Constitutive model

A nonlinear-dynamics transient computational analysis of the explosion phenomena associated with detonation of 100g of C4 high-energy explosive buried at different depths in sand is carried out using the AUTODYN computer program. The results obtained are compared with the corresponding experimental results obtained in Ref. . To validate the computational procedure and the materials constitutive models used in the present work, a number of detonation-related phenomena such as the temporal evolutions of the shape and size of the over-burden sand bubbles and of the detonation-products gas clouds, the temporal evolutions of the side-on pressures in the sand and in air, etc. are determined and compared with their experimental counterparts. The results obtained suggest that the agreement between the computational and the experimental results is reasonable at short postdetonation times. At longer post-detonation times, on the other hand, the agreement is less satisfactory primarily with respect to the size and shape of the sand crater, i.e. with respect to the volume of the sand ejected during explosion. It is argued that the observed discrepancy is, at least partly, the result of an inadequacy of the generic materials constitutive model for the sand which does not explicitly include the important effects of the sand particle size and the particle size distribution, as well as the effects of moisture-level controlled inter-particle friction and cohesion. It is further shown that by a relatively small adjustment of the present materials model for sand to include the potential effect of moisture on inter-particle friction can yield a significantly improved agreement between the computed and the experimentally determined sand crater shapes and sizes .

A recently developed three-dimensional concrete law is used for the analysis of concrete specimens and reinforced concrete columns subjected to different load patterns. The hypoelastic, orthotropic concrete constitutive model includes coupling between the deviatoric and volumetric stresses, works with both proportional and non-proportional loads and is implemented as a strain driven module. The finite element (FE) implementation is based on the smeared crack approach with rotating cracks parallel to the principal strain directions. The concrete model is validated through correlation studies with: (a) experimental tests on concrete cylinders confined by different mechanisms, including steel and fiber reinforced polymer jackets; (b) experimental results on three reinforced concrete columns tested at the University of California, San Diego. The correlations are overall very good, and the FE responses capture all the main phenomena observed in the experimental tests.

A newly developed and validated constitutive model that accounts for primary compression and timedependent mechanical creep and biodegradation is used for parametric study to investigate the effects of model parameters on the predicted settlement of municipal solid waste (MSW) with time. The model enables the prediction of stress strain response and yield surfaces for three components of settlement: primary compression, mechanical creep, and biodegradation. The MSW parameters investigated include compression index, coefficient of earth pressure at-rest, overconsolidation ratio, and biodegradation parameters of MSW. A comparison of the predicted settlements for typical MSW landfill conditions showed significant differences in time-settlement response depending on the selected model input parameters. The effect of lift thickness of MSW on predicted settlement is also investigated. Overall, the study shows that the variation in the model parameters can lead to significantly different results; therefore, the model parameter values should be carefully selected to predict landfill settlements accurately. It is shown that the proposed model captures the time settlement response which is in general agreement with the results obtained from the other two reported models having similar features.

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Extensive research activities in the field of blast loads have taken place in the last few decades. There are many experimental results related to underground explosions. The mechanism of crater formation is complex and it is related to the dynamic physical properties of air, soil and soil-air interface. Studies concerned with the characteristics of craters caused by explosions usually resort to dimensional analysis and statistics. Some empirical equations proposed for the evaluation of crater dimensions can be found in the literature. Nevertheless, they were obtained for particular type of soils, shapes of explosives, ranges of explosive mass and depth of explosive and they present considerable variability. The main objective of this paper is to prove the accuracy of numerical simulation of craters produced by underground explosions. For this purpose, the numerical analysis of crater formation due to underground explosions is performed with a hydrocode. Several numerical approaches are carried out using different models and processors for the soil. Moreover, different alternatives for the constitutive model of the soil are used. In order to validate the numerical approach and prove its ability to model the crater formation, comparison with experimental results is performed. Many simulations of the same physical model lead to the same crater dimensions and a good agreement between the test results and the predicted crater measures is achieved.

Single crystal plasticity based on a representative characteristic length is proposed and introduced into a homogenization approach based on finite element analyses, which are applied to characterization of distinctive yielding behaviors of polycrystalline metals, yield-point elongation, and grain size strengthening. The computational manner for an implicit stress update is derived with the framework of a standard multi-surface plasticity at finite strain, where the evolution of the characteristic lengths are numerically converted from the accumulated slips of all of slip systems by exploiting the mathematical feature of the characteristic length as the intermediate function of the plastic internal variables. Furthermore, a constitutive model for a single crystal reproduces the stress-strain curve divided into three parts. Using two-scale finite element analysis, the macroscopic stressstrain response with yield-point elongation under a situation of low dislocation density is reproduced. Finally, the grain size effect on the yield strength is analyzed with modeling of the grain boundary in the context of the proposed constitutive model and is discussed from both macroscopic and microscopic views.

On the basis of continuum mechanics, a rate dependent directional damage model for fibred materials with application to soft biological tissues is presented. The structural model is formulated using the concept of internal variables that provides a very general description of materials involving irreversible effects. Continuum damage mechanics is used to describe the softening behavior of soft tissues under large deformation. To account for the rate dependency and to regularize the localization problems associated with strain-softening, a viscous damage mechanism is presented in this paper in decoupled form for matrix and fibers. The numerical implementation in the context of the finite element method is discussed in detail. In order to show the performance of the constitutive model and its algorithmic counterpart some simple examples are included. Results show that the model is able to capture the typical stress–strain behavior observed in fibrous soft tissues and appear to confirm the soundness of the proposed formulation.

