Constitutive Modelling

The typical shear behaviour of rock joints has been studied under a constant normal load (CNL) or zero normal stiffness condition, but recent studies have shown that this boundary condition may not replicate more practical situations, and that constant normal stiffness (CNS) is a more appropriate boundary condition to describe the stress-strain response of field joints. In addition to the effect of boundary conditions, the shear behaviour of a rough joint also depends on its surface properties and the initial stress acting on its interface. Despite this, exactly how these parameters affect the shear behaviour of joints is not fully understood because the stress-strain response of joints is governed by non-uniform asperity damage and the resulting gouge that accumulates on their interfaces. Therefore, an attempt has been made in this study to predict the complete shear behaviour of rough joints incorporating the asperity deformation under CNS conditions. In order to validate this analytical model, a series of CNS shear tests were conducted on rough tensile (natural) joints and their replicas at a range of initial normal stresses that varied from 0.4 to 1.6 MPa. Comparisons between the predicted shear behaviour and the experimental results show close agreement.

A representative volume element (RVE) involving a single carbon nanotube (CNT) embedded in a plastic matrix is used to model the elastic behavior of the nanocomposite using finite elements. When the RVE is loaded axially, the maximum shear stress at the CNT-matrix interface can exceed the interfacial shear strength causing slippage of the CNT inside the matrix. Cyclic loading causes hysteretic stress-strain behavior of the nanocomposite and dependencies on the interfacial strength, geometry, relative elastic properties of the CNT and the matrix, and volume fraction of the CNTs are investigated.

The paper deals with constitutive modelling of contiguous rock located between rock joints. A fully explicit kinematically constrained microplane-type constitutive model for hardening and softening non-linear triaxial behaviour of isotropic porous rock is developed. The microplane framework, in which the constitutive relation is expressed in terms of stress and strain vectors rather than tensors, makes it possible to model various microstructural physical mechanisms associated with oriented internal surfaces, such as cracking, slip, friction and splitting of a particular orientation. Formulation of the constitutive relation is facilitated by the fact that it is decoupled from the tensorial invariance restrictions, which are satisfied automatically. In its basic features, the present model is similar to the recently developed microplane model M4 for concrete, but there are significant improvements and modifications. They include a realistic simulation of (1) the effects of pore collapse on the volume changes during triaxial loading and on the reduction of frictional strength, (2) recovery of frictional strength during shearing, and (3) the shearenhanced compaction in triaxial tests, manifested by a deviation from the hydrostatic stress-strain curve. The model is calibrated by optimal fitting of extensive triaxial test data for Salem limestone, and good fits are demonstrated. Although these data do not cover the entire range of behaviour, credence in broad capabilities of the model is lend by its similarity to model M4 for concrete}an artificial rock. The model is intended for large explicit finite-element programs.

The aim of this paper is the development of suitable mechanical models able to reproduce and, hence, to predict the response of masonry structures. In particular, the study is addressed to the modelling of strengthened masonry structures in which the introduction of new types of reinforcement, particularly the FRP (fibre-reinforced plastic) materials, strongly affects the structural response through complex interaction mechanisms between masonry and strengthening elements. In this paper two different approaches able to model the behaviour of un-reinforced and reinforced masonry structures are proposed. The first one is based on a micro-mechanical and multiscale analysis combined with the use of the kinematic and static theorems of the limit analysis; in this case a rigid-perfectly plastic constitutive relationship is considered for the masonry material and for the FRP-masonry interaction. The second approach is based on the use of macroscopic models. In this case, the constitutive relationship for the masonry material accounts for the softening effect throughout the use of a smeared crack approach. Moreover, different modelling strategies and constitutive laws are adopted for the FRP-reinforcement addressing particular regard to the delamination phenomenon. Numerical computations are developed for un-strengthened and FRP-strengthened masonry panels. The obtained results, in terms of the global response of the examined panels, are compared with the data available from experimental tests and interesting aspects are remarked.

This paper presents the numerical results obtained from the finite element analyses of the superplastic forming (SPF) of Al–Ti alloys. The models are used to optimise the process and predict forming times in terms of deformed shapes, stress–strain distributions and ...

