# Constitutive Models (constitutive + models)

Distribution by Scientific Domains

## Selected Abstracts

### Cyclic behavior of laterally loaded concrete piles embedded into cohesive soil

EARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS, Issue 1 2008

### Probabilistic yielding and cyclic behavior of geomaterials

INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 15 2010
Kallol Sett
Abstract In this paper, the novel concept of probabilistic yielding is used for 1-D cyclic simulation of the constitutive behavior of geomaterials. Fokker,Planck,Kolmogorov equation-based probabilistic elastic,plastic constitutive framework is applied for obtaining the complete probabilistic (probability density function) material response. Both perfectly plastic and hardening-type material models are considered. It is shown that when uncertainties in material parameters are taken into consideration, even the simple, elastic-perfectly plastic model captures some of the important features of geomaterial behavior, for example, modulus reduction with cyclic strain, which, deterministically, is only possible with more advanced constitutive models. Furthermore, it is also shown that the use of isotropic and kinematic hardening rules does not significantly improve the probabilistic material response. Copyright © 2010 John Wiley & Sons, Ltd. [source]

### Explicit integration of bounding surface model for the analysis of earthquake soil liquefaction

INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 15 2010
Konstantinos I. Andrianopoulos
Abstract This paper presents a new plasticity model developed for the simulation of monotonic and cyclic loading of non-cohesive soils and its implementation to the commercial finite-difference code FLAC, using its User-Defined-Model (UDM) capability. The new model incorporates the framework of Critical State Soil Mechanics, while it relies upon bounding surface plasticity with a vanished elastic region to simulate the non-linear soil response. Stress integration of constitutive relations is performed using a recently proposed explicit scheme with automatic error control and substepping, which so far has been employed in the literature only for constitutive models aiming at monotonic loading. The overall accuracy of this scheme is evaluated at element level by simulating cyclic loading along complex stress paths and by using iso-error maps for paths involving change of the Lode angle. The performance of the new constitutive model and its stress integration scheme in complex boundary value problems involving earthquake-induced liquefaction is evaluated, in terms of accuracy and computational cost, via a number of parametric analyses inspired by the successful simulation of the VELACS centrifuge Model Test No. 2 studying the lateral spreading response of a liquefied sand layer. Copyright © 2009 John Wiley & Sons, Ltd. [source]

### Rheological characteristics of solid,fluid transition in dry granular dense flows: A thermodynamically consistent constitutive model with a pressure-ratio order parameter

INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 9 2010
Chung Fang
Abstract Dry granular flows are characterized as quasi-static, dense and collisional states by the interactions among the grains, which is indexed macroscopically by an internal variable, called the order parameter defined as the square root of the static pressure to the total pressure. The solid,fluid state transition is regarded as a second-order phase transition process, and is described by a kinematic evolution of the order parameter. The thermodynamic analysis, based on the Müller,Liu entropy principle, is employed to deduce the equilibrium responses of the constitutive equations, while the dynamic responses are postulated on the basis of a quasi-linear and the second-order Ginzburg,Landau phase transition theories. The obtained model is applied to study the rheological characteristics of a dry granular dense flow between two infinite parallel plates, of which the results are compared with those from DEM simulations to estimate the model validity. The present study provides a general framework for the theoretical justifications on the thermodynamic consistencies of order-parameter-based constitutive models, and can be extended to flows in quasi-static or collisional states. Copyright © 2009 John Wiley & Sons, Ltd. [source]

### Non-coaxial elasto-plasticity model and bifurcation prediction of shear banding in sands

INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 9 2010
Maosong Huang
Abstract Numerous constitutive models built on coaxial theory and validated under axi-symmetric condition often describe the stress,stain relationships and predict the inceptions of shear banding in sands inaccurately under true triaxial condition. By adopting an elaborated Mohr,Coulomb yield function and using non-coaxial non-associated flow rule, a 3D non-coaxial elasto-plasticity model is proposed and validated by a series of true triaxial tests on loose sands. The bifurcation analysis of true triaxial tests on dense sands predicts the influence of the intermediate principal stress ratio on the onset of shear band accurately. The failure of soils is shown to be related to the formation of shear band under most intermediate principal stress ratio conditions except for those which are close to the axi-symmetric compression condition. Copyright © 2009 John Wiley & Sons, Ltd. [source]