In this paper, a strategy for developing self-learning ®nite element codes is presented. At the heart of these codes is a neural network based constitutive model (NNCM). In contrast to the normal practice of training neural networks for constitutive models with the data from homogenous material tests, training is accomplished here with stresses and strains at certain calibrating points in tests on structures where the stress/strain states are not homogenous. This strategy has a distinct advantage since a considerable eort is devoted by the experimentalists to achieve as homogenous state of stress/strain as possible. In many situations this is impractical for many reasons such as the samples being too small, precious or may require expensive methods of preparation.

This paper presents the results of the first phase of a research project dealing with the constitutive description of the behaviour of well-graded granular materials when used for base or subbase layers in flexible pavement structures (so-called "unbound granular materials", UGMs). Monotonic and cyclic loading is under consideration. The present paper concentrates on test results and the constitutive description of monotonic loading. Hypoplasticity in the version proposed by von Wolffersdorff is used as the constitutive model. Sets of material constants for typical UGM materials do not exist in the literature. The experimental determination of a set of constants according to the procedure proposed by Herle is described in this paper. In the monotonic triaxial tests specimens with a square cross-section were used. The paper presents a preliminary test series comparing triaxial results obtained with cylindrical and with prismatic specimens. Re-calculations of the element tests are also presented. The simulations show a good congruence with the experiments.

Strain localisation in soils and rocks has been studied extensively for the last 20 years. A part of these studies have been devoted to the response of specimens submitted to tests in undrained situation. It was shown that shear banding can take place in both contractive and dilative specimens, with some special features due to the coupling between the granular skeleton and the pore fluid. In the paper, the relevance of the bifurcation criterion in shear band mode in the case of hydromechanical coupling is assessed by numerical study of the response of the constitutive model CLoE -the Hypoplastic model developed in L3S-Grenoble-in two kinds of numerical integration: local, i.e. at the material point level and global, i.e. in boundary value problems analyzed by finite elements.

A three-dimensional model developed for the slow deformation, without macroscopic failure, of a stratified snow cover has been used to simulate laboratory mechanical tests performed on sieved snow. The model is based on a non-linear visco-elastic constitutive law for snow whose parameters depend on the snow temperature and density. Snow densification is derived from the bulk viscous strain. The model has been implemented in the Flac3D finite-difference code. The experimental device is a convergent channel in which snow is forced at a constant velocity in the range 1-100 μm s − 1. Although snow is compressed under plane strain conditions, the channel geometry allows obtaining a multi-axial stress-state. Since the testing conditions involve ranges of variation of both the snow density and the strain-rate wider than those encountered for a natural snowpack, the constitutive relations of the model had to be modified. In this paper we present the constitutive model for snow, some details about its implementation into the Flac3D code, and its application to the numerical simulation of the mechanical tests. The comparison of the model and experimental results shows a relatively good agreement, although snow microstructure is accounted for only through its density. However, the treatment of the non-linearity of the viscosity must be improved. This 3D numerical model can be regarded as an interesting tool for assessing a constitutive law for snow on the basis of cold-room experiments, as well as for studying natural snow covers.

Using explosion source, seismic refraction data, recorded in the 1978 and 1980 Yellowstone-Snake River Plain seismic experiments, a three-dimensional inversion of differential P wave attenuation was used to assess the relative variations in Q-1 in and around the volcanically active, 45 km by 70 km, Yellowstone caldera, northwestem Wyoming. Differential attenuation was derived from spectral decay of upper crustal Pg phases, observed from six explosions and recorded at 90 temporary stations. Because of the relatively short •xme windows used to determine the spectral content, a maximum entropy technique was employed to estimate the spectra that yielded an optimally small variance. Differential P wave attenuation was calculated from least squares determinations of the spectral ratios corrected for source and path effects. The observed differential attenuation parameters were then inverted using a weighted least squares technique for a discretized, 70 km x 105 km, three-dimensional surface and upper crustal Q-1 model of the Yellowstone caldera and surrounding region. Results showed that the surface layer, to depths of 2 km within the Yellowstone caldera, is characterized by relatively high attenuation with low Q values less than 30, compared to values of 38 to 50 outside the caldera. The higher attenuation in the caldera's surface layer is thought to be associated with Quaternary lake sediments, highly altered rhyolites, and the possible influence of steam in areas of hydrothermal activity. In the crystalline upper crust, at depths of 2 km to 12 km, Q values of 40 to 70 were observed in areas of thick sedimentary fill northwest of the caldera and in areas of hydrothermal activity. Within the caldera, upper crustal attenuation generally corresponded to Q of 200 in areas that are interpreted to be associated with hot but now solidified granitic material. In comparison, relatively high attenuation, Q = 40, was observed in the upper crust of the northeastern Yellowstone caldera in an area that also corresponds to a 20% reduction in Pg velocity, a prominent negative Bouguer gravity low of-20 mGal, near Yellowstone's largest area of hydrothermal activity and near a Quatemary, volcanic resurgent dome. On the basis of constitutive models of velocity and density, this zone of high attenuation is likely a product of unusual hydrothermal activity, highly altered upper-crustal rocks, a shallow magmatic source or a highly porous, steam-saturated body. Outside the caldera, the upper crust is relatively unaffected by high temperatures and thermal alteration, and the corresponding attenuation is low with Q values greater than 200. the late Cenozoic, Yellowstone-Snake River Plain bimodal silicic-basaltic volcanic system making up the Yellowstone Plateau (Figure 1). Within the plateau, the Quaternary Yellowstone caldera and surrounding areas are world famous for their spectacular displays of hydrothermal activity, i.e., geysers, fumeroles, and hot springs that suggest shallow sources of heat. Low seismic velocities, high attenuation, and shallow earthquake loci corroborate an anomalous crustal structure associated with the Yellowstone caldera. Combined with the three-dimensional seismic velocity structure, the inverted three-dimensional Q structure discussed in this paper provides additional information on the unusual properties of this active silicic volcanic region. The Yellowstone caldera (noted by III in Figure 1), measuring 45 km by 70 km, was formed 600,000 years ago by the catastrophic eruption of 1000 km 3 of rhyolitic ash

