Constitutive model

In a recent paper, Starr and Segalman demonstrated that any Masing model can be represented as a parallel-series Iwan model. A preponderance of the constitutive models that have been suggested for simulating mechanical joints are Masing models, and the purpose of this discussion is to demonstrate how the Iwan representation of those models can yield insight into their character. In particular, this approach can facilitate a critical comparison among numerous plausible constitutive models. It is explicitly shown that three-parameter models such as Smallwood's (Ramberg-Osgood) calculate parameters in such a manner that macro-slip is not an independent parameter, yet the model admits macro-slip. The introduction of a fourth parameter is therefore required. It is shown that when a macro-slip force is specified for the Smallwood model the result is a special case of the Segalman four-parameter model. Both of these models admit a slope discontinuity at the inception of macro-slip. A fiveparameter model that has the beneficial features of Segalman's four-parameter model is proposed. This model manifests a force-displacement curve having a continuous first derivative.

A nonlinear viscoelastic constitutive model for the solid propellant is proposed. In their earlier work, the authors have developed an isotropic constitutive model and veri®ed it for one-dimensional case. In the present work, the validity of the model is extended to three-dimensional cases. Also, implementation of the model into a commercial code for the use of the constitutive model in the ®nite element analysis of solid propellant is discussed. Large deformation, dewetting and cyclic loading eects are treated as main sources of nonlinear behavior of the solid propellant. The softening of the solid propellant due to dewetting is treated by the modulus decrease. The nonlinearities during cyclic loading are accounted for by the functions of the octahedral shear strain measure. The constitutive equation is implemented into a ®nite element code for the analysis of propellant grains. A commercial ®nite element package `ABAQUS' is used for the analysis and the model is introduced into the code through a user subroutine. The model is evaluated with dierent loading conditions and the predicted values are in good agreement with the biaxial test results.

The viscoelastic behavior of carbon-black-filled rubber under small oscillatory loads superimposed on large static deformation is dealt with. In this class of problems, as the strain amplitudes of the load increase, the dynamic stiffness decreases, and this phenomenon is known as the Payne effect. Besides the effects of the static deformation and the frequencies of the superimposed dynamic load, the Payne effect is considered in this study. Influence factors are introduced in this model in order to consider the influence of static predeformation, the dynamic-strain-dependent properties, and frequency-dependent properties. For simplicity, separation of the three dominant variables, frequency, prestatic deformation, and dynamic amplitude of strain, is assumed. The Kraus model is used for describing the Payne effect. Dynamic tension tests are executed to obtain the model parameters and also for the verification of the proposed model. The suggested constitutive equation shows reasonable agreement with test data.

This paper deals with the development of a non-linear constitutive model of a rock mass and its application to predict the extension of the excavation damaged zone (EDZ) around openings. A comparison of the model results with the simulations of triaxial compression tests shows a good agreement between predictions and theoretical values of peak and residual strengths as well as a good reproduction of the transition between brittle failure and ductile response. The relevance of the proposed model to evaluate the potential failure around stopes of the Garpenberg mine was examined. The comparison of the results proved satisfactory and highlighted the interest of considering a more realistic mechanical behavior of hard rock masses in rock engineering compared with the elastic perfectly plastic models generally used in numerical modeling of underground deep mines. Finally, a 3D simulation of the complete mine geometry was carried out in order to model the first phases of stope mining operations. The predicted stresses were compared with the continuous measurements of induced in situ stresses recorded by stress cells at different points around the stope. The predictions of the proposed constitutive model provided a much better agreement with stress measurements than those obtained with elastic perfectly plastic models.

A looal damage constitutive model based on Kachanov' s theory is used within a finite element frame and applied to the case of 2D and 3D Timoshenko beam elements. The model takes into account viscous effects, thus allowing damping to be considered in a rigorous way. A damage index based on potential energy criteria, useful in evaluating the behaviour of structures or of parts of structures, is proposed. The procedure is applied to estimate the damage produced by seismic actions in reinforced concrete building structures, whose response is computed by using a non-linear Newmark-type incremental time integration scheme. Three numerical examples are included ; one of them compares results obtained by using the proposed model with results of a laboratory test.