### Bifurcation modeling in geomaterials: From the second-order work criterion to spectral analyses

INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 9 2009
F. Prunier
Abstract The present paper investigates bifurcation analysis based on the second-order work criterion, in the framework of rate-independent constitutive models and rate-independent boundary-value problems. The approach applies mainly to nonassociated materials such as soils, rocks, and concretes. The bifurcation analysis usually performed at the material point level is extended to quasi-static boundary-value problems, by considering the stiffness matrix arising from finite element discretization. Lyapunov's definition of stability (Annales de la faculté des sciences de Toulouse 1907; 9:203,274), as well as definitions of bifurcation criteria (Rice's localization criterion (Theoretical and Applied Mechanics. Fourteenth IUTAM Congress, Amsterdam, 1976; 207,220) and the plasticity limit criterion are revived in order to clarify the application field of the second-order work criterion and to contrast these criteria. The first part of this paper analyses the second-order work criterion at the material point level. The bifurcation domain is presented in the 3D stress space as well as 3D cones of unstable loading directions for an incrementally nonlinear constitutive model. The relevance of this criterion, when the nonlinear constitutive model is expressed in the classical form (d, = Md,) or in the dual form (d, = Nd,), is discussed. In the second part, the analysis is extended to the boundary-value problems in quasi-static conditions. Nonlinear finite element computations are performed and the global tangent stiffness matrix is analyzed. For several examples, the eigenvector associated with the first vanishing eigenvalue of the symmetrical part of the stiffness matrix gives an accurate estimation of the failure mode in the homogeneous and nonhomogeneous boundary-value problem. Copyright © 2008 John Wiley & Sons, Ltd. [source]

### On generalization of constitutive models from two dimensions to three dimensions

INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 17 2008
N. Khalili
Abstract In this paper, a study is made of the generalization of constitutive models for geomaterials from two-dimensional stress and strain states to three-dimensional stress and strain states. Existing methods of model generalization are reviewed and their deficiencies are highlighted. A new method is proposed based on geometries of the model imprints on two normal planes. Using the proposed method, various three-dimensional failure criterions suitable for geomaterials are implemented directly into a two-dimensional model and the generalized model is identical to its original form for the axially symmetric condition. To demonstrate the application of the proposed method, the Modified Cam Clay model is extended using the Matsuoka,Nakai failure criterion. Simulations of soil behaviour for loading in the principal stress space are presented and analysed. Copyright © 2008 John Wiley & Sons, Ltd. [source]

### Implicit integration of a mixed isotropic,kinematic hardening plasticity model for structured clays

INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 10 2008
Angelo Amorosi
Abstract In recent years, a number of constitutive models have been proposed to describe mathematically the mechanical response of natural clays. Some of these models are characterized by complex formulations, often leading to non-trivial problems in their numerical integration in finite elements codes. The paper describes a fully implicit stress-point algorithm for the numerical integration of a single-surface mixed isotropic,kinematic hardening plasticity model for structured clays. The formulation of the model stems from a compromise between its capability of reproducing the larger number of features characterizing the behaviour of structured clays and the possibility of developing a robust integration algorithm for its implementation in a finite elements code. The model is characterized by an ellipsoid-shaped yield function, inside which a stress-dependent reversible stiffness is accounted for by a non-linear hyperelastic formulation. The isotropic part of the hardening law extends the standard Cam-Clay one to include plastic strain-driven softening due to bond degradation, while the kinematic hardening part controls the evolution of the position of the yield surface in the stress space. The proposed algorithm allows the consistent linearization of the constitutive equations guaranteeing the quadratic rate of asymptotic convergence in the global-level Newton,Raphson iterative procedure. The accuracy and the convergence properties of the proposed algorithm are evaluated with reference to the numerical simulations of single element tests and the analysis of a typical geotechnical boundary value problem. Copyright © 2007 John Wiley & Sons, Ltd. [source]