An annular shear cell-type cohesive powder rheometer has been fabricated, which measures the shear and normal stress states over a range of shear rate and powder concentration. The rheological behavior of a 30-mm spherical silica powder and a 40-mm industrial polymer powder have been experimentally investigated for powder flow in the frictional regime. Although the silica powder appears to be cohesionless, based on Jenike shear cell yield locus measurements, and the industrial powder has strong cohesion, they both demonstrate similar rheological behavior in the frictional flow regime. At low shear rates, the shear stress increases with increasing shear rate until a critical shear rate is reached, at which point the shear stress decreases with increasing shear rate. The shear-to-normal stress relation with shear rate, for frictional flow, is apparently independent of powder concentration, and the data approximately collapse into a single curve for a given powder. The requirements for a constitutive model relating the stress tensor to the rate of deformation for the powder assembly are discussed. q 2000 Elsevier Science S.A. All rights reserved.

A model is presented to analyze material microstructures subjected to quasi-static and dynamic loading. A representative volume element (RVE) composed of a set of grains is analyzed with special consideration to the size distribution, morphology, chemical phases, and presence and location of initial defects. Stochastic effects are considered in relation to grain boundary strength and toughness. Thermo-mechanical coupling is included in the model so that the evolution of stress induced microcracking, from the material fabrication stage, can be captured. Intergranular cracking is modeled by means of interface cohesive laws motivated by the physics of breaking of atomic bonds or grain boundary sliding by atomic diffusion. Several cohesive laws are presented and their advantages in numerical simulations are discussed. In particular, cohesive laws simulating grain boundary cracking and sliding, or shearing, are proposed. The equations governing the problem, as well as their computer implementation, are presented with special emphasis on selection of cohesive law parameters and time step used in the integration procedure. This feature is very important to avoid spurious effects, such as the addition of artificial flexibility in the computational cell. We illustrate this feature through simulations of alumina microstructures reported in part II of this work. A technique for quantifying microcrack density, which can be used in the formulation of continuum micromechanical models, is addressed in this analysis. The density is assessed spatially and temporally to account for damage anisotropy and evolution. Although this feature has not been fully exploited yet, with the continuous development of cheaper and more powerful parallel computers, the model is expected to be particularly relevant to those interested in developing new heterogeneous materials and their constitutive modeling. Stochastic effects and other material design variables, although difficult and expensive to obtain experimentally, will be easily assessed numerically by Monte Carlo grain level simulations. In particular, extension to three-dimensional simulations of RVEs will become feasible.

In this work the simulation of the powder compaction process, in the context of Powder Metallurgy, is numerically investigated. The procedure considers that the powder is being modeled by a complete smooth three surface Cap model and makes use of a spatial approximation which is performed in the context of the element-free Galerkin (EFG) method. The constitutive model is written in terms of the rotated Kirchhoff stress and of its logarithmic strain conjugate measure. A total Lagrangian description is considered and the imposition of the essential boundary condition is made by the augmented Lagrangian method. The contact formulation used in this work assumes the Signorini condition. In order to apply the EFG method, the body domain is partitioned into a triangular background integration mesh, with the particles positioned at the vertices. Some numerical results are presented, in order to attest the performance of the proposed methodology.

It is known that cells proliferate and produce extracellular matrix in response to biochemical and mechanical stimuli. Constitutive models considering these phenomena are needed to quantitatively describe the process of tissue growth in the context of tissue engineering and regenerative medicine. In this paper we reexamine the theoretical framework provided by Ambrosi and Guana (2007) and Ambrosi and Guillou (2007). We show how a volumetric growth rate term can be obtained (both in a large and small strain setting), which is consistent with the laws of thermodynamics and then apply the model to a simple geometry of tissue growth within a circular pore. The model, despite its simplicity, is comparable with experimental measurements of tissue growth and highlights the contribution of the mechanical stresses produced during tissue growth on the growth rate itself.