This paper presents a new constitutive model for the time dependent mechanical behaviour of rock which takes into account both viscoplastic behaviour and evolution of damage with respect to time. This model is built by associating a viscoplastic constitutive law to the damage theory. The main characteristics of this model are the account of a viscoplastic volumetric strain (i.e. contractancy and dilatancy) as well as the anisotropy of damage. The latter is described by a second rank tensor. Using this model, it is possible to predict delayed rupture by determining time to failure, in creep tests for example. The identification of the model parameters is based on experiments such as creep tests, relaxation tests and quasi-static tests. The physical meaning of these parameters is discussed and comparisons with lab tests are presented. The ability of the model to reproduce the delayed failure observed in tertiary creep is demonstrated as well as the sensitivity of the mechanical response to the rate of loading. The model could be used to simulate the evolution of the excavated damage zone around underground openings.

Predicting the deformations of deep reservoirs due to fluid withdrawal/injection is a challenging task that could have important environmental, social, and economical impacts. Finite element models, if endowed with an appropriate constitutive law, represent a useful tool for computing the displacements, the deformations, and the stress distributions in reservoir applications. Several studies show that hypoelastic laws, based on a stress-dependent vertical compressibility, are able to provide accurate results, confirmed by in situ and satellite measurements. On the other hand, such laws present some weaknesses related to the numerical implementation, in particular due to the nonsymmetry of the tangent operator. This paper presents a new constitutive model based on 2 invariants (the mean normal and deviatoric stresses), characterized by a variable pressure-dependent bulk modulus K. This constitutive law allows for overcoming most shortcomings of the hypoelastic law, although preserving the same accuracy, reliability, and ease of use and calibration. This paper presents a procedure to identify the parameters of the new model, starting from the typically available data on the vertical compressibility. Numerical results show a good agreement between the 2 laws, suggesting the proposed approach as a valid alternative in reservoir applications.

Polymer nanocomposites refer to a broad range of composite materials with polymer acting as the matrix and any material which has at least one dimension in the order of 1 ~ 100 nanometer acting as the filler. Due to unprecedented improvement observed in properties of the nanocomposites, research interest in this area has grown exponentially in recent years. In designing better nano-composites for advanced technological applications some of the major challenges are: understanding the structure-property relationships, interaction and integrity of the two components at the interface, the role of nanofillers in enhancing the properties of the resulting material. In our work, we have utilized first principle calculations, atomistic simulations, coarse-grained modeling and constitutive equations to develop structureproperty relationships for an amorphous aromatic piezoelectric polyimide substituted with nitrile dipole, carbon nanotubes and resulting nanocomposites. We have studied in detail structure-property relationships for carbon nanotubes and (β -CN)APB /ODPA polyimide. We have developed chemically sound coarse-grained model based on atomic level simulations of the piezoelectric polyimide to address the larger length and time scale phenomena. The challenge of coarse grain model for these polymers is to reproduce electrical properties in addition to the structure and energetics; our model is the first to successfully achieve this goal. We have compared and analyzed atomistic scale simulation results on the nanocomposite with those predicted from micromechanics analysis. Notably, we have investigated the time dependent response of

The main objective of the present paper is the numerical investigation of dynamic shear bands in inelastic solids generated by impact-loaded adiabatic processes. Particular attention is focused on the proper description of a ductile mode propagating along the shear band for high impact velocities.

Application of the thermodynamic-based strain gradient plasticity theory in high velocity impact problems GEORGE VOYIADJIS, YOOSEOB SONG, Louisiana State University -In this work, a thermodynamicbased framework of the higher-order strain gradient plasticity is presented to investigate the thermo-mechanical material response of the metallic volumes at extreme conditions such as high velocity impact related problems. The need of the plastic strain gradients and their corresponding rates is discussed along with the mechanism associated with geometrically necessary dislocations. One of the major issues in the strain gradient plasticity is the determination of the intrinsic material length scales that scale with the gradient of the plastic strain. Explicit and implicit microstructural length scales, which preserve the well-posed nature of the differential equations, are introduced through the use of the viscosity and gradient localization limiters. Numerical simulations of the dynamic deformation response of tantalum hat-shaped specimens, subjected to compressive loading at the ambient initial temperatures and three different strain rates, are carried out and the comparisons of the numerical results to experimental measurements are also made. Another numerical application of a blunt projectile impacting a target is examined and the direct comparison between numerical and experimental results is presented.

In this companion article, we present, within the finite element context, the numerical algorithms for the integration of the thermodynamically consistent formulation of the elastic plastic and damage model for concrete materials derived in part I of this work. The proposed unified integration scheme is based on the spectral return-mapping algorithm accounting for the use of the principal stresses along with the stress tensor invariants. An operator split structure is used, consisting of a trial stress state followed by corrector steps applied through imposing the generalized plastic and damage consistency conditions. Furthermore, a trivially incrementally objective integration scheme is established for the rate constitutive relations. The proposed elastic-predictor and uncoupled plastic and damage corrector algorithms allow for a straightforward integration scheme that can be easily implemented into the existing finite element codes. The nonlinear algebraic system of equations is solved by consistent linearization and the Newton-Raphson iteration scheme. The proposed model is implemented in the implicit finite element code ABAQUS via the user subroutine UMAT. Model capabilities are illustrated through its application to the analysis of Reinforced Concrete (RC) beams tested experimentally and available in literature. The simulated results illustrate the potential of the proposed model in dealing with the reduction of the effect of the well known mesh sensitivity problem through the application of the fracture energy concept-related parameters.