### SANISAND: Simple anisotropic sand plasticity model

INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 8 2008
Mahdi Taiebat

### Modelling strain localization in granular materials using micropolar theory: mathematical formulations

INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 15 2006
Mustafa I. Alsaleh
Abstract It has been known that classical continuum mechanics laws fail to describe strain localization in granular materials due to the mathematical ill-posedness and mesh dependency. Therefore, a non-local theory with internal length scales is needed to overcome such problems. The micropolar and high-order gradient theories can be considered as good examples to characterize the strain localization in granular materials. The fact that internal length scales are needed requires micromechanical models or laws; however, the classical constitutive models can be enhanced through the stress invariants to incorporate the Micropolar effects. In this paper, Lade's single hardening model is enhanced to account for the couple stress and Cosserat rotation and the internal length scales are incorporated accordingly. The enhanced Lade's model and its material properties are discussed in detail; then the finite element formulations in the Updated Lagrangian Frame (UL) are used. The finite element formulations were implemented into a user element subroutine for ABAQUS (UEL) and the solution method is discussed in the companion paper. The model was found to predict the strain localization in granular materials with low dependency on the finite element mesh size. The shear band was found to reflect on a certain angle when it hit a rigid boundary. Applications for the model on plane strain specimens tested in the laboratory are discussed in the companion paper. Copyright © 2006 John Wiley & Sons, Ltd. [source]

### Directional response of a reconstituted fine-grained soil,Part I: experimental investigation

INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 13 2006
Daniele Costanzo
Abstract This paper discusses the results of a large experimental program designed to investigate in a systematic manner the main features of the incremental response of fine-grained soils. The results are obtained from triaxial stress probing experiments carried out on a French silty clay (Beaucaire Marl). All the tests have been performed on reconstituted specimens, normally consolidated to an initial state which is either isotropic or anisotropic. In the interpretation of the experimental results, extensive use is made of the concept of strain response envelope. The response envelopes obtained for different stress increment magnitudes are remarkably consistent with each other and indicate an inelastic and irreversible material response, i.e. a strong dependence on the stress increment direction, also at relatively small strain levels. A companion paper (Int. J. Numer. Anal. Meth. Geomech., this issue, 2006) assesses the performance of some advanced constitutive models in reproducing the behaviour of reconstituted Beaucaire Marl as observed in this experimental program. Copyright © 2006 John Wiley & Sons, Ltd. [source]

### Directional response of a reconstituted fine-grained soil,Part II: performance of different constitutive models

INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 13 2006
David Ma
Abstract In this paper, the performance of different advanced constitutive models for soils is evaluated with respect to the experimentally observed behaviour of a soft reconstituted clay subject to a wide range of loading directions, see (presented in the companion paper). The models considered include a three-surface kinematic hardening elastoplastic model; the CLoE hypoplastic model; a recently proposed K-hypoplastic model for clays, and an enhanced version of the same model incorporating the concept of intergranular strain. A clear qualitative picture of the relative performance of the different models as a function of the loading direction is obtained by means of the incremental strain response envelopes. The definition of suitable error measures allows to obtain further quantitative information in this respect. For the particular initial conditions and loading programme considered in this study, the kinematic hardening and the enhanced K-hypoplastic models appear to provide the best performance overall. Copyright © 2006 John Wiley & Sons, Ltd. [source]

### Modelling the behaviour of an embankment on soft clay with different constitutive models

INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 10 2006
M. Karstunen
Abstract The paper investigates the effect of constitutive models on the predicted response of a simplified benchmark problem, an embankment on soft soil. The soft soil is assumed to have the properties of POKO clay from Finland and five different constitutive models are used to model the deposit. Two of the models are isotropic models, i.e. the Modified Cam Clay model and the Soft-Soil model. The other models are recently proposed constitutive models that account for plastic anisotropy. The S-CLAY1 and S-CLAY1S models are embedded in a standard elasto-plastic framework and account for anisotropy via a rotational hardening law. In addition, the S-CLAY1S model accounts for bonding and destructuration. In contrast, the Multilaminate Model for Clay (MMC) accounts for plastic anisotropy by utilizing so-called multilaminate framework. The results of numerical simulations show that accounting for anisotropy results in notable differences in the predicted settlements and horizontal movements compared to the predictions using the isotropic models. There are also significant differences in the K0 predictions by the different constitutive models and this has a significant impact on the results. Copyright © 2006 John Wiley & Sons, Ltd. [source]