Aubin and her coworkers conducted a unique set of experiments demonstrating the influence of loading non-proportionality on ratcheting responses of duplex stainless steel. In order to further explore their new observation, a set of experiments was conducted on stainless steel (SS) 304L under various biaxial stress-controlled non-proportional histories. This new set of data reiterated Aubin and her coworkers’ observation and illustrated many new responses critical to model development and validation. Two recent and different classes of cyclic plasticity models, the modified Chaboche model proposed by Bari and Hassan and the version of the multi-mechanism model proposed by Taleb and Cailletaud, are evaluated in terms of their simulations of the SS304L non-proportional ratcheting responses. A modeling scheme for non-proportional ratcheting responses using the kinematic hardening rule parameters in addition to the conventionally used isotropic hardening rule parameter (yield surface size change) in the modified Chaboche model is evaluated. Strengths and weaknesses of the models in simulating the non-proportional ratcheting responses are identified. Further improvements of these models needed for improving the non-proportional ratcheting simulations are suggested in the paper.

After the self-criticism of Richard Posner (A failure of capitalism. The crisis of '08 and the descend to depression. Harvard University Press, Cambridge, 2009a and some later papers), a position shared in part by Gary Becker, it is right to ask what exactly remains of the Chicago School, which came into being in the early 1930s with Knight and made a name for itself in the 1980s as the new orthodoxy with Lucas (Reh) and Fama (Emh). The financial crisis has, in this sense, cast the debate between the Saltwater school (the American universities on the coast) and the Freshwater school (the universities near the Great Lakes, including Chicago) in a new light. This article traces the development of the Chicago School, the consolidation of conservative think-tanks (especially the Mont Pelerin Society whose members have included, among others, von Hayek and Friedman) and the more recent positions of the School, including some that are less organic (Diamond, Kashyap, Rajan, Zingales). At the centre of the debate is the question of the failures of the State vs the failures of the market and the role of institutions. On a methodological level the relationship between law and economics (L&E) is also in discussion, which leads to an interesting comparison between Chicago (again Posner, past and present) and Yale (Calabresi). After having described the echoes of the debate across the Atlantic (with particular reference to Italy), it will be asked if the anomalies that can be found in the consolidated paradigm (Reh, Emh, but also L&E) will lead to the abandonment of pre-constituted models in favour of a less rigid theoretical framework (Ike together with Keynes and the Chicagoan Knight, but also to a certain extent, von Hayek) or simply a pause for reflection.

Cyclic mobility is exhibited by saturated medium to dense cohesionless soils during liquefaction, due to soil skeleton dilation at large shear strain excursions. This volume-shear coupling mechanism results in phases of significant regain in soil shear stiffness and strength, and limits the magnitude of cyclic shear deformations. Motivated by experimental observations, a plasticity model is developed for capturing the characteristics of cyclic mobility. This model extends an existing multi-surface plasticity formulation with newly developed flow and hardening rules. The new flow rule allows for reproducing cyclic shear strain accumulation, and the subsequent dilative phases observed in liquefied soil response. The new hardening rule enhances numerical robustness and efficiency. A model calibration procedure is outlined, based on monotonic and cyclic laboratory sample test data.

Many cold and hot worked metals undergo strain hardening and softening when subjected to cyclic plastic straining. The degree of strain softening depends on the amount of prior cold work or heat treatment introduced into the material and upon the magnitude and the number of cycles of applied cyclic plastic strain. Cyclic strain softening leads to a lower flow stress, higher ductility, reduced tensile strength upon subsequent straining and lower energy consumption during material processing. In order to optimise metal forming processes, the work hardening and softening should be analysed to include the influence of deformation conditions within the constitutive model. This paper developed a constitutive model based on the Estrin and Mecking phenomenological model for cyclic hardening without prestraining whilst using a combined Estrin and Mecking model and Avrami equation for cyclic softening with prestraining. As cyclic softening is largely dependent on the work hardening previously achieved and on deformation conditions, the constitutive model takes account of these conditions in addition to those used in conventional constitutive models.

This paper presents a complete finite-element treatment for unsaturated soil problems. A new formulation of general constitutive equations for unsaturated soils is first presented. In the incremental stress-strain equations, the suction or the pore water pressure is treated as a strain variable instead of a stress variable. The global governing equations are derived in terms of displacement and pore water pressure. The discretized governing equations are then solved using an adaptive time-stepping scheme which automatically adjusts the time-step size so that the integration error in the displacements and pore pressures lies close to a specified tolerance. The non-linearity caused by suction-dependent plastic yielding, suction-dependent degree of saturation , and saturation-dependent permeability is treated in a similar way to the elastoplasticity. An explicit stress integration scheme is used to solve the constitutive stress-strain equations at the Gauss point level. The elastoplastic stiffness matrix in the Euler solution is evaluated using the suction as well as the stresses and hardening parameters at the start of the subincrement, while the elastoplastic matrix in the modified Euler solution is evaluated using the suction at the end of the subincrement. In addition, when applying subincrementation, the same rate is applied to all strain components including the suction.

A series of experiments were performed to further investigate the phenomenon of shear-banding in surfactant solutions. Many surfactant solutions, through their unique amphiphilic chemistry, form long wormlike micelle structures which behave like living polymers. These wormlike micelles have interesting viscoelastic properties and have been the subject of a number of recent studies. These water-based surfactant systems are widely used in

Paperboard is a widely used material in industrial processes, in particular for packaging purposes. Packages are obtained through a forming process, in which a flat laminated sheet is converted into the final 3-D solid. In the package forming process, it is common practice to score the paperboard laminate with crease lines, in order to obtain folds with sharp edges and to minimize the initiation and propagation of flaws during the subsequent folding procedures. In this work, a constitutive model for the mechanical response of crease lines is proposed and validated on the basis of experimental tests available in the literature. The model has been implemented in an interface finite element to be placed between adjacent shell elements and is intended for large-scale computations of package forming processes. For this reason, the material model has been developed at the macroscopic scale in terms of generalized variables, aiming at computational effectiveness.