In this work use is made of functional forms of hardening state variables within a consistent thermodynamic formulation to model the elasto-plastic behavior of materials. The formulation is then numerically implemented using the developed plasticity model. In deriving the constitutive model, a local yield surface is used to determine the occurrence of plasticity. Isotropic hardening and kinematic hardening are incorporated as state variables to describe the change of the yield surface. The hardening conjugate forces (stress-like terms) are general nonlinear functions of their corresponding hardening state variables (strain-like terms) and can be defined basing on the desired material behavior. Various exponential and power law functional forms are studied in this formulation. The paper discusses the general concept of using such functional forms; however, it does not address the relevant appropriateness of certain forms to solve different problems. It is shown that, depending on the functions used, standard models known from the literature can be recovered. The use of this formulation in solving boundary value problems will be presented in future.

Proper life-time prediction modeling of single crystalline components is of increasing importance due to their common use in turbine industry. Viscoplastic damage approaches are of great interest in that context. However, mechanical properties of single crystals are strongly anisotropic and nonlinear in service conditions, bringing certain complexity into constitutive and numerical modeling. The aim of this work is to develop a thermodynamically consistent constitutive model based on generalized continua in order to simulate fatigue crack initiation and growth in single crystals. For that purpose, a standard crystal plasticity model is taken as a basis and coupled with the continuous damage model developed by [

Solid state dynamics experiments at very high pressures (P >> 10 GPa) and strain rates (C: >> lo5 s-') have been demonstrated on high energy laser facilities, albeit over brief intervals of time and small spatial scales. We have developed two methods for driving samples to high pressures (10-100 GPa) at high strain rate (lo6-lo8 s-') in the solid state. One method uses a shockless compression technique, and the other uses multiple staged shocks. These drives are calibrated with VISAR measurements of the resulting compression wave. Deformation mechanisms are inferred under these conditions by characterizing recovered samples. Material strength at high pressures and strain rates is deduced by measuring the reduced growth of material perturbations at a hydrodynamically unstable interface. Microscopic lattice response is determined by time-resolved Bragg diffraction and x-ray absorption spectroscopy (EXAFS). Largescale simulations, both at the continuum level using constitutive models and at the lattice level using molecular dynamics simulation, are used to interpret these integral experiments. We will review our progress in this new area of laser-based materials science research, then present a vision for carrying these solid-state experiments to much higher pressures, P > 1000 GPa, on the National Ignition Facility (NIF) laser facility.

A constitutive model is proposed for clays based on the experimental observations from a series of flexible boundary true triaxial shear tests on cubical specimens of light to heavily overconsolidated kaolin clay. The proposed model adequately captures the combined effect of overconsolidation and intermediate principal stress. Overconsolidated clays often exhibit nonlinear stress-strain response at much lower stress levels than what is predicted by the existing constitutive theories/models. Experimental results for kaolin clay demonstrated sudden failure response before reaching the critical state, which became more prominent for higher relative magnitudes of intermediate principal stress. The observed stress state at failure is governed by the third invariant of stress tensor and the pre-failure yielding of the material by the second invariant of deviatoric stress tensor. The proposed constitutive model considers these issues with a few simplifying assumptions. The assumed yield surface has a droplet shape in q-p 0 stress space with hardening based on both plastic volumetric and shear deformations. A dynamic failure criterion is employed in the current formulation that grows in size as a function of consolidation history. Prefailure yielding is governed by a reference surface, which is different from the failure surface.

Higher-order polynomial functions can be used as a constitutive model to represent the mechanical behaviour of biological materials. The goal of this study was to present a method for assessing the fit of a given constitutive three-dimensional material model. Goodness of fit was assessed using multiple parameters including the root mean square error and Hotelling's T 2 -test. Specifically, a polynomial model was used to characterise the stress-strain data, varying the number of model terms used (45 combinations of between 3 and 11 terms) and the manner of optimisation used to establish model coefficients (i.e. determining coefficients either by parameterisation of all data simultaneously or averaging coefficients obtained by parameterising individual data trials). This framework for model fitting helps to ensure that a given constitutive formulation provides the best characterisation of biological material mechanics.