### A unified bounding surface plasticity model for unsaturated soils

INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 3 2006
A.R. Russell
Abstract A unified constitutive model for unsaturated soils is presented in a critical state framework using the concepts of effective stress and bounding surface plasticity theory. Consideration is given to the effects of unsaturation and particle crushing in the definition of the critical state. A simple isotropic elastic rule is adopted. A loading surface and a bounding surface of the same shape are defined using simple and versatile functions. The bounding surface and elastic rules lead to the existence of a limiting isotropic compression line, towards which the stress trajectories of all isotropic compression load paths approach. A non-associated flow rule of the same general form is assumed for all soil types. Isotropic hardening/softening occurs due to changes in plastic volumetric strains as well as suction for some unsaturated soils, enabling the phenomenon of volumetric collapse upon wetting to be accounted for. The model is used to simulate the stress,strain behaviour observed in unsaturated speswhite kaolin subjected to three triaxial test load paths. The fit between simulation and experiment is improved compared to that of other constitutive models developed using conventional Cam-Clay-based plasticity theory and calibrated using the same set of data. Also, the model is used to simulate to a high degree of accuracy the stress,strain behaviour observed in unsaturated Kurnell sand subjected to two triaxial test load paths and the oedometric compression load path. For oedometric compression theoretical simulations indicate that the suction was not sufficiently large to cause samples to separate from the confining ring. Copyright © 2005 John Wiley & Sons, Ltd. [source]

### Parameter sensitivity in finite element analysis with constitutive models of the rate type

INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 2 2006
Wolfgang Fellin
Abstract Non-linear soil,structure interactions are usually analysed using an incremental finite element approach. There a constitutive subroutine provides for each element the stress increment for a given strain increment. In geotechnical calculations, uncertainties in material parameters and initial conditions are abundant. Sensitivity analysis can be a first step to account for such uncertainties. Sensitivities of the system response with respect to material parameters and initial conditions can be calculated by differentiating the whole numerical scheme. It turns out that the essential information from the constitutive subroutine are the derivatives of the stress increment with respect to the strain increment, as well as the derivatives with respect to material parameters and all state variables involved in the problem. We propose a method to compute these quantities numerically for any constitutive model that can be written in rate form and for any suitable integrator of such a model. We further present a concise way to supply the output of the sensitivity analysis to the designing engineer. Our theoretical investigations are illustrated with element tests and with a typical geotechnical application. Copyright © 2005 John Wiley & Sons, Ltd. [source]

### Visualization of material stiffness in geomechanics analysis

INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 1 2006
Donald C. Wotring
Abstract This paper presents novel visualization techniques to simplify representation of the fourth-order material stiffness tensor as a set of three-dimensional geometric objects. Stiffness visualization aids in understanding the complex stiffness characteristics of highly non-linear constitutive models including modelled material anisotropy and loading path dependent stiffness variation. Stiffness visualization is relevant for understanding the relationship of material stiffness to global behaviour in the analysis of a boundary value problem. The spherical pulse stiffness visualization method, developed in the acoustics field, is extended to visualize stiffness of geomaterials using three three-dimensional objects. This method is limited to relatively simple constitutive models with symmetric stiffness matrices insensitive to loading magnitude and direction. A strain dependent stiffness visualization method is developed that allows the examination of material stiffness for a range of loading directions and is suitable for highly non-linear and path dependent material models. The proposed stiffness visualization can be represented as 3-D, 2-D and 1-D objects. The visualization technique is used to represent material stiffness and its evolution during simulated soil laboratory tests and deep excavation construction. Copyright © 2005 John Wiley & Sons, Ltd. [source]

