Determination of Constitutive Model Parameters and 3-D Finite Element Formulation for Powder Compaction

ABSTRACT

The knowledge of stress-strain distribution of particulate materials during compression is crucial to the powder processing industries. The finite element technology holds the potential to accurately describe the powder's stress-strain (pressure-density) response during compression. At present, most of the FEMs are two-dimensional or axisymmetric. which can not precisely model the compaction process. In this project, a 3-D finite element formulation for powder compression is presented. The material parameters (for an elastoplastic model and an elasto-viscoplastic model) for three selected materials have been measured. The flexible boundary cubical triaxial tester was used to determine the constitutive model parameters. The constitutive models were verified using data from cubical triaxial tests.     

Stochastic nonlinear bending response of functionally graded material plate with random system properties in thermal environment

This study deals with the stochastic nonlinear bending response of functionally graded materials (FGMs) plate with uncertain system properties subjected to transverse uniformly distributed load in thermal environments. The system properties such as material properties of each constituent’s material, volume fraction index and transverse load are taken as independent random input variables. The material properties are assumed to be temperature independent (TID) and temperature dependent (TD). The basic formulation is based on higher order shear deformation theory with von-Karman nonlinear strain kinematics using modified C ⁰ continuity. A direct iterative based nonlinear finite element method in conjunction with first-order perturbation technique developed by last two authors for the composite plate is extended for the FGM plate to compute the second order statistics (mean and standard deviation) of the nonlinear bending response of the FGM plates. Effects of TD, TID material properties, aspect ratios, volume fraction index and boundary conditions, uniform temperature and non-uniform temperature distribution on the nonlinear bending are presented in detail through parametric studies. The present outlined approach has been validated with the results available in the literature and independent Monte Carlo simulation.     

Non‐local dispersive model for wave propagation in heterogeneous media: one‐dimensional case

Non‐local dispersive model for wave propagation in heterogeneous media is derived from the higher‐order mathematical homogenization theory with multiple spatial and temporal scales. In addition to the usual space–time co‐ordinates, a fast spatial scale and a slow temporal scale are introduced to account for rapid spatial fluctuations of material properties as well as to capture the long‐term behaviour of the homogenized solution. By combining various order homogenized equations of motion the slow time dependence is eliminated giving rise to the fourth‐order differential equation, also known as a ‘bad’ Boussinesq problem. Regularization procedures are then introduced to construct the so‐called ‘good’ Boussinesq problem, where the need for C¹ continuity is eliminated. Numerical examples are presented to validate the present formulation. Copyright © 2002 John Wiley & Sons, Ltd.     

Quantitative Polarization-Resolved Second-Harmonic-Generation Microscopy of Glycine Microneedles

Second-harmonic generation (SHG) is a nonlinear optical process that can provide disease diagnosis through characterization of biological building blocks such as amino acids, peptides, and proteins. The second-order nonlinear susceptibility tensor χ⁽²⁾ of a material characterizes its tendency to cause SHG. Here, a method for finding the χ⁽²⁾ elements from polarization-resolved SHG microscopy in transmission mode is presented. The quantitative framework and analytical approach that corrects for micrometer-scale morphology and birefringence enable the determination and comparison of the SHG susceptibility tensors of β- and γ-phase glycine microneedles. The maximum nonlinear susceptibility coefficients are d₃₃ = 15 pm V⁻¹ for the β and d₃₃ = 5.9 pm V⁻¹ for the γ phase. The results demonstrate glycine as a useful biocompatible nonlinear material. This combination of the analytical model and polarization-resolved SHG transmission microscopy is broadly applicable for quantitative SHG material characterization and diagnostic imaging.     

Static Response of Geometrically Nonlinear Laminated Composite Plates Having Uncertain Material Properties

The effect of uncertainty in material properties on the transverse bending of laminated composite plate is investigated. The transverse shear and large rotations have been included in the system equation in the framework of higher order shear deformation theory. The analysis uses Green–Lagrange nonlinear strain displacement equations to model geometric nonlinearity. The stochastic finite element analysis is performed using a direct iteration approach to handle deterministic geometric nonlinearity and perturbation approach to handle the randomness in the material properties. Mean and variance of the transverse deflection have been obtained by employing a C⁰ isoparametric nonlinear finite element model.     