The present article is concerned with the response of structural concrete prisms to high rates of uniaxial tensile loading. The numerical investigation carried out is based on a finite-element (FE) program capable of carrying out three-dimensional (3D) nonlinear static and dynamic analyses. This program is known to yield realistic predictions to the response of a wide range of plain-and reinforced-concrete structural forms subjected to arbitrary static and earthquake actions. Furthermore, its application has recently been successfully extended in predicting the response of plain-concrete prism elements under high rates of uniaxial compressive loading. The main feature of the FE program is that it incorporates a 3D material model which is characterized by both its simplicity and its attention to the actual physical behaviour of concrete in a structure. Its analytical formulation is based on the assumption that the material properties of concrete are independent of the applied loading rate (strain rate) thus attributing the effect of the applied loading rate on the prism's response to inertia. The validation of this assumption is based on a comparative study between numerical and experimental data which reveals good agreement. This constitutes a major departure from current thinking as regards material modelling of concrete under highrate loading. In addition, the available data (numerical and experimental) show that the response of the concrete prism elements depends on a number of parameters linked to geometry and material properties of the structural forms under investigation as well as the testing method adopted. This dependence explains, to a significant extent, the scatter that characterizes the available experimental data, and it also suggests that both experimental and numerical results describe structural rather than material behaviour thus raising questions regarding the validity of the use of such data in the constitutive modelling of concrete-material behaviour under high-rate loading conditions. r

The present article is concerned with the response of structural concrete prisms to high rates of uniaxial tensile loading. The numerical investigation carried out is based on a finite-element (FE) program capable of carrying out three-dimensional (3D) nonlinear static and dynamic analyses. This program is known to yield realistic predictions to the response of a wide range of plain-and reinforced-concrete structural forms subjected to arbitrary static and earthquake actions. Furthermore, its application has recently been successfully extended in predicting the response of plain-concrete prism elements under high rates of uniaxial compressive loading. The main feature of the FE program is that it incorporates a 3D material model which is characterized by both its simplicity and its attention to the actual physical behaviour of concrete in a structure. Its analytical formulation is based on the assumption that the material properties of concrete are independent of the applied loading rate (strain rate) thus attributing the effect of the applied loading rate on the prism's response to inertia. The validation of this assumption is based on a comparative study between numerical and experimental data which reveals good agreement. This constitutes a major departure from current thinking as regards material modelling of concrete under highrate loading. In addition, the available data (numerical and experimental) show that the response of the concrete prism elements depends on a number of parameters linked to geometry and material properties of the structural forms under investigation as well as the testing method adopted. This dependence explains, to a significant extent, the scatter that characterizes the available experimental data, and it also suggests that both experimental and numerical results describe structural rather than material behaviour thus raising questions regarding the validity of the use of such data in the constitutive modelling of concrete-material behaviour under high-rate loading conditions. r

The present article is concerned with the response of structural concrete prisms to high rates of uniaxial tensile loading. The numerical investigation carried out is based on a finite-element (FE) program capable of carrying out three-dimensional (3D) nonlinear static and dynamic analyses. This program is known to yield realistic predictions to the response of a wide range of plain-and reinforced-concrete structural forms subjected to arbitrary static and earthquake actions. Furthermore, its application has recently been successfully extended in predicting the response of plain-concrete prism elements under high rates of uniaxial compressive loading. The main feature of the FE program is that it incorporates a 3D material model which is characterized by both its simplicity and its attention to the actual physical behaviour of concrete in a structure. Its analytical formulation is based on the assumption that the material properties of concrete are independent of the applied loading rate (strain rate) thus attributing the effect of the applied loading rate on the prism's response to inertia. The validation of this assumption is based on a comparative study between numerical and experimental data which reveals good agreement. This constitutes a major departure from current thinking as regards material modelling of concrete under highrate loading. In addition, the available data (numerical and experimental) show that the response of the concrete prism elements depends on a number of parameters linked to geometry and material properties of the structural forms under investigation as well as the testing method adopted. This dependence explains, to a significant extent, the scatter that characterizes the available experimental data, and it also suggests that both experimental and numerical results describe structural rather than material behaviour thus raising questions regarding the validity of the use of such data in the constitutive modelling of concrete-material behaviour under high-rate loading conditions. r

Modelling the mechanical behaviour of unsaturated soils has been the subject of many research works in the past few decades. A number of constitutive models have been developed to describe the complex behaviour of unsaturated soils. Despite the significant advances in the constitutive theories for unsaturated soils, none of the existing models can completely describe the various aspects of the real behaviour of unsaturated soils. In this paper, a new unified approach is presented, based on the integration of a neural network and a genetic algorithm, for the modelling of unsaturated soils. In the proposed approach, a genetic algorithm was used to optimise the weights of the neural network. A three-layer sequential architecture was chosen for the neural network. The network had eight input neurons, five neurons in the hidden layer and three neurons in the output layer. The eight input neurons represented the initial gravimetric water content, initial dry density, degree of saturation, net mean stress with respect to pore-air pressure, axial strain, deviatoric stress, soil suction and volumetric strain, and the three neurons in the output layer represented the deviatoric stress, suction and volumetric strain at the end of each increment. The network was trained and tested using a database that included results from a comprehensive set of triaxial tests on unsaturated soils from the literature. The predictions of the proposed model were compared with the experimental results. The comparison of the results indicates that the proposed approach was accurate and robust in representing the mechanical behaviour of unsaturated soils.