### Generalized strain probing of constitutive models

INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 15 2004
Youssef M. A. Hashash
Abstract Advanced material constitutive models are used to describe complex soil behaviour. These models are often used in the solution of boundary value problems under general loading conditions. Users and developers of constitutive models need to methodically investigate the represented soil response under a wide range of loading conditions. This paper presents a systematic procedure for probing constitutive models. A general incremental strain probe, 6D hyperspherical strain probe (HSP), is introduced to examine rate-independent model response under all possible strain loading conditions. Two special cases of HSP, the true triaxial strain probe (TTSP) and the plane-strain strain probe (PSSP), are used to generate 3-D objects that represent model stress response to probing. The TTSP, PSSP and general HSP procedures are demonstrated using elasto-plastic models. The objects resulting from the probing procedure readily highlight important model characteristics including anisotropy, yielding, hardening, softening and failure. The PSSP procedure is applied to a Neural Network (NN) based constitutive model. It shows that this probing is especially useful in understanding NN constitutive models, which do not contain explicit functions for yield surface, hardening, or anisotropy. Copyright © 2004 John Wiley & Sons, Ltd. [source]

### Shear band evolution and accumulated microstructural development in Cosserat media

INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 10 2004
A. Tordesillas
Abstract This paper prepares the ground for the continuum analysis of shear band evolution using a Cosserat/micropolar constitutive equation derived from micromechanical considerations. The nature of the constitutive response offers two key advantages over other existing models. Firstly, its non-local character obviates the mathematical difficulties of traditional analyses, and facilitates an investigation of the shear band evolution (i.e. the regime beyond the onset of localization). Secondly, the constitutive model parameters are physical properties of particles and their interactions (e.g. particle stiffness coefficients, coefficients of inter-particle rolling friction and sliding friction), as opposed to poorly understood fitting parameters. In this regard, the model is based on the same material properties used as model inputs to a discrete element (DEM) analysis, therefore, the micromechanics approach provides the vehicle for incorporating results not only from physical experiments but also from DEM simulations. Although the capabilities of such constitutive models are still limited, much can be discerned from their general rate form. In this paper, an attempt is made to distinguish between those aspects of the continuum theory of localization that are independent of the constitutive model, and those that require significant advances in the understanding of micromechanics. Copyright © 2004 John Wiley & Sons, Ltd. [source]

### Visual framework for development and use of constitutive models

INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 15 2002
Youssef M. A. Hashash
Abstract Advanced constitutive relations are used in geotechnical engineering to capture measured soil and rock behaviour in the laboratory, and in numerical models to represent the material response. These constitutive relations have traditionally been difficult to use, understand, and develop except by a limited number of specialists. This paper describes a framework for transforming the representation of constitutive relations, as well as stress and strain quantities from a series of mathematical equations and matrix quantities to multidimensional geometric/visual objects in a dynamic interactive colour-rich display environment. The paper proposes a shift in current approaches to the development of constitutive equations and their use in numerical simulations by taking advantage of rapid advancements in information technology and computer graphics. A novel interactive visualization development and learning environment for material constitutive relations referred to as VizCoRe is presented. Visualization examples of two constitutive relations, the linear elastic with von Mises failure criteria and the Modified Cam Clay (MCC) are shown. These include two- and three-dimensional renderings of stress states and paths and yield and failure surfaces. In addition, the environment allows for the visualization of the implicit integration algorithm used for the numerical integration of both constitutive models. Copyright © 2002 John Wiley & Sons, Ltd. [source]

### Consistent tangent matrices for density-dependent finite plasticity models

INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 11 2001
Agustí Pérez-Foguet
Abstract The consistent tangent matrix for density-dependent plastic models within the theory of isotropic multiplicative hyperelastoplasticity is presented here. Plastic equations expressed as general functions of the Kirchhoff stresses and density are considered. They include the Cauchy-based plastic models as a particular case. The standard exponential return-mapping algorithm is applied, with the density playing the role of a fixed parameter during the nonlinear plastic corrector problem. The consistent tangent matrix has the same structure as in the usual density-independent plastic models. A simple additional term takes into account the influence of the density on the plastic corrector problem. Quadratic convergence results are shown for several representative examples involving geomaterial and powder constitutive models. Copyright © 2001 John Wiley & Sons, Ltd. [source]