A significant step forward in modelling polymer melt rheology has been the introduction of the Pom-Pom constitutive model of McLeish and Larson [T.C.B. McLeish, R.G. Larson, Molecular constitutive equations for a class of branched polymers: the Pom-Pom polymer, J. Rheol. 42 (1) (1998) 81-110]. Various modifications of the Pom-Pom model have been published over the years in order to overcome several inconveniences of the original model. Amongst those modified models, the eXtended Pom-Pom (XPP) model of Verbeeten et. al. [W.M.H. Verbeeten, G.W.M. Peters, F.P.T. Baaijens, Differential constitutive equations for polymer melts: the extended Pom-Pom model, J. Rheol. 45 (4) ( ) 823-843] has received quite some attention. However, the XPP model has been criticized for the generation of multiple and unphysical solutions. This paper deals with two issues. First, in the XPP model, anisotropy is implemented in a Giesekus-like manner which is known to result in unphysical solutions for non-linear parameter values ˛≥ 0.5. Hence, we put forward the conjecture that a similar limitation holds for the XPP model. In the present paper, the limits for the anisotropy parameter are elaborated on and result to be most restraining at high deformation rates where the backbone tube is oriented and the backbone tube stretch approaches the number of arms q. By restricting the anisotropy parameter to a maximum critical value the XPP model produces only one solution, which is the correct physical rheology. In the second part we show that, contrary to the results published by Inkson and Phillips [N.J. Inkson, T.N. Phillips, Unphysical phenomena associated with the extended Pom-Pom model in steady flow, J. Non-Newton. Fluid 145 (2-3) (2007) 92-101], for the special case where the anisotropy parameter equals zero, only one physically relevant solution exists in unaxial extensional. In addition to this physically relevant solution, also solutions exist in the physically unattainable part of the conformation space. However, the existence of these physically unattainable solutions is not a unique feature of the XPP model but rather general for non-linear differential type rheological equations.

In this study we develop a first‐order, nonstationary stochastic model for steady state, unsaturated flow in randomly heterogeneous media. The model is applicable to the entire domain of a bounded vadose zone, unlike most of the existing stochastic models. Because of its nonstationarity, we solve it by the numerical technique of finite differences, which renders the flexibility in handling different boundary conditions, input covariance structures, and soil constitutive relationships. We illustrate the model results in one and two dimensions for soils described by the Brooks‐Corey constitutive model. It is found that the flow quantities such as suction head, effective water content, unsaturated hydraulic conductivity, and velocity are nonstationary near the water table and approach stationarity as the vertical distance from the water table increases. The stationary limits and the critical vertical distance at which stationarity is attained depend on soil types and recharge rates. Th...

A rate dependent theory of polycrystalline plasticity is presented in which the solid is modeled as an isotropic continuum with internal variables. The rate of plastic deformation is shown to be a function of the deviatoric portion of the Cauchy stress tensor as well as two scalar internal variables. The scalar internal variables, which are the dislocation density and mobile fraction, are governed by rate equations which reflect the evolution of microstructural processes. The model has been incorporated into a two dimensional finite element code and several example multidimensional problems are presented which exhibit the rate dependence of the material model.

The linear stability analysis of an uniform shear flow of granular materials is revisited using several cases of a Navier–Stokes-level constitutive model in which we incorporate the global equation of states for pressure and thermal conductivity (which are accurate up to the maximum packing density νm) and the shear viscosity is allowed to diverge at a density νμ (<νm), with all other transport coefficients diverging at νm. It is shown that the emergence of shear-banding instabilities (for perturbations having no variation along the streamwise direction), that lead to shear-band formation along the gradient direction, depends crucially on the choice of the constitutive model. In the framework of a dense constitutive model that incorporates only collisional transport mechanism, it is shown that an accurate global equation of state for pressure or a viscosity divergence at a lower density or a stronger viscosity divergence (with other transport coefficients being given by respectiv...

The aim of the present work is to present two operational numerical methods allowing for integrating rate constitutive equations accounting for large strains and rotations. Both methods can be applied in the development of home-made computation codes or/and in the development of user material subroutines in commercial computation codes.