The constitutive model presented in this work is built on a conceptual approach for unsaturated expansive soils in which the fundamental characteristic is the explicit consideration of two pore levels. The distinction between the macro-and microstructure provides the opportunity to take into account the dominant phenomena that affect the behaviour of each structural level and the main interactions between them. The microstructure is associated with the active clay minerals, while the macrostructure accounts for the largerscale structure of the material. The model has been formulated considering concepts of classical and generalized plasticity theories. The generalized stress-strain rate equations are derived within a framework of multidissipative materials, which provides a consistent and formal approach when there are several sources of energy dissipation. The model is formulated in the space of stresses, suction and temperature; and has been implemented in a finite element code. The approach has been applied to explaining and reproducing the behaviour of expansive soils in a variety of problems for which experimental data are available. Three application cases are presented in this paper. Of particular interest is the modelling of an accidental overheating, that took place in a large-scale heating test. This test allows the capabilities of the model to be checked when a complex thermo-hydro-mechanical (THM) path is followed. 29:751-787 M. SÁ NCHEZ ET AL.

The constitutive model presented in this work is built on a conceptual approach for unsaturated expansive soils in which the fundamental characteristic is the explicit consideration of two pore levels. The distinction between the macro-and microstructure provides the opportunity to take into account the dominant phenomena that affect the behaviour of each structural level and the main interactions between them. The microstructure is associated with the active clay minerals, while the macrostructure accounts for the largerscale structure of the material. The model has been formulated considering concepts of classical and generalized plasticity theories. The generalized stress-strain rate equations are derived within a framework of multidissipative materials, which provides a consistent and formal approach when there are several sources of energy dissipation. The model is formulated in the space of stresses, suction and temperature; and has been implemented in a finite element code. The approach has been applied to explaining and reproducing the behaviour of expansive soils in a variety of problems for which experimental data are available. Three application cases are presented in this paper. Of particular interest is the modelling of an accidental overheating, that took place in a large-scale heating test. This test allows the capabilities of the model to be checked when a complex thermo-hydro-mechanical (THM) path is followed. 29:751-787 M. SÁ NCHEZ ET AL.

Spark plasma sintering has been applied to the production of aluminium-based functionally graded material systems to be used in abrasive and high temperature conditions. The overall mechanical properties of these metal matrix composites were determined during the optimization phases of the production process by a fast and reliable identification procedure based on instrumented indentation, which can be easily performed on small specimens. The experimental information gathered from conical (Rockwell) indentation was used as input data for the calibration of the material parameters entering the elastic-plastic Drucker-Prager constitutive model. Eventually, the so identified material parameters were used to predict the result of pyramidal (Vickers) indentation, in order to validate the model selection and the output of the identification procedure. The good matching between modelling and experimental results for the different test configurations confirmed the soundness of the considered approach, especially evidenced on the light of the strong influence on the overall mechanical characteristics of the material microstructure and defectiveness resulting from the production process, which prevent the use of classical homogenization rules to evaluate the macroscopic material properties.

The response to mechanical loading of the thermosetting resin system RTM-6 has been investigated experimentally as a function of strain rate and a constitutive model has been applied to describe the observed and quantified material behaviour. In order to determine strain rate effects and to draw conclusions about the hydrostatic stress dependency of the material, specimens were tested in compression and tension at strain rates from 10 À3 to 10 4 s À1 . A Standard screw-driven tensile machine was used for quasi-static testing, with an 'in house' hydraulic rig and Hopkinson bars for medium and high strain rates, respectively. At all rates appropriate photography and optical metrology have been used for direct strain measurement, observation of failure and validation of experimental procedures. In order to enable the experimental characterisation of this brittle material at very high rates in tension, a novel pulse shaping technique has been applied. With the help of this device, strain rates of up to 3800 s À1 have been achieved while maintaining homogeneous deformation state until specimen fracture in the gauge section of the tensile specimens. The yield stress and initial modulus increased with increasing strain rate for both compression and tension, while the strain to failure decreased with strain rate in tension. An existing constitutive model, the Goldberg model has been extended in order to take into account the nonlinear strain rate dependence of the elastic modulus. The model has been validated against 3-point impact bending tests of prismatic RTM-6 beams.