Microstructural physical based constitutive models are developed in this work in order to characterize the deforma-11 tion behavior of body centered cubic (bcc) and face centered cubic (fcc) metals under different strain rates and temper-12 atures. The concept of thermal activation energy as well as the dislocations interaction mechanisms is used in the 13 derivation procedure taking into consideration the effect of the mobile dislocation density evolution on the flow stress 14 of the deformed material. The derivation of the Zerilli-Armstrong (Z-A) physical based model for both (bcc) and (fcc) 15 metals is investigated and a number of modifications are incorporated such as the evolution of mobile dislocation den-16 sity. The authors conclude that in spite of the physical basis used in the derivation of the Z-A model, its parameters can 17 not be interpreted physically since the approximation ln(1 + x) % x is used in the final step of the derivation. This expan-18 sion, however, is valid only for values x ( 1.0 which is not the case at high strain rates and temperatures. New bcc and 19 fcc relations for the flow stress are therefore suggested and derived using the exact results of the expansion of ln(1 + x). 20 Several experimental data obtained by different authors for tantalum (Ta), niobium (Nb), molybdenum, (Mo), vana-21 dium (V) (bcc metals) and Oxygen Free High Conductivity (OFHC) Copper (Cu) (an fcc metal) are used in evaluating 22 the proposed models. A good agreement between the experimental results and the proposed models are obtained. More-23 over, the predicted results show that the assumption of ignoring the generation of dislocation density during the plastic 24 deformation is not appropriate particularly in the case of high strain rates and temperatures. This causes the values of 25 the thermal stresses to be overestimated. Numerical identification for the physical quantities used in the definition of the 26 model parameters is also presented. 27

The undrained response of cohesive soils is of paramount importance in geomechanics and it has been modelled extensively for the last 50 years. In comparison, drained behaviour of clays has received only modest attention. Drained and undrained behaviour is significantly affected by past consolidation stress history. This paper evaluates the capabilities of the MIT-S1 effective stress model, described in a companion paper, for predicting the anisotropic stress-strain-strength behaviour of clays. The paper illustrates the selection of model parameters for Lower Cromer Till, using data from standard types of laboratory tests. Comparison of model simulations with measured response for Lower Cromer Till and Boston Blue Clay illustrate model capabilities. The work focuses initially on comparisons of model predictions with measurements from undrained triaxial and plane strain tests on initially K 0 -consolidated specimens. Comparisons with measured data from undrained shear tests performed in different modes of shearing for LCT and BBC show that the model: (a) gives excellent predictions of maximum shear stress conditions and accurately describes the non-linear shear stress-strain behaviour; (b) accurately describes the anisotropic shear stress-strain-strength conditions for different consolidation stress histories; and (c) gives realistic description of mobilized friction angles, especially at large OCR's. The paper then focuses on the effects of consolidation stress history for isotropically consolidated specimens of resedimented Lower Cromer Till and Boston Blue Clay. Finally, the paper compares model predictions for drained shear tests on K 0 and isotropically consolidated specimens with overconsolidation ratios, OCR410; used to evaluate particular aspects of the critical state framework of soil behaviour. Overall, the model gives excellent predictions of the effect of initial anisotropy and overconsolidation stress history on the shear stress-strain and volumetric behaviour of clays.

Presented here are the results of a systematic study of the viscoelastic properties of polyurea over broad ranges of strain rates and temperatures, including the high-pressure effects on the material response. Based on a set of experiments and a master curve developed by Knauss (W.G. Knauss, Viscoelastic Material Characterization relative to Constitutive and Failure Response of an Elastomer, Interim Report to the Office of Naval Research (GALCIT, Pasadena, CA, 2003.) for time-temperature equivalence, we have produced a model for the large deformation viscoelastic response of this elastomer. Higher strain-rate data are obtained using Hopkinson bar experiments. The data suggest that the response of this class of polymers is strongly pressure dependent. We show that the inclusion of linear pressure sensitivity successfully reproduces the results of the Hopkinson bar experiments. In addition, we also present an equivalent but approximate model that involves only a finite number of internal state variables and is specifically tailored for implementation into explicit finiteelement codes. The model incorporates the classical Williams-Landel-Ferry (WLF) time-temperature transformation and pressure sensitivity (M.L. Williams, R.F. Landel, and J.D. Ferry, J. Am. Chem. Soc., 77 3701 (1955)), in addition to a thermodynamically sound dissipation mechanism. Finally, we show that using this model for the shear behaviour of polyurea along with the elastic bulk response, one can successfully reproduce the very high strain rate pressure-shear experimental results recently reported by Jiao et al.