Statistical monitoring of nonlinear product and process quality profiles

In many quality control applications, use of a single (or several distinct) quality characteristic(s) is insufficient to characterize the quality of a produced item. In an increasing number of cases, a response curve (profile) is required. Such profiles can frequently be modeled using linear or nonlinear regression models. In recent research others have developed multivariate T² control charts and other methods for monitoring the coefficients in a simple linear regression model of a profile. However, little work has been done to address the monitoring of profiles that can be represented by a parametric nonlinear regression model. Here we extend the use of the T² control chart to monitor the coefficients resulting from a parametric nonlinear regression model fit to profile data. We give three general approaches to the formulation of the T² statistics and determination of the associated upper control limits for Phase I applications. We also consider the use of non‐parametric regression methods and the use of metrics to measure deviations from a baseline profile. These approaches are illustrated using the vertical board density profile data presented in Walker and Wright (Comparing curves using additive models. Journal of Quality Technology 2002; 34:118–129). Copyright © 2007 John Wiley & Sons, Ltd.     

Layerwise modeling of progressive damage in fiber-reinforced composite laminates

This paper investigates the effects of discrete layer transverse shear strain and discrete layer transverse normal strain on the predicted progressive damage response and global failure of fiber-reinforced composite laminates. These effects are isolated using a hierarchical, displacement-based 2-D finite element model that includes the first-order shear deformation model (FSD), type-I layerwise models (LW1) and type-II layerwise models (LW2) as special cases. Both the LW1 layerwise model and the more familiar FSD model use a reduced constitutive matrix that is based on the assumption of zero transverse normal stress; however, the LW1 model includes discrete layer transverse shear effects via in-plane displacement components that are C ⁰ continuous with respect to the thickness coordinate. The LW2 layerwise model utilizes a full 3-D constitutive matrix and includes both discrete layer transverse shear effects and discrete layer transverse normal effects by expanding all three displacement components as C ⁰ continuous functions of the thickness coordinate. The hierarchical finite element model incorporates a 3-D continuum damage mechanics (CDM) model that predicts local orthotropic damage evolution and local stiffness reduction at the geometric scale represented by the homogenized composite material ply. In modeling laminates that exhibit either widespread or localized transverse shear deformation, the results obtained in this study clearly show that the inclusion of discrete layer kinematics significantly increases the rate of local damage accumulation and significantly reduces the predicted global failure load compared to solutions obtained from first-order shear deformable models. The source of this effect can be traced to the improved resolution of local interlaminar shear stress concentrations, which results in faster local damage evolution and earlier cascading of localized failures into widespread global failure.     

A cyclic multiaxial model for concrete

A rate-independent plasticity constitutive model is proposed, for the stress-strain and strength behavior of plain concrete, under complex multiaxial stress-paths, including stress reversals. The only material parameters required by the model are the uniaxial cylinder strength f _cand the strain at the peak of the monotonic stress-strain curve, ₀ . The model is based on a bounding surface in stress space, which is the outermost surface that can be reached by the stress point. When the size of the bounding surface decreases with increasing maximum compressive principal strain _max on the material, strength degradation during cyclic loading as well as the falling post-failure branch of the stress-strain curves, can be modeled. The distance from the current stress point to the bounding surface, determines the values of the main parameters of the inelastic stress-strain relations, i.e. of the plastic shear modulus H ^P, and the shear-compaction/dilatancy factor Strains are almost completely inelastic from the beginning of deformation. The inelastic portion of the incremental strain is computed by superposition of 1) the deviatoric strain increment, which occurs in the direction of the deviatoric stress and is proportional to the octahedral shear stress increment and inversely proportional to the plastic shear modulus 2) the volumetric strain increment, which consists of a portion which is proportional to the hydrostatic stress increment, and another which equals the product of the octahedral shear strain increment and the shear compaction/dilatancy factor Stress reversals are defined separately for the hydrostatic and the deviatoric component of the stress tensor, and the parameters of the inelastic stress-strain relations are given as different functions of the stress and strain history, for virgin loading, unloading, reloading, or for the post-failure falling branch.The incremental stress-strain law is set in the form of incremental compliance and rigidity matrices, and implemented into a nonlinear dynamic finite element code.     