Biomechanical data and related constitutive modelling of the mitral apparatus served as a basis for finite element analyses to better understand the physiology of mitral valves in health and disease. Human anterior and posterior leaflets and chordae tendinae from an elderly heart showing no disease and a hypertrophic obstructive cardiomyopathic heart (HOCM) were mechanically tested by means of uniaxial cyclic extension tests under quasistatic conditions. Experimental data for the leaflets and the chordae tendinae showed highly nonlinear mechanical behaviours and the leaflets were anisotropic. The mitral valve from the HOCM heart exhibited a significantly softer behaviour than the valve from the healthy one. A comparison with porcine data was included because many previous mitral modelling studies have been based on porcine data. Some differences in mechanical response were observed. Material parameters for hyperelastic, transversely isotropic constitutive laws were determined. The experimental data and the related model parameters were used in two finite element studies to investigate the effects of the material properties on the mitral valve response during systole. The analyses showed that during systole the mitral valve from the HOCM heart bulged into the left atrium by taking on the shape of a balloon, whereas the anterior leaflet of the healthy valve remained in the left ventricle. .no (B. Skallerud). by Krishnamurthy et al. (2008) has shown that an estimation of the in vivo material properties of ovine mitral leaflets is feasible. However, in vivo stress measurements are not possible. Therefore, numerical techniques such as the finite element method are valuable tools to estimate the local stress-stretch distribution in the mitral valve. Previously, finite element simulations of the mitral apparatus have been conducted with different types of constitutive models for 1751-6161/$ -see front matter c

This work concerns the micromechanical constitutive modelling, algorithmic implementation and numerical simulation of polycrystalline superelastic alloys under multiaxial loading. The model is formulated in finite deformations and incorporates the effect of texture. The numerical implementation is based on the constrained minimization of the Helmholtz free energy with dissipation. Simulations are conducted for thin tubes of Nitinol under tension-torsion, as well as for a simplified model of a biomedical stent.

Purpose-The purpose of this paper is to describe a general theoretical and finite element implementation framework for the constitutive modelling of biological soft tissues. Design/methodology/approach-The model is based on continuum fibers reinforced composites in finite strains. As an extension of the isotropic hyperelasticity, it is assumed that the strain energy function is decomposed into a fully isotropic component and an anisotropic component. Closed form expressions of the stress tensor and elasticity tensor are first established in the general case of fully incompressible plane stress which orthotropic and transversely isotropic hyperelasticity. The incompressibility is satisfied exactly. Findings-Numerical examples are presented to illustrate the model's performance. Originality/value-The paper presents a constitutive model for incompressible plane stress transversely isotropic and orthotropic hyperelastic materials.

Recently, several flexible constitutive equations have been proposed for sheet forming simulations. However, various mechanical tests are required to determine the material parameters needed for such models. In the present work, effort has been made to investigate the correlation between the polycrystal plasticity based yield loci and those determined from mechanical tests, in order to define yield functions easily and accurately with minimum experimental work. The results for different materials indicate that, in many cases, the Hill'48 quadratic yield function conventionally fitted with the plastic anisotropy R-values deviates significantly from measured yield loci. The Hill'48 yield function fitted with the uniaxial and biaxial yield stresses is quite close to the measured one, but with large deviation in the strain ratios for strong anisotropic materials. A careful comparison of the measured yield loci and those calculated from the Taylor full constraint model and the relaxed model indicates that the yield loci derived from the Taylor full constraint model capture the shape of the measured ones in general, but they are less elongated in the stretching direction, and the stretching factor is usually smaller than that derived from the relaxed Taylor model. The measured biaxial points are between those calculated from the two Taylor models. Based on the two yield loci derived from the Taylor models, a new combined model referred to as CTFP is proposed. The new model retains roughly the shape of the yield loci derived from the Taylor full constraint model, but the size is scaled using the averaged biaxial points of each model in the stretching regime. The proposed new description has been validated using several forming steel grades. This model can be used as virtual experiment for complicated mechanical tests, such as the plane strain tension, balanced biaxial stretching and shear test. The stress and strain data from the virtual experiments, together with the stress and plastic anisotropy measured in the uniaxial tensile test, are easily deployed as input data for other constitutive equations used in sheet metal forming simulations. Forming limit diagrams were predicted using different material constitutive models. The difference between the measured FLD and the calculated ones is remarkable. A profound analysis of the phenomena and a systematic study of intrinsic material parameters on the FLDs is needed.

Federico II (Italy) to investigate the effects of partial saturation on the volumetric behaviour and the initial shear stiffness of a compacted silt. Tests were performed by using suction-controlled triaxial and resonant column cells. Herein, the compatibility of the results with a Single Stress Model (SSM) is discussed. The SSM allows to highlight that suction can have two effects on the mechanical behaviour of an unsaturated soil: it increases the average volumetric stress acting on the soil skeleton and it has a sort of cementing effect on the soil packing (hardening and cementation).