This article experimentally evaluates the influence of shearing rate on the monotonic and cyclic response of isotropically-consolidated samples of Malaysian kaolin. On the one hand, a series of undrained monotonic triaxial tests were performed with varying shearing displacement rate. On the other hand, undrained cyclic triaxial tests were conducted considering different deviatoric stress amplitudes and loading frequencies. The well-known soil rate-dependency under monotonic loading was confirmed up to a displacement rate threshold. The experimental results under cyclic loading suggest that for the given loading frequency, the variation of the deviatoric stress amplitude remarkably influences the strains and pore water pressure accumulation rates. In addition, the results suggest that depending on the loading frequency different shapes of mobilized effective stress loops are obtained. Larger loading frequencies lead to banana-shaped effective stress loops, while smaller frequencies reproduce eight-shaped effective stress loops. Furthermore, higher loading frequencies result in a larger number of cycles required to reach failure conditions. The reasons for the observed differences in the behavior are thoroughly analyzed and discussed.

The aim of this paper is to show that recent advances made in the field of speckle image processing give valuable information useful in understanding and modelling of localisation phenomena. The potentialities of the proposed imaging method are illustrated by examples extracted from tensile tests performed on steel specimens. Having introduced the underlying motivations of this experimental work, this paper briefly focuses on the image processing technique and its reliability. Then, it describes the characteristics of the strain field within and outside of a propagating Lüders band. The properties of strain states associated with diffuse and localised necking are also investigated. The catalyst role of possible geometrical defects is pointed out. Finally, a method is proposed to construct, despite localisation, a local stress-strain correspondence.

In the present study, the microstructural changes of a Nickel based superalloy Nimonic 80A during a non-isothermal deformation were studied. Therefore, microstructure evolution during hot side pressing test was predicted with combined methods of finite element analysis and processing map of the material. The predicted results were validated through experimental microstructural studies. The results show that the distribution of deformation parameters (i.e. strain, strain rate, and temperature) is non-uniform in the deformed samples. The severity of this non-uniformity depends on the amount of sample reduction. High reduction value at one step forging can cause flow localization and non-uniform dynamic recrystallization, which results the formation of adiabatic shear bands, while using the lower reduction value at each forging step, leads to more uniformly distribution of the deformation parameters and thus uniform the dynamic recrystallization with the stable flow. Hence the workabil...

In this study the influence of precipitates on the mechanical properties and plastic anisotropy of an age hardenable aluminum alloy during uniaxial loading was investigated using crystal plasticity modeling. The kinetics model of Myhr et al. was used to obtain the solute and precipitate features after different cycles of aging treatment. The amounts of solute, precipitate size and volume fraction, and dislocation density varying during deformation, were used to calculate the slip system strength. An explicit term was obtained based on the elastic inclusion model for the directional dependency of internal stress developed by non-shearable rod shape precipitates. Also, a dislocation evolution model was modified to assess the anisotropic influence of non-shearable precipitate on work hardening, and the effects of solute content on the rate of dynamic recovery. It was found that the model results were in good agreement with experimental uniaxial flow stress obtained under different aging conditions. The application of the model to single crystal revealed that the precipitates can reduce crystallography anisotropy, which in part was attributed to the precipitate induced anisotropy.

Several theoretical expressions of the at rest earth pressure coefficient for normally consolidated soils ( 0( NC ) k ) are available in the literature. Some of them have been derived using Critical State Soil Mechanics constitutive models. However, these models usually over-predict the 0( NC ) k values. The possibility to improve, in principle, the 0( NC ) k prediction simply changing the plastic potential surface shape of the Modified Cam-Clay model, i.e. adopting a non-associated flow rule, is described in the paper.

This work presents a fully nonlinear Kirchhoff-Love shell model. In contrast with shear flexible models, our approach is based on the Kirchhoff-Love theory for thin shells, so that transversal shear deformation is not accounted for. We define energetically conjugated cross-sectional generalized stresses and strains. The fact that both the first Piola-Kirchhoff stress tensor and the deformation gradient appear as primary

In order to obtain high-quality products in powder metallurgy, it is important to control and understand the densification behavior of metallic powders. The effect of the powder characteristics of magnesium powders on the compaction behavior was investigated in this study by experimental and theoretical methods. A modified version of Lee-Kim's plastic yield criterion, known as the critical relative density model, was applied to simulate the densification behavior of magnesium powders, and a new approach that extracts both the powder and the matrix characteristics was developed. The model was implemented via the finite element method, and powder compaction under upsetting conditions was simulated. The calculated and experimental results are in good agreement.