Numerical implementation and validation of a consistently homogenized higher order plasticity model

A homogenization theory was developed earlier that starts with a meso‐scale gradient plasticity model at the bottom and recovers a macroscopically continuous micromorphic model at the top. Through the scale transition framework, the granular mechanics are smeared consistently over a single grain such that the fine scale properties, microstructural length scale (l), and grain size (L) manifest themselves naturally in the homogenized relations, a point of departure from many continuous higher order theories that assume the constitutive relations a priori. This paper elaborates on the numerical implementation of the homogenized model and benchmark its performance through a plane indentation example against detailed numerical simulations. For the two limiting cases of microfree and microhard condition at grain boundaries, the excellent predictive capability of the homogenized model is demonstrated for a range of l/L ratios, at a significantly lower computational cost. It is furthermore highlighted that a more realistic response at grain boundaries can be achieved easily in the homogenized model, by changing the interfacial resistance parameter. In contrast, a non‐trivial numerical treatment is required at the grain boundaries with meso‐scale models. Finally, the homogenized model is shown to perform well even in the absence of a strong scale separation between meso and macro. Copyright © 2015 John Wiley & Sons, Ltd.     

Coupled heat conduction and thermal stress analyses in particulate composites

This study introduces two micromechanical modeling approaches to analyze spatial variations of temperatures, stresses and displacements in particulate composites during transient heat conduction. In the first approach, a simple micromechanical model based on a first order homogenization scheme is adopted to obtain effective mechanical and thermal properties, i.e., coefficient of linear thermal expansion, thermal conductivity, and elastic constants, of a particulate composite. These effective properties are evaluated at each material (integration) point in three dimensional (3D) finite element (FE) models that represent homogenized composite media. The second approach treats a heterogeneous composite explicitly. Heterogeneous composites that consist of solid spherical particles randomly distributed in homogeneous matrix are generated using 3D continuum elements in an FE framework. For each volume fraction (VF) of particles, the FE models of heterogeneous composites with different particle sizes and arrangements are generated such that these models represent realistic volume elements “cut out” from a particulate composite. An extended definition of a RVE for heterogeneous composite is introduced, i.e., the number of heterogeneities in a fixed volume that yield the same expected effective response for the quantity of interest when subjected to similar loading and boundary conditions. Thermal and mechanical properties of both particle and matrix constituents are temperature dependent. The effects of particle distributions and sizes on the variations of temperature, stress and displacement fields are examined. The predictions of field variables from the homogenized micromechanical model are compared with those of the heterogeneous composites. Both displacement and temperature fields are found to be in good agreement. The micromechanical model that provides homogenized responses gives average values of the field variables. Thus, it cannot capture the discontinuities of the thermal stresses at the particle-matrix interface regions and local variations of the field variables within particle and matrix regions.     

Ultrafast optical Kerr gate of bismuth–plumbum oxide glass for time-gated ballistic imaging

We demonstrated the time-gated ballistic imaging technique using a femtosecond optical Kerr gate (OKG) of bismuth–plumbum oxide glass, the nonlinear optical properties of which were also investigated. The third-order nonlinear refractive-index n₂ of the bismuth–plumbum oxide glass was measured to be 2.19?×?10^?15?cm²/W, and the nonlinear response time was estimated to be shorter than 180?fs. For the time-gated ballistic imaging, the maximum measurable optical density of turbid media using the OKG of bismuth–plumbum oxide glass was 9.3, while only 7.0 for the OKG of quartz glass. And the intensities of the images for the bismuth–plumbum oxide glass were approximately two orders of magnitude higher than that for the quartz glass. The experimental results indicated that the bismuth–plumbum oxide glass was an excellent optical material for nonlinear optical applications.     

Optimal composition of an acrylamide and N,N′-methylenebisacrylamide holographic recording material

Abstract

We study the effect of the addition of a cross-linking agent (N,N′-methylenebisacrylamide) to a photopolymerizable matrix for real-time holography. Optimization of the concentration of this component has been achieved, paying attention to holographic parameters such as energy sensitivity and diffraction efficiency. Diffraction efficiencies of around 88% have been obtained with energy exposures of 12 mJ cm^?2. At the same time considering a nonlinear response of the material we have carried out a theoretical study of the experimental results. We observed a nonlinear response of the material with regard to the storage intensity. This is a very interesting point in reflection holographic optical elements.     