A new seismic design philosophy is illuminated, taking advantage of soil "failure" to protect the superstructure. Instead of over-designing the foundation to ensure that the loading stemming from the structural inertia can be "safely" transmitted onto the soil (as with conventional capacity design), and then reinforce the superstructure to avoid collapse, why not do exactly the opposite by intentionally under-designing the foundation to act as a "safety valve" ? The need for this "reversal" stems from the uncertainty in predicting the actual earthquake motion, and the necessity of developing new more rational and economically efficient earthquake protection solutions. A simple but realistic bridge structure is used as an example to illustrate the effectiveness of the new approach. Two alternatives are compared : one complying with conventional capacity design, with over-designed foundation so that plastic "hinging" develops in the superstructure; the other following the new design philosophy, with under-designed foundation, "inviting" the plastic "hinge" into the soil. Static "pushover" analyses reveal that the ductility capacity of the new design concept is an order of magnitude larger than of the conventional design: the advantage of "utilising" progressive soil failure. The seismic performance of the two alternatives is investigated through nonlinear dynamic time history analyses, using an ensemble of 29 real accelerograms. It is shown that the performance of both alternatives is totally acceptable for moderate intensity earthquakes, not exceeding the design limits. For large intensity earthquakes, exceeding the design limits, the performance of the new design scheme is proven advantageous, not only avoiding collapse but hardly suffering any inelastic structural deformation. It may however experience increased residual settlement and rotation: a price to pay that must be properly assessed in design.

Tests on specimens of reconstituted illitic clay have examined the influence of temperature on the mechanical behaviour of clay soils. The program involved consolidation to effective confining pressures up to 1.5 MPa, heating to lOO"C, and tests on normally consolidated and overconsolidated specimens with OCR=2. The tests included isotropic consolidation, undrained triaxial compression with pore water pressure measurement, drained tests along controlled stress paths to investigate yielding behaviour, and undrained tests which involved heating and measurement of the resulting induced pore water pressures. The large strain strength envelope is independent of temperature. However, peak undrained strengths increase with temperature because smaller pore water pressures are generated during shearing. An important contribution from the study is a series of results for the yielding of illitic clay at three different temperatures. For the first time, there is clear evidence of yield loci decreasing in size with increasing temperature. An associated flow rule can be assumed without serious error. The results contribute to the confirmation of a thermal elastic-plastic soil model developed by the authors from cam clay following the addition of a small number of extra assumptions. Depending on the initial stress state, heating under undrained conditions may produce shear failure. #Q 1997 Elsevier Science B.V.

The present article is concerned with the response of structural concrete prisms to high rates of uniaxial tensile loading. The numerical investigation carried out is based on a finite-element (FE) program capable of carrying out three-dimensional (3D) nonlinear static and dynamic analyses. This program is known to yield realistic predictions to the response of a wide range of plain-and reinforced-concrete structural forms subjected to arbitrary static and earthquake actions. Furthermore, its application has recently been successfully extended in predicting the response of plain-concrete prism elements under high rates of uniaxial compressive loading. The main feature of the FE program is that it incorporates a 3D material model which is characterized by both its simplicity and its attention to the actual physical behaviour of concrete in a structure. Its analytical formulation is based on the assumption that the material properties of concrete are independent of the applied loading rate (strain rate) thus attributing the effect of the applied loading rate on the prism's response to inertia. The validation of this assumption is based on a comparative study between numerical and experimental data which reveals good agreement. This constitutes a major departure from current thinking as regards material modelling of concrete under highrate loading. In addition, the available data (numerical and experimental) show that the response of the concrete prism elements depends on a number of parameters linked to geometry and material properties of the structural forms under investigation as well as the testing method adopted. This dependence explains, to a significant extent, the scatter that characterizes the available experimental data, and it also suggests that both experimental and numerical results describe structural rather than material behaviour thus raising questions regarding the validity of the use of such data in the constitutive modelling of concrete-material behaviour under high-rate loading conditions. r