Aiming at the acid-etched freeze-thaw rock for geotechnical engineering in cold regions, chemical damage variables, freeze-thaw damage variables, and force damage variables were introduced to define the degree of degradation of rock materials, the law of damage evolution, the total damage variable of acid-corroded rock under the coupling action of freeze-thaw and confining pressure was deduced. The continuous damage mechanics theory was adopted to derive the damage evolution equation and constitutive model of acid-eroded rock under the coupling action of freeze-thaw and confining pressure. The theoretical derivation method was used to obtain the required model parameter expressions. Finally, the model’s rationality and accuracy were verified by the triaxial compression test data of frozen-thawed rocks. Comparing the test curve’s peak point with the peak point of the model theoretical curve, the results show that the two are in suitable agreement. The damage constitutive model can be...

The constitutive model with a single damage parameter describing creep-damage behaviour of metals with respect to the different sensitivity of the damage process due to tension and compression is incorporated into the ANSYS ®nite element code by modifying the user de®ned creep material subroutine. The procedure is veri-®ed by comparison with solutions for beams and rectangular plates in bending based on the Ritz method. Various numerical tests show the sensitivity of long-term predictions to the mesh sizes and element types available for the creep analysis of thinwalled structures.

The large-deformation three-dimensional glass±rubber constitutive model for isotropic, amorphous, linear polymers near the glass transition, previously proposed, has been extended to include a spectrum of network relaxations. In addition, an experimental programme of uniaxial tension and compression tests was carried out on high molecular weight cast sheets of poly(methyl methacrylate) (PMMA), with varying strain-rate and temperature across the range from 114 to 190 8C, encompassing the thermoforming range of practical importance. The extended model was found to ®t successfully the data for PMMA, provided a doublet network relaxation spectrum was employed. The original model, with only a single network relaxation, was found to be grossly inadequate when there was signi®cant network relaxation by entanglement slippage. Parameters of the model for PMMA, obtained by ®tting to the new data, were compared with values obtained by other routes.

Two recently proposed developments of the Glass-Rubber constitutive model for glassy polymers treat the viscoplastic deformation as intrinsically anisotropic, and incorporate the kinetics of structural evolution. These features enable the model to capture better the distinctive features of glassy polymers' constitutive response: post-yield strain-softening and strain-hardening and effects of pre-existing molecular orientation. They have been combined to form a new variant of the model, and the consequences for necking have been explored. Uniaxial extension of prismatic bars was simulated using the finite element method, employing a numerical implementation of the new model, with material parameters of polystyrene. Strain localization predicted with the new model was found to be systematically retarded as compared to predictions with the original (intrinsically isotropic) version of the model, for the same conditions. In particular, the effect of frozen-in molecular orientation was examined. This was found to retard strain localization for stretching parallel to the orientation direction, for both models. But the localization predicted with the new model was always significantly less pronounced than with the original model. Indeed, for sufficiently high pre-orientation (e.g. a uniaxial stretch of 2.2), localization could be effectively prevented with the new model, under conditions when otherwise failure by necking is predicted. Such results can all be explained in terms of a linear stability analysis. They suggest that all previous simulations of necking in glassy polymers made using intrinsically isotropic representations of polymer viscoplasticity may have over-predicted the rate of strain localization.

This research is aimed at determining the effect of thermo-mechanical ageing experimentally and numerically on the Mechanical Properties of Al-Cu Alloy by formulating a model (constitutive) to determine the nodal value of certain parameters and to simulate the obtain results using Matlab (fematiso).The development and morphology of Al-9.37Cu alloy was characterized through metallographic examination and failure rate. The alloy was obtained by employing Die -Casting Technique before being subjected to series of mechanical and materials tests. The result showed that the strength of Al9.37Cu was greatly enhanced when the alloy was under different percent of deformations between 5-15%. Constitutive model was adopted to determine the isotropic material property in which the plane stress and plain strain conditions were considered as boundary conditions. Consequently, the effect of temperature was able to influence the strain rate in which the fracture strain determined the failure rate o...

Most structures exposed to severe loadings may suffer damage, possibly resulting in safety risk or economic loss. In complement to experimental studies and design codes and standards, advanced numerical simulation of damage appears as a promising approach to describe such critical regimes. However, damage modelling still faces several difficulties. In the case of ductile damage, characterized by a large amount of plastic strain, spurious strain localization and plastic volumetric locking are observed and should be dealt with.

