended compaction in a cylindrical die. To validate the proposed model, finite element simulation results of powder compaction are compared with experimental results. It was found that finite element analyses gave a good prediction of both the loading-unloading curves during powder compaction and the compaction force required for making a tablet with a specified density. Further, the failure mechanisms of chipping, lamination and capping during tabletting are investigated by analysing the stress and density distributions of powders during the three different phases of the tabletting processes, i.e. compression, decompression and ejection. The results indicate that the model has excellent potential to describe the compaction process for generic pharmaceutical powders.

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.

Plastic Behaviour of Green Powder Metallurgical Compacts

The results of monotonic and cyclic uniaxial compression tests, in which the deviatoric component of the stress is predominant, carried out on green and recrystallized iron compacts with different levels of density are presented and discussed in order to analyse the macro and micromechanisms governing the mechanical behaviour of non-sintered PM materials. The plastic deformation of the particles, especially at the contact areas between neighbouring particles, produces an internal friction responsible for the main features observed in the behaviour of green metallic compacts. These experimental results show important discrepancies with the plasticity models, Cam-Clay and Drucker-Prager Cap, used to simulate the powder compaction stage. Possible causes for these discrepancies are pointed out.

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.

Computational modeling of the cold compaction of ceramic powders

A finite-element model of the cold compaction of ceramic powders by uniaxial pressing is developed and validated by comparison with experimental data. The mechanical behavior of processing powders is assumed according to the modified Drucker-Prager cap model. The frictional effects and the mechanical behavior of tools involved in the process are taken into account. The proposed model allows evaluation of the density distribution into the processed part, as well as stress and strain fields. Variations of the density distribution due to the unloading and the ejection of the part are evaluated