The present article is concerned with the response of structural concrete prisms to high rates of uniaxial tensile loading. The numerical investigation carried out is based on a finite-element (FE) program capable of carrying out three-dimensional (3D) nonlinear static and dynamic analyses. This program is known to yield realistic predictions to the response of a wide range of plain-and reinforced-concrete structural forms subjected to arbitrary static and earthquake actions. Furthermore, its application has recently been successfully extended in predicting the response of plain-concrete prism elements under high rates of uniaxial compressive loading. The main feature of the FE program is that it incorporates a 3D material model which is characterized by both its simplicity and its attention to the actual physical behaviour of concrete in a structure. Its analytical formulation is based on the assumption that the material properties of concrete are independent of the applied loading rate (strain rate) thus attributing the effect of the applied loading rate on the prism's response to inertia. The validation of this assumption is based on a comparative study between numerical and experimental data which reveals good agreement. This constitutes a major departure from current thinking as regards material modelling of concrete under highrate loading. In addition, the available data (numerical and experimental) show that the response of the concrete prism elements depends on a number of parameters linked to geometry and material properties of the structural forms under investigation as well as the testing method adopted. This dependence explains, to a significant extent, the scatter that characterizes the available experimental data, and it also suggests that both experimental and numerical results describe structural rather than material behaviour thus raising questions regarding the validity of the use of such data in the constitutive modelling of concrete-material behaviour under high-rate loading conditions. r

Finite element (FE)-simulations are a useful tool to evaluate the thermo-mechanical behavior of electronic packages. However, the use of the FE-method generates special difficulties, in particular concerning the proper constitutive modeling of materials used in the assembly. One more general problem in the numerical investigations of encapsulated silicon chips is the occurrence of interfaces between the dissimilar materials. Due to the assumption of sharp interface edges and interface crack tips stress singularities arise which might be accounted for only approximately in the FE-calculation.

There is a scarcity of investigation into the mechanical properties of subdermal fat. Recently, progress has been made in the determination of subdermal stress and strain distributions. This requires accurate constitutive modelling and consideration of the subdermal tissues. This paper reports the results of a study to estimate non-linear elastic and viscoelastic properties of porcine subdermal fat using a simple constitutive model. High-resolution magnetic resonance imaging (MRI) was used to acquire a time series of coincident images during a confined indentation experiment. Inverse finite element analysis was used to estimate the material parameters. The Neo Hookean model was used to represent the elastic behaviour (μ = 0.53 ± 0.31 kPa), while a single-element Prony series was used to model the viscoelastic response (α = 0.39 ± 0.03, τ = 700 ± 255 s).

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.

The aim of this paper is the development of suitable mechanical models able to reproduce and, hence, to predict the response of masonry structures. In particular, the study is addressed to the modelling of strengthened masonry structures in which the introduction of new types of reinforcement, particularly the FRP (fibre-reinforced plastic) materials, strongly affects the structural response through complex interaction mechanisms between masonry and strengthening elements.

This work concerns the micromechanical constitutive modelling, algorithmic implementation and numerical simulation of polycrystalline superelastic alloys under multiaxial loading. The model is formulated in finite deformations and incorporates the effect of texture. The numerical implementation is based on the constrained minimization of the Helmholtz free energy with dissipation. Simulations are conducted for thin tubes of Nitinol under tension-torsion, as well as for a simplified model of a biomedical stent.

In a recent article [P.D. Patil, J.J. Feng, S.G. Hatzikiriakos, Constitutive modelling and flow simulation of polytetrafluoroethylene paste extrusion, J. Non-Newtonian Fluid Mech. 139 (2006), 44-53], a rheological constitutive equation was proposed to model the incompressible flow of poly-tetra-fluoro-ethylene (PTFE) paste and its structural development (fibrillation between the PTFE particles) during flow. The constitutive model was a combination of shear-thinning and shear-thickening viscosity terms, depending on a structural parameter, , which obeyed a convective-transport equation. In the latter, a non-objective flow type parameter, , was employed, which depended on the magnitudes of the rate-of-strain and vorticity tensors. In the present work, an objective flow type parameter is used instead [R.G. Larson, Flows of constant stretch history for polymeric materials with power-law distributions of relaxation times, Rheol. Acta 24 (1985), 443-449]. Despite its complexity and the severe slip at the wall, good convergence has been obtained even for very high apparent shear rates. New results are shown as contours of the -parameter in the flow field as well as contours of the new objective flow type parameter, *, and compared with previous results. It is shown that the corrected model predicts higher structural levels (more fibrils) in PTFE paste flow through extrusion dies and that the new results are more consistent with experimental observations. to study in detail the effect of compressibility on the structure formation and flow kinematics of paste. These results offered a better understanding of the flow behaviour of PTFE in flow through extrusion dies. A problem with the previous models [1,2] arises from using a non-objective flow type parameter, , that represents the strength of the flow. This measure of flow type was originally introduced by Giesekus [3] and later used by Fuller and Leal for homogeneous flows . It is given by

a b s t r a c t In a recent article [P.D. Patil, J.J. Feng, S.G. Hatzikiriakos, Constitutive modelling and flow simulation of polytetrafluoroethylene paste extrusion, J. Non-Newtonian Fluid Mech., 139 (2006) 44-53], a rheological constitutive equation was proposed to model the flow of polytetrafluoroethylene (PTFE) paste. Steadystate flow simulations were carried out, governed by the conservation equations of mass and momentum under isothermal, incompressible conditions, and taking into account a linear slip law at the wall due to the presence of lubricant in the paste. The constitutive model was a combination of shear-thinning and shearthickening viscosity terms, depending on a structural parameter, , which obeyed a convective-transport equation.