### A novel approach to the analysis of distributed shear banding in polymer blends

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 5 2003
K. G. W. Pijnenburg
Abstract The toughness of glassy polymers can be enhanced by blending with rubber particles. The consensus is that this toughening is due to massive plastic deformation of the matrix that takes place once the particles have cavitated. Micromechanical studies of regular stackings of particles in a polymer matrix have provided much insight into the localized plastic flow in blends at the microscale of individual particles (or voids, once cavitated). Even some steps towards macroscopic constitutive models have been made. However, at intermediate length scales (i.e. larger than several particles, but smaller than the scale at which the material may be regarded as homogeneous) the situation is unclear. It is this length scale that becomes important around crack tips, for example, where a thorough understanding of the toughening effect has to be derived from. In this paper, we therefore present a novel approach to the analysis of distributed shear banding in polymer,rubber blends. A coarse-grain description, in which much of the morphology is retained but the local shear banding is idealized into ,shear surfaces', will enable us to analyse ensembles with large numbers of particles. The parameters of this model will be validated with results from detailed cell analyses. Copyright © 2003 John Wiley Sons, Ltd. [source]

### Improvements and algorithmical considerations on a recent three-dimensional model describing stress-induced solid phase transformations

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 11 2002
Ferdinando Auricchio
Abstract During mechanical loading,unloading cycles shape-memory alloys (SMA) are able to undergo large deformations without showing residual strains (pseudoelasticity) or recovering them through thermal cycles (shape memory effect). Motivated by stress-induced solid phase transformations, these unique behaviours induce the SMA exploitation in innovative and commercially valuable applications, stimulating, consequently, the interest in the development of constitutive models. Also if many models are now available in the literature, effective three-dimensional proposals are still few and limited in several aspects. In this paper, a three-dimensional thermomechanical model recently proposed by Souza et al. (European Journal of Mechanics,A/Solids, 1998; 17: 789,806.) is taken into consideration; such a model is of particular interest for its effectiveness and flexibility, but it also shows some limitations and missing links in the algorithmical counterparts. This work discusses some improvements to the original model as well as the development and the implementation of a robust integration algorithm to be adopted in a numerical scheme, such as a finite-element framework. Copyright © 2002 John Wiley & Sons, Ltd. [source]

### Simulation of the Stress-Assisted Densification Behavior of a Powder Compact: Effect of Constitutive Laws

JOURNAL OF THE AMERICAN CERAMIC SOCIETY, Issue 3 2008
Héctor Camacho-Montes
The densification of powders with linear and nonlinear viscous behavior (Scherer and Riedel models) and with power-law-deformation (Khun,McMeeking) behavior was studied under hot pressing and sintering forging conditions. Several numerical experiments, designated cases in this work, were performed to study the effect of (i) the uniaxial stress exerted by the piston and (ii) the rate of the uniaxial stress. The stress state was calculated using the finite-element program ANSYS for each case. Considering the mesoscopic behavior of the powders, densification rates were obtained. The similarities and differences between predictions from the three constitutive models are highlighted. The relationship between the constitutive behavior and the most effective stress state is one of the focuses of this study. For example, we show that under constant stress loading, hot pressing more effectively promotes densification than sinter forging for constitutive behaviors that do not follow the power-law creep. In general, as expected, the increase of uniaxial applied stress and piston velocity favored densification. However, the increase in densification depends strongly on the constitutive law. [source]

### A comparative analysis of a modified picture frame test for characterization of woven fabrics

POLYMER COMPOSITES, Issue 4 2010
A.S. Milani
An experimental, finite-element analysis framework is utilized to estimate the deformation state in a modified version of the picture frame test. During the analysis, the effect of fiber misalignment and the deformation heterogeneity in the tested fabric, a 2 × 2 PP/E-Glass twill, is accounted for and a force prediction model is presented. Using an equivalent stress,strain normalization scheme, the comparison of the modified test with the conventional (original) picture frame and bias-extension tests is also made, and results reveal similarities and differences that should receive attention in the identification of constitutive models of woven fabrics using these basic tests. Ideally, the trellising behavior should not change from one test to another but results show that in the presence of fiber misalignment, the modified picture frame test yields a behavior closer to that of the bias-extension test, while the general form of the test's repeatability, measured by a signal-to-noise metric, remains similar to the original picture frame test. POLYM. COMPOS., 2010. © 2009 Society of Plastics Engineers [source]

### Creep of Single Crystals , Modelling and Numerical Aspects

PROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2005