The excess pressure losses due to end effects in the capillary flow of two linear low-density polyethylene resins (LLDPE) were studied. These losses were first determined experimentally by using two methods: 1) by extrapolating experimental data of pressure drop versus length-to-radius ratios (L/R) to zero capillary length and 2) by means of using orifice dies (L/R≅0). Both methods resulted in practically the same end corrections. Numerical simulation was also used to model this important aspect of experimental rheology. The constitutive equations used in the simulations are a multimode K-BKZ equation, a multimode Phan-Thien/Tanner, and finally a purely viscous Carreau equation. It was found that the numerical predictions agreed qualitatively but underestimated the experimental data for the various geometries used to determine the end effects. Furthermore, it is demonstrated that the entrance pressure loss is also insensitive to extensional rheology, while it depends more strongly on the shear rheology. This finding raises doubts as to the usefulness of end pressure (known also as Bagley correction) as a method of determining the extensional viscosity of polymer melts at high rates.

In this work, tensile creep tests for Sn-1.0Ag-0.5Cu-0.02Ni solder have been conducted at various temperatures and stress levels to determine its creep properties. The effects of stress level and temperature on creep strain rate were investigated. Creep constitutive models (such as the simple power-law model, hyperbolic sine model, double power-law model, and exponential model) have been reviewed, and the material constants of each model have been determined based on experimental results. The stress exponent and creep activation energy have been studied and compared with other researchers' results. These four creep constitutive models established in this paper were then implemented into a user-defined subroutine in the ANSYSä finite-element analysis software to investigate the creep behavior of Sn-1.0Ag-0.5Cu-0.02Ni solder joints of thin fine-pitch ball grid array (TFBGA) packages for the purpose of model comparison and application. Similar simulation results of creep strain and creep strain energy density were achieved when using the different creep constitutive models, indicating that the creep models are consistent and accurate.

This paper presents a new geometric nonlinear formulation for static problems involving space trusses. Based on the finite element method (FEM), the proposed formulation uses nodal positions rather than nodal displacements to describe the problem. The strain is determined directly from the proposed position concept, using a Cartesian coordinate system fixed in space. Bilinear constitutive hardening relations are considered here to model the elastoplastic effects, but any other constitutive model can be used. The proposed formulation is simple and yields good results, as shown in the example section. Four examples are presented here to validate the formulation. ᭧

A micromechanics framework for the development of continuum-level constitutive models for the large-strain deformation of porous hyperelastic materials is presented. A kinematically admissible deformation field is assumed which enables the derivation of a strain energy density function for the porous material. The strain energy density function depends on the properties of the incompressible hyperelastic matrix material, the initial level of porosity, and the macroscopic deformation. Differentiation of the strain energy density function, with respect to deformation, provides an expression for the stress–strain behavior of the porous hyperelastic material. Example calculations are carried out for porous hyperelastic materials with a Neo–Hookean matrix. The constitutive model is used to predict the stress–strain behavior of the pore-containing matrix as a function of initial porosity and macroscopic loading conditions. Predictions of the dependence of the small-strain elastic response on porosity are compared to various estimates of effective elastic moduli for porous materials found in the literature. Constitutive model predictions of the small to large-strain deformation behavior compare well with results from numerical three-dimensional micromechanical multi-void cell models.

Storing contaminant soils, such as dredge materials, sludge and mine tailings, and reclaiming contaminant soil storage areas back into the economy has arisen as an important economical and environmental problem in today's world. The scientific studies in the last thirty years have revealed critical new information regarding the deformation behavior of high water content soils.

Strain energy concept has been employed by the researchers for the assessment of liquefaction phenomenon which is a disastrous type of earthquake-induced failure in saturated soils. The efficiency and predictability conditions of strain energy concept for liquefaction potential assessment are investigated herein using effective stress numerical analyses. Several earthquake ground motions were introduced to the base of a calibrated numerical model using an advanced fully coupled constitutive model. Results of the numerical analyses indicate that earthquake-induced excess pore pressure is more rigorously proportional to strain energy compared with the other examined intensity measures. Subsequently, a simple relationship was derived using the results of dynamic analyses to predict cumulative strain energy density in terms of magnitude, source to site distance, and effective overburden pressure. This relationship, which tries to guarantee the predictability condition of strain energy demand, has demonstrated a successful capability in discrimination between the liquefied and non-liquefied case histories recorded after several well-known earthquakes. This study has provided a practical linkage between numerical analysis and field observations. Finally, it is concluded that although strain energy approach possesses a great conceptual efficiency in liquefaction potential assessment, its precise prediction in actual field conditions involves some difficulties.

In this paper the results of 2D FE analyses of the seismic ground response of a clayey deposit, performed adopting linear visco-elastic and visco-elasto-plastic constitutive models, are presented. The viscous and linear elastic parameters are selected according to a novel calibration strategy, leading to FE results comparable to those obtained by 1D equivalent-linear visco-elastic frequency-domain analyses. The influence of plasticity on the numerical results is also investigated, with particular reference to the relation between the hysteretic and viscous damping effects. Finally, different boundary conditions, spatial discretisation and time integration parameters are considered and their role on the FE results discussed.

This paper presents the results of the analysis of teaching and learning activities in state subsidized schools in Chile. The study is based on the data collected through a national survey applied to all state subsidized schools (census) and a sample of private schools and examines teachers' and students' reported teaching and learning activities in general and with the use of Information and Communication Technologies (ICT). Additionally, it compares the frequency of these activities between primary and secondary schools as well as between a set of the highest and lowest performing schools.