The suitability of the internal friction models by Reid [Free vibration and hysteretic damping, Journal of the Royal Aeronautical Society 69 (1956) 283] and Muravskii [On frequency independent damping, Journal of Sound and Vibration 274 (2004) 653-668] for modelling hysteretic damping is investigated. Time-domain dynamical simulations of Reid's model reveal the presence of artefacts, which cause significant errors and solution stiffness in sub-resonant conditions.

This paper presents the results of finite element simulations made on a bent pipe subjected to an in-plane variable cyclic displacement combined with internal pressure. Special emphasis is put on the capacity of the model to illustrate different failure modes depending on the internal pressure applied on the pipe. The results of the numerical analyses will be compared to experimental ones. The constitutive model used for the simulation of Ultra Low Cycle Fatigue (ULCF) loading and the hardening-softening law used are only briefly touched upon. The monotonic behavior of a large diameter pipe, as obtained from the constitutive model proposed, is also shown and compared to experimental results under two different loading conditions. The total axial load at failure for this case resulted in less than 10% error as compared to the experiments. Regarding the ULCF in-plane bending simulations conducted on a 16-inch 90° elbow, the results were in good agreement with the experimental test in terms of force-displacement hysteresis loops and total fatigue life of the specimen. An analysis of the dependence of the failure mode to the internal pressure applied has been conducted, showing that the formulation is capable of obtaining both habitual failure types.

Interventions in historic brick buildings require an exhaustive analysis of the current characteristics of bricks in order to establish the role performed by these elements in the buildings. This study presents the results of an experimental analysis of the compressive strength of brick specimens extracted from different buildings built in the 19th and 20th centuries in the province of Zamora (Spain). The study analyses specimens with very different characteristics to compare results from different masonry units and manufacturing processes. Specimens are classified into four groups according to their macroscopic and microscopic analyses. Compressive strength results are correlated to the above classification and to the results of density, absorption and open porosity of the samples. The compressive strength results present high variation between clay bricks (9.2–64.4 N/mm2) and between samples extracted from the same brick due to the heterogeneity of the material. Correlations betwe...

Application of a micro-mechanics cell model to dentin composites for determination of their effective mechanical properties is discussed in this paper. The dilute micro-mechanics model for fibre-reinforced composites is utilized and the corresponding cell model is chosen to consist of a circular hollow cylinder filled with liquid or gas phase, which is surrounded by two circular cylindrical shells, a thin shell and a matrix phase. Each layer of cylindrical shell is here considered as a composite consisting of collagen fibrils, with mineralized hydroxyapatite, loosely connected to their neighbours, and water (or gas in the case of dry dentin composite). Determination of the effective material properties of such a three phase composite is discussed. Using the cell model the effect of porosity, thickness of each cylindrical shell, and mineral content on material properties is analysed. Results obtained from nanoindentation observations are compared with numerical predictions of the analytical model.

The results of a simple geotechnical benchmark problem, an embankment on soft clay, are presented and discussed. The problem has been simulated with several constitutive models: models that are commonly used for practical geotechnical engineering problems, as well as advanced models developed by SCMEP Network partners. These advanced constitutive models account for initial and induced anisotropy, destructuration and creep or combinations of these features. The comparisons highlight the effects of these features on soft clay response and demonstrate the differences between alternative constitutive modelling approaches.

Fracture is the main reason for the non-linear behaviour of hard rocks. The fracture mechanics of rock is studied in this article by analysis of the fracture process under compression. A constitutive model that describes the relationship between the macro deformation of rock and the micro fracture within rock is developed. The propagation of microcracks, the non-linearity of deformation, the loading-and-unloading hysteresis and the variation of the apparent Young's modulus and Poisson's ratio are studied using the developed model. The model simulations demonstrate that: (1) the fracture toughness, initial crack length, crack density, and Young's modulus are four crucially important parameters that affect the deformation behaviour of rock; (2) the elastic parameters (E and v) of the rock matrix should be measured in triaxial tests. If they are measured in uniaxial tests, the upper straight unloading portion of the stress-strain curve is suggested to be used for the purpose, unless the closure effect of open cracks will be included in the estimations. In addition (3), the slope of the reloading stress-strain curve is a measure of the damage in material.