Yakai Zhao, Division of Materials Science and Engineering, Hanyang University, Seoul 133-791, Korea Email address: [email protected] In-Chul Choi, Institute for Applied Materials, Karlsruhe Institute of Technology, Karlsruhe 76344, Germany Moo-Young Seok, Division of Materials Science and Engineering, Hanyang University, Seoul 133-791, Korea Jin-Yoo Suh, High Temperature Energy Materials Research Center, Korean Institute of Science and Technology, Seoul 136-791, Korea Jae-il Jang, Division of Materials Science and Engineering, Hanyang University, Seoul 133-791, Korea

A numerical approach for structural analysis of masonry walls in plane stress conditions is presented. The assumption of a perfectly no-tension material (NTM) constitutive model, whose relevant equations are in the form of classical rate-independent associated flow laws of elastoplastic material, allows one to adopt numerical procedures commonly used in computational plasticity. An accuracy analysis on the integration algorithm employed in the solution of constitutive relations has been carried out. The results obtained for some relevant case-studies and their comparison with data, available in the literature show the effectiveness of the proposed method. Sommarlo. Si presenta un approccio numerico per l'analisi strutturale di pareti in muratura in stato piano di tensione. L'assunzione di un modello costitutivo per materiale perfettamente non resistente a trazione (NTM), le cui equazioni sono esprimibili neIla classica forma incrementale delle leggi dello scorrimento plastico di tipo associato per materiali elastoplastici, consente di adottare procedure numeriche comunemente utilizzate in plasticith computazionale. Si conduce un'analisi di accuratezza dell'algoritmo utilizzato nell'integrazione delle equazioni costitutive del modello esaminato. I risultati ottenuti per alcuni casi analizzati ed il confronto effettuato con esempi riportati in letteratura mostrano l'efficienza dell'approccio proposto.

We develop a constitutive model of paper's in-plane biaxial tensile response accounting for the elastic-plastic hardening behavior, and its orthotropic character. The latter aspect is motivated by machine-made papers, which, in contrast to isotropic laboratory handsheets, are strongly oriented. We focus on modeling paper's response under monotonic loading, this restriction allowing us to treat the elastic-plastic response as a physically nonlinear elastic one. A strain energy function of a hyperbolic tangent form is developed so as to fit the entire range of biaxial and uniaxial experiments on a commercial grade paper. This function may then be introduced as the free energy function into a model based on thermomechanics with internal variables.

Water flow in partially saturated heterogeneous porous formations is modelled by regarding the hydraulic parameters as stationary random space functions (RSFs). As a consequence, the flow variables are also RSFs, and we aim to develop a procedure to derive the effective hydraulic conductivity (EHC). The methodology relies on a perturbation approach which regards the variances of the hydraulic parameters as small quantities. By using the GardnerÕs [Gardner WR. Some steady state solutions of unsaturated moisture flow equations with application to evaporation from a water table. Soil Sci 1958;85:228-32] two-parameters (K s , a) model for the local unsaturated conductivity, we obtain the EHC for any dimensionality d of the flow domain, and arbitrary correlation functions of the input RSFs. Unlike previous studies [e.g. Yeh T-CJ, Gelhar J, Gutjahr A. Stochastic analysis of unsaturated flow in heterogenous soils. 1. Statistically isotropic media. Water Resour Res 1985;21;447-56, Yeh T-CJ, Gelhar J, Gutjahr A. Stochastic analysis of unsaturated flow in heterogenous soils. 2. Statistically anisotropic media with variable a. Water Resour Res 1985:21:457-64], the EHC is represented here as product between the local scale conductivity valid for a domain of mean parameters, and a correction function j * which depends on the medium heterogeneity structure and the mean pressure head. Generally, the correction function j * is expressed by d-fold quadrature. These quadratures are further reduced after adopting specific (i.e. exponential and Gaussian) structure for the (cross) correlation functions involved in the computation of j * . We have also focused on some particular formation structures which are relevant for the applications, and permit simplification of the computational aspect, as well. We investigate effects of the heterogeneity formation properties as well as the mean head on the structure of j * . Overall, results suggest that, given the formation statistics, the impact of the heterogeneity upon j * is enhanced as the medium becomes drier. This is particularly so when the variability of the fluctuation of Y = lnK s is small compared with that of f = lna. Conversely, when the heterogeneity of Y is prevalent upon that of f, j * is influenced solely by the anisotropic structure of the formation unless the horizontal correlation scales are much greater than the vertical ones.

The e!ect of the nonlinear magnetoelastic coupling on the magnetostrictive stress and the magnetic anisotropy of epitaxially grown ultrathin Ni "lms with large epitaxial strain is investigated by the ab initio density functional electron theory. The nonlinear coupling has a considerable in#uence on the magnetostrictive stress, in agreement with the experimental results from the optical bending beam technique, but a weaker in#uence on the stress-induced magnetic anisotropy. Estimates are given for the nonlinear magnetoelastic coupling coe$cients mA and mA . The results are compared with those for Fe.