Elastoplastic behavior of metal matrix composites based on incremental plasticity and the Mori-Tanaka averaging scheme

The applicability of the Mori-Tanaka averaging method for the prediction of the response of binary composites loaded in the plastic range is investigated. The applied loading is subdivided into small increments and the Eshelby solution for the inhomogeneity problem is used in conjunction with the Mori-Tanaka averaging scheme to obtain the load increments in the various phases. Since the Eshelby solution depends on the instantaneous matrix material properties and these are updated at the end of each load increment by using the backward difference scheme, an iterative procedure is necessary for the calculation of the correct load increments in the phases (concentration factors). The performance of the Mori-Tanaka method is compared with results obtained using the periodic hexagonal array (PHA) finite element model and experimental results for a B-Al unidirectional fibrous composite; it is also compared with numerical simulations obtained from the modified PHA model for a SiC _w -Al particulate composite.     

Backcalculation of viscoelastic and nonlinear flexible pavement layer properties from falling weight deflections

Appropriate characterisation of individual layer properties is crucial for mechanistic analysis of flexible pavements. Typically in inverse analyses, pavements are modelled as elastic or nonlinear elastic to obtain layer material properties through non-destructive falling weight deflectometer (FWD) testing. In this study, a layered viscoelastic–nonlinear forward model (called LAVAN) was used to develop a genetic algorithm-based backcalculation scheme (called BACKLAVAN). The LAVAN can consider both the viscoelastic behaviour of asphalt concrete (AC) layer and nonlinear elastic behaviour of unbound layers. The BACKLAVAN algorithm uses FWD load-response history at different test temperatures to backcalculate both the (damaged) E(t) and |E^*| master curve of AC layers and the linear and nonlinear elastic moduli of unbound layers of in-service pavements. The BACKLAVAN algorithm was validated using two FWD tests run on a long-term pavement performance section. Comparison between the backcalculated and measured results indicates that it should be possible to infer linear viscoelastic properties of AC layer as well as nonlinear elastic properties of unbound layers from FWD tests.     

The implementation of a constitutive model with weighted dynamic recovery and its application

An explicit updating algorithm has been developed, based on the backward Euler integration methods for the modified Armstrong–Frederick type of nonlinear kinematic hardening constitutive model with weighted dynamic recovery. This has been achieved by considering the consistency of the updated stresses, back stresses and the yield function, resulting in three sets of nonlinear equations which are then linearised using the Newton method. The developed algorithm and a linearised version have been implemented in ABAQUS as user material subroutines. Numerical simulations show that as long as the size of the incremental plastic strain is small so that k₂ⁱp0.1, both the linearised and the nonlinear algorithm converge to the same solution. Numerical analysese have been conducted to predict the strain response near the fuel ventilation hole on a wing pivot fitting of fighter aircraft, and good agreement has been observed between the experimental and numerical results.     

Influence of plastic deformation in flexible pad laser shock forming – experimental and numerical analysis

Flexible Pad Laser Shock Forming (FPLSF) is a new microforming process using laser-induced shock pressure and a hyperelastic flexible pad to induce high strain-rate (~10⁵ s^?1) plastic deformation on metallic foils to produce 3D microcraters. This paper studies the effect of two significant process parameters of FPLSF, flexible pad material and its thickness, on the deformation characteristics of the metal foils using experiments and finite element analysis. A finite element model is developed to simulate the FPLSF process. The stress-strain distribution across the foil and the flexible pad at different process stages of FPLSF are studied using FE analysis. Flexible pad materials including silicone rubber, polyurethane rubber, and natural rubber with thicknesses ranging between 300 μm and 3000 μm have been investigated in detail. Experimental results highlight that both the hardness and thickness of the flexible pad significantly influence the deformed crater geometry, thickness distribution across the formed crater and surface hardness at the crater surfaces. The experimental results are correlated with the stress-strain distributions from finite element analysis to study the underlying behaviors.     

Optical nonlinearity and optical limiting of CdSeS/ZnS quantum dots

CdSeS/ZnS quantum dots (QDs) were synthesized through the chemical route. The optical limiting behavior of these QDs was observed. The quantum dots’ nonlinear absorption and nonlinear refraction were investigated by the Z-scan technique using a Nd:YAG laser second-harmonic radiation (λ = 532 nm, t = 35 ps). Based on the absorption and fluorescence spectra, it is reasonable for us to infer that the nonlinear absorption arises from free carrier absorption (FCA). These QDs have average absorption cross-section of 1.26 × 10^?16cm² and nonlinear refractive index in the order of 10^?8esu. The large nonlinear absorption perhaps allows them to be candidate material for the optical limiting devices.     