The aim of this work was to improve the constitutive model of the human mandible and dentition system by taking into account the non-linear material properties of the structural boney matrix that forms the human jaw bone or mandible. Due to the specific structure of the jaw bone the time dependence of the mechanical properties also forms an important stage of the quantification process. The lack of specific experimental data of this type of material prevents the implementation of these properties into finite element simulations which results in poor quality modelling. Here an attempt was made to determine elastic and viscoelastic mechanical characteristics of the compact bone tissue forming the mandible. The elastic properties of compact bone were determined experimentally from 3 point bending tests and the viscoelastic properties were evaluated from creep tests in compression. A particular human jaw from this complex study was used to reconstruct a geometric model for further numerical experiments.

The analysis of the interaction phenomena occurring between biorobots and biological tissues requires in-depth knowledge of the biomechanical response of tissues. Most phenomenological models are based on hyperelastic formulation and this entails a careful evaluation of the model constitutive parameters, which are defined on the basis of data obtained from experimental tests. The choice of the test to be developed depends on the tissue characteristics to be studied and the procedure to be used to define the parameters . The aim of the present work is to describe a procedure used to define constitutive parameters for hyperelastic soft tissue constitutive models by considering combinations of data from uniaxial, equibiaxial and shear testing conditions of tissue specimens and to discuss the results obtained. The parameters are estimated using a stochastic optimization procedure, considering the complex behaviour of the cost function. The mechanical tests to be adopted and their combination are discussed with regard to the reliability and efficiency of the procedure to be used in the numerical modelling of tissue-robot interaction phenomena.

The large-strain constitutive behavior of cold-rolled 1018 steel has been characterized at strain rates ranging from $\dot \varepsilon = 10^{ - 3} $ to 5 × 104 s−1 using a newly developed shear compression specimen (SCS). The SCS technique allows for a seamless characterization of the constitutive behavior of materials over a large range of strain rates. The comparison of results with those obtained by cylindrical specimens shows an excellent correlation up to strain rates of 104 s−1. The study also shows a marked strain rate sensitivity of the steel at rates exceeding 100 s−1. With increasing strain rate, the apparent average strain hardening of the material decreases and becomes negative at rates exceeding 5000 s−1. This observation corroborates recent results obtained in torsion tests, while the strain softening was not clearly observed during dynamic compression of cylindrical specimens. A possible evolution scheme for shear localization is discussed, based on the detailed characterization of deformed microstructures. The Johnson-Cook constitutive model has been modified to represent the experimental data over a wide range of strain rates as well as to include heat-transfer effects, and model parameters have been determined for 1018 cold-rolled steel.

Polypropylene (PP), a semi-crystalline material, is typically solid phase thermoformed at temperatures associated with crystalline melting, generally in the 150° to 160° Celsius range. In this very narrow thermoforming window the mechanical properties of the material rapidly decline with increasing temperature and these large changes in properties make Polypropylene one of the more difficult materials to process by thermoforming. Measurement of the deformation behaviour of a material under processing conditions is particularly important for accurate numerical modelling of thermoforming processes. This paper presents the findings of a study into the physical behaviour of industrial thermoforming grades of Polypropylene. Practical tests were performed using custom built materials testing machines and thermoforming equipment at Queen's University Belfast. Numerical simulations of these processes were constructed to replicate thermoforming conditions using industry standard Finite Element Analysis software, namely ABAQUS and custom built user material model subroutines. Several variant constitutive models were used to represent the behaviour of the Polypropylene materials during processing. This included a range of phenomenological, rheological and blended constitutive models. The paper discusses approaches to modelling industrial plug-assisted thermoforming operations using Finite Element Analysis techniques and the range of material models constructed and investigated. It directly compares practical results to numerical predictions. The paper culminates discussing the learning points from using Finite Element Methods to simulate the plug-assisted thermoforming of Polypropylene, which presents complex contact, thermal, friction and material modelling challenges.

A biomechanical model for traumatic brain injury and soft tissue damage is presented. A variational constitutive model for soft biological tissues is utilized to reproduce axonal damage and cavitation injury through inelastic deformation. The material response is split into elastoplastic and viscoelastic components, including rate effects, shear and porous plasticity, and finite viscoelasticity. Mechanical damage of brain tissue is classified as volumetric (compression/tension) and shear-type. Finite element simulations of brain injuries are presented, examining frontal and oblique head impacts with external objects. Localization, extension, intensity and reversibility/irreversibility of tissue damage are predicted. Future directions of this work, relating mechanical damage and physiological brain dysfunction, and application to relevant medical and engineering problems are discussed.

To predict the earthquake response of saturated porous media it is essential to correctly simulate the generation, redistribution, and dissipation of excess pore water pressure during and after earthquake shaking. To this end, a reliable numerical tool requires a dynamic, fully coupled formulation for solidfluid interaction and a versatile constitutive model. Presented in this paper is a 3D finite element framework that has been developed and utilized for this purpose. The framework employs fully coupled dynamic field equations with a u-p-U formulation for simulation of pore fluid and solid skeleton interaction and a SANISAND constitutive model for response of solid skeleton. After a detailed verification and validation of the formulation and implementation of the developed numerical tool, it is employed in the seismic response of saturated porous media. The study includes examination of the mechanism of propagation of the earthquake-induced shear waves and liquefaction phenomenon in uniform and layered profiles of saturated sand deposits.