Creep tests are carried out under tension, pure torsion, and combined tension and torsion at an elevated temperature of 523K for pure copper and 423K for an aluminium alloy. Different creep and rupture properties of the materials are observed throughout the deformation process under the different stress states. The effects of stress states on primary creep, secondary creep, the failure

In the present study we consider an adaptation of Nguyen’s model [G.D. Nguyen, A thermodynamic approach to constitutive modelling of concrete using damage mechanics and plasticity theory, D.Phil. Thesis, Dept. of Engng. Sci., University of Oxford, 2005] for brittle materials to the case of ductile rupture. We focus our attention on the formulation of a consistent tangent stiffness matrix which is essential for the efficiency and convergence of the implementation within a finite element framework. We demonstrate the capability of the model to generate mesh-independent results and to follow the rupture process very close to failure. Rupture analysis of thin plates of different geometry is presented (symmetric double notch-edged specimen, asymmetric double notch-edged specimen, double notch-edged specimen containing a hole). Further modifications are outlined required to simulate crack growth and paths under the conditions of creep and fatigue.

Recently, several flexible constitutive equations have been proposed for sheet forming simulations. However, various mechanical tests are required to determine the material parameters needed for such models. In the present work, effort has been made to investigate the correlation between the polycrystal plasticity based yield loci and those determined from mechanical tests, in order to define yield functions easily and accurately with minimum experimental work. The results for different materials indicate that, in many cases, the Hill'48 quadratic yield function conventionally fitted with the plastic anisotropy R-values deviates significantly from measured yield loci. The Hill'48 yield function fitted with the uniaxial and biaxial yield stresses is quite close to the measured one, but with large deviation in the strain ratios for strong anisotropic materials. A careful comparison of the measured yield loci and those calculated from the Taylor full constraint model and the relaxed model indicates that the yield loci derived from the Taylor full constraint model capture the shape of the measured ones in general, but they are less elongated in the stretching direction, and the stretching factor is usually smaller than that derived from the relaxed Taylor model. The measured biaxial points are between those calculated from the two Taylor models. Based on the two yield loci derived from the Taylor models, a new combined model referred to as CTFP is proposed. The new model retains roughly the shape of the yield loci derived from the Taylor full constraint model, but the size is scaled using the averaged biaxial points of each model in the stretching regime. The proposed new description has been validated using several forming steel grades. This model can be used as virtual experiment for complicated mechanical tests, such as the plane strain tension, balanced biaxial stretching and shear test. The stress and strain data from the virtual experiments, together with the stress and plastic anisotropy measured in the uniaxial tensile test, are easily deployed as input data for other constitutive equations used in sheet metal forming simulations. Forming limit diagrams were predicted using different material constitutive models. The difference between the measured FLD and the calculated ones is remarkable. A profound analysis of the phenomena and a systematic study of intrinsic material parameters on the FLDs is needed.

Experimental results of in vivo measurements to characterize the mechanical behaviour of human uterine cervices are documented. Aspiration experiments were performed on eight uteri in vivo, before vaginal/abdominal hysterectomy, and four uteri were also tested ex vivo, approximately 1.5h after extraction. The reproducibility of the mechanical data from the in vivo aspiration experiments has been analysed. For an introduced "stiffness parameter" the organ specific SD is 22%, so that the proposed experimental procedure allows detections of 30% changes with respect to a reference value of the stiffness parameter. A comparison of in vivo and ex vivo data from the same organ has shown that: (i) the ex vivo mechanical response of the uterine cervix tissue does not differ considerably from that observed in vivo; (ii) some differences can be identified in tissue pre-conditioning with ex vivo showing a stronger history dependence with respect to in vivo; (iii) the differences in the time dependence of the mechanical response are not significant and might be masked by the variability of the measured data. This study represents a first step of a clinical application aiming at analysing the mechanical response of normal cervical tissue at different gestational ages, and identifying the mechanical properties that characterize pathologic conditions such as cervical insufficiency leading to preterm delivery.

In the present study we consider an adaptation of Nguyen’s model [G.D. Nguyen, A thermodynamic approach to constitutive modelling of concrete using damage mechanics and plasticity theory, D.Phil. Thesis, Dept. of Engng. Sci., University of Oxford, 2005] for brittle materials to the case of ductile rupture. We focus our attention on the formulation of a consistent tangent stiffness matrix which is essential for the efficiency and convergence of the implementation within a finite