Surface plasmon-enhanced third-order optical non-linearity of silver triangular nanoplate

Abstract

We have obtained Ag triangular nanoplates with plasmon resonance bands locating from 750 to 950 nm by wet chemical method. The third-order optical non-linear response property of Ag triangular nanoplate is investigated using z-scan technique. The incident wavelength dependence of χ⁽³⁾ (the third-order susceptibility) shows the third-order nonlinear behaviour of Ag nanoplate is greatly modified by its plasmon resonance property, for the largest value of χ⁽³⁾ is observed around the wavelength of plasmon resonant peak. Also, we find the maximum value of Ag nanoplate’s χ⁽³⁾ is 7.46 × 10^?11 esu, which is about 1–3 orders of magnitude larger than that of many other nanomaterials including Au nanorod, nanobipyramid and nanocube, as well as Ag nanosphere and nanodisc. This fact indicates the Ag triangular nanoplate is a kind of useful nonlinear material with larger third-order nonlinearity, showing great potentials in the explorations of functional non-linear devices.     

Optical and dielectric properties of nitrophenolate based nonlinear optical crystal

A semi-organic nonlinear optical (NLO) material, lithium-p-nitrophenolate trihydrate (LPNP) was synthesized. Single crystals of dimensions 20 × 7 × 3 mm³ were harvested following the solvent evaporation technique. The functional groups present in the compound were identified from FT-IR and FT-Raman spectral analyses, and its molecular structure was confirmed. Identification of the compound was accomplished by X-ray diffraction technique (powder and single crystal XRD). The unit-cell dimensions and the morphology of the grown crystals were identified from single crystal XRD measurements. The thermal transport properties, thermal effusivity (e), thermal diffusivity (α), thermal conductivity (k) and heat capacity (C _p) were measured by the photopyroelectric technique at room temperature. Dielectric constant and dielectric loss were also measured as a function of frequency between 42 Hz and 5 MHz, and temperature between 32 and 100 °C. From optical transmittance measurements, the direct optical band gap of the LPNP crystal was estimated to be 2.47 eV. Laser damage threshold is 60.91 GW cm⁻². Powder second harmonic generation (SHG) measurement was carried out using a modified Kurtz–Perry technique. Third order nonlinear response was studied using Z-scan technique with a He–Ne laser (632.8 nm, 35 mW). The magnitude and the sign of the nonlinear absorption and nonlinear refraction are derived from a transmittance curve. The NLO parameters Intensity dependent refractive index n ₂, nonlinear absorption coefficient β and third order susceptibility χ⁽³⁾ were estimated.     

A two‐scale failure model for heterogeneous materials: numerical implementation based on the finite element method

In the first part of this contribution, a brief theoretical revision of the mechanical and variational foundations of a Failure‐Oriented Multiscale Formulation devised for modeling failure in heterogeneous materials is described. The proposed model considers two well separated physical length scales, namely: (i) the macroscale where nucleation and evolution of a cohesive surface is considered as a medium to characterize the degradation phenomenon occurring at the lower length scale, and (ii) the microscale where some mechanical processes that lead to the material failure are taking place, such as strain localization, damage, shear band formation, and so on. These processes are modeled using the concept of Representative Volume Element (RVE). On the macroscale, the traction separation response, characterizing the mechanical behavior of the cohesive interface, is a result of the failure processes simulated in the microscale. The traction separation response is obtained by a particular homogenization technique applied on specific RVE sub‐domains. Standard, as well as, Non‐Standard boundary conditions are consistently derived in order to preserve objectivity of the homogenized response with respect to the micro‐cell size. In the second part of the paper, and as an original contribution, the detailed numerical implementation of the two‐scale model based on the finite element method is presented. Special attention is devoted to the topics, which are distinctive of the Failure‐Oriented Multiscale Formulation, such as: (i) the finite element technologies adopted in each scale along with their corresponding algorithmic expressions, (ii) the generalized treatment given to the kinematical boundary conditions in the RVE, and (iii) how these kinematical restrictions affect the capturing of macroscopic material instability modes and the posterior evolution of failure at the RVE level. Finally, a set of numerical simulations is performed in order to show the potentialities of the proposed methodology, as well as, to compare and validate the numerical solutions furnished by the two‐scale model with respect to a direct numerical simulation approach. Copyright © 2013 John Wiley & Sons, Ltd.