A Reissner-Mindlin model for analyzing laminated composite plates including piezoelectric layers under mechanical, thermal and electric loads has been constructed using the variational-asymptotic method. The present work formulates the original nonlinear, three-dimensional, one-way coupled, thermopiezoelasticity problem allowing for arbitrary deformation of the normal line and using a set of intrinsic variables defined on the reference plane. The variational-asymptotic method is used to rigorously split the three-dimensional problem into two problems: a nonlinear, two-dimensional, plate analysis over the reference plane to obtain the global deformation, and a linear analysis through the thickness to provide both the two-dimensional generalized constitutive model and recovery relations to approximate the original three-dimensional results. The obtained asymptotically correct second-order electric enthalpy is cast into the form of the commonly used Reissner-Mindlin model to account for transverse shear deformation. The present theory is implemented into the computer program VAPAS (variational-asymptotic plate and shell analysis). Results for several cases obtained from VAPAS are compared with the exact thermopiezoelasticity solutions, classical lamination theory and first-order shear-deformation theory for the purpose of demonstrating the advantages of the present theory and the use of VAPAS. The proposed theory can achieve an accuracy comparable to higher-order layerwise theories at the cost of a first-order shear-deformation theory. possibility of building structures that are self-monitorable and self-controllable. Such smart structures are promising candidates to meet the demanding requirements of highstrength, high-stiffness and light-weight structures for modern engineering, especially aerospace applications. Among many possible candidates for actuators and sensors, piezoelectrics receive the most attention. One reason for this preference is that piezoelectrics can directly relate electric signals to strain components in the material and vice versa. Thus, they can

The steady extrusion of viscoelastic materials from a straight, annular die is studied theoretically. The viscoelastic behavior is modelled using the affine Phan-Thien and Tanner (PTT) constitutive equation of the exponential form. For the numerical solution of the governing equations the mixed finite element method is combined with a quasi-elliptic mesh generation scheme in order to capture the large deformations of the two free surfaces of the extrudate. The elastic-viscous stress splitting technique (EVSS-G) is used to separate the elastic and viscous contributions to the polymeric part of the stress tensor together with a streamline upwind Petrov-Galerkin (SUPG) weighting for the discretization of the constitutive equation. This combination of solution methods and constitutive model allows us (i) to compute accurate steadystate solutions up to very high Weissenberg numbers resulting in very high deformations of the free surfaces (ii) construct and store the Jacobian matrix, which is necessary to conduct linear stability analysis for this flow. First, results for the fully developed flow of a PTT liquid inside an annular die are presented. They reveal a complex interplay between material elasticity, shear thinning and solvent viscosity. Next, a complete parametric analysis of annular extrusion is performed. Such a complete study using the PTT model has not been reported before, even at much lower Wi numbers. It is found that swelling of the material increases sharply up to moderate Weissenberg numbers, whereas its rate of increase is reduced for higher values of Wi, as shear thinning becomes increasingly important. The latter generally plays a crucial role, in addition to elasticity, on the swelling of the extrudate. Moreover, as the contribution of the solvent viscosity increases, the contribution of elastic stresses decreases causing a decrease in the swelling of the material which approaches the Newtonian limit. The predicted swelling ratios, which characterize the geometry of the extrudate, are in satisfactory agreement with earlier experimental and theoretical data for three particular HDPE resins. (J. Tsamopoulos). publications in the past. Next we will mention briefly only those that seem to be most relevant to the present study.

In the current work the ferrocement construction technique is revisited with the purpose of applying the material in civil engineering structures, particularly in large water tanks for water treatment stations. Although it is not a new technology, ferrocement continues to be an attractive alternative. The plastic potential, the unsophisticated construction techniques and the low cost justify its use, especially suitable for developing countries. However, modelling studies of this material are rare in the literature; this is what justifies the studies currently being conducted to improve current practices of design, as well as to further advance the understanding of the material. This work describes experimental and numerical tests for large ferrocement tanks, part of the water treatment facility in Divin o opolis, Brazil. Different finite element models have been used in the analyses in order to evaluate the effect of some adopted simplifications. Some comparisons of the investigated approaches with the experimental data are also included, as well as remarks on the use of different constitutive models, homogenisation techniques and accuracy of the modelling data.

Over the past half-century, democratic constitutional design has undergone a sea change. After the Second World War, newly independent countries tended simply to copy the basic constitutional rules of their former colonial masters, without seriously considering alternatives. Today, constitution writers choose more deliberately among a wide array of constitutional models, with various advantages and disadvantages. While at first glance this appears to be a beneficial development, it has actually been a mixed blessing: Since they now have to deal with more alternatives than they can readily handle, constitution writers risk making ill-advised decisions. In my opinion, scholarly experts can be more helpful to constitution writers by formulating specific recommendations and guidelines than by overwhelming those who must make the decision with a barrage of possibilities and options.

The paper reports the findings of a laboratory study on six different types of cement-based grouts and two types of steel rock anchors. The physical and mechanical characteristics of cement grouts employing silica fume, aluminium powder, superplasticizer or sand are compared with those of conventional cement grouts. Pullout tests of grouted, 7-strand steel cable and solid steel threadbar were conducted under similar conditions for different grouts and embedment lengths. From the results obtained, an empirical equation is derived for the estimation of anchor pullout resistance for a given embedment length. A simple trilinear constitutive model for shear bond stress-slip relation at the anchor-grout interface is proposed and discussed.