The finite element method is used for simulating the compaction process of powders. Attention is focused on both the metal powders and ceramics on which experiments have been conducted and test data made available for comparison purposes. The implementation of advanced finite element techniques such as adaptive remeshing and frictional interface elements are briefly discussed. Macroscopic constitutive laws are presented on the basis of an elastoplastic approach in which the elastic rebound, or springback, effect after compaction can be taken into consideration. Two case studies are presented to demonstrate the validation of the method.

The notion of a two-point susceptibility kernel used to describe linear electromagnetic responses of dispersive continuous media in non-relativistic phenomena is generalized to accommodate the constraints required of a causal formulation in spacetimes with background gravitational fields. In particular the concepts of spatial material inhomogeneity and temporal non-stationarity are formulated within a fully covariant spacetime framework. This framework is illustrated by re-casting the Maxwell-Vlasov equations for a collisionless plasma in a form that exposes a 2-point electromagnetic susceptibility kernel in spacetime. This permits the establishment of a perturbative scheme for non-stationary inhomogeneous plasma configurations. Explicit formulae for the perturbed kernel are derived in both the presence and absence of gravitation using the general solution to the relativistic equations of motion of the plasma constituents. In the absence of gravitation this permits an analysis of collisionless damping in terms of a system of integral equations that reduce to standard Landau damping of Langmuir modes when the perturbation refers to a homogeneous stationary plasma configuration. It is concluded that constitutive modelling in terms of a 2-point susceptibility kernel in a covariant spacetime framework offers a natural extension of standard non-relativistic descriptions of simple media and that its use for describing linear responses of more general dispersive media has wide applicability in relativistic plasma modelling.

In order to characterize the mechanical behavior of HDPE pipes, the ASTM D 2290-04 standard recommends carrying out tensile tests on notched rings, cut out from the pipe. This very simple test is also utilized to investigate the aging effect of the pipe by determining the strain at failure. Comparison between full ring and notched ring mechanical responses are discussed. Constitutive modeling including strain rate effects was performed by finite element analysis. This allowed a better understanding of the stress state in the cross section perpendicular to the loading direction. Additionally, the influence of a thin layer of oxidized HDPE in the inner wall of the ring was studied in the light of the finite element results.

In the present paper theoretical and experimental investigations are made to verify viscoplastic theories applied to thin-walled structures. The vibrations of plates are studied under the assumption of small strains and moderate rotations theoretically and numerically by using constitutive models of Chaboche and Bodner-Partom. The numerical results are compared with experiments.

An elastoplastic pressuremeter theory for cohesive soil has been used in the design of construction, such as retaining walls, slope stability, or foundation engineering. This theory takes into account the plasticity along the vertical and horizontal planes and allows for the determination of the conventional limit pressure. We compute here the conventional limit pressure using the Plaxis program to check the validity of the theoretical results. First, we present the theory used for the interpretation of the pressuremeter test in cohesive soil and its extension to the conventional limit pressure, which is defined as the pressure at the borehole wall for a volume increase
V equal to the initial volume of the borehole. One of the main results is the theoretical expression of the conventional limit pressure. This
volume variation is linked to a radial strain of
2−1. This conventional limit pressure can be directly measured with the pressuremeter,
whereas the theoretical limit pressure is expressed as an infinite expansion and cannot be directly measured. Then, we validate this theory by using finite elements, and determine the conventional limit pressure with the Tresca standard model of Plaxis, which is compared to the theoretical expression. Conclusions are drawn on the validity of this new theory which allows the measurement and the control of the shearing modulus and shear strength of the natural soil.

An elastoplastic pressuremeter theory for cohesive soil has been used in the design of construction, such as retaining walls, slope stability, or foundation engineering. This theory takes into account the plasticity along the vertical and horizontal planes and allows for the determination of the conventional limit pressure. We compute here the conventional limit pressure using the Plaxis program to check the validity of the theoretical results. First, we present the theory used for the interpretation of the pressuremeter test in cohesive soil and its extension to the conventional limit pressure, which is defined as the pressure at the borehole wall for a volume increase ⌬V equal to the initial volume of the borehole. One of the main results is the theoretical expression of the conventional limit pressure. This volume variation is linked to a radial strain of ͱ 2 -1. This conventional limit pressure can be directly measured with the pressuremeter, whereas the theoretical limit pressure is expressed as an infinite expansion and cannot be directly measured. Then, we validate this theory by using finite elements, and determine the conventional limit pressure with the Tresca standard model of Plaxis, which is compared to the theoretical expression. Conclusions are drawn on the validity of this new theory which allows the measurement and the control of the shearing modulus and shear strength of the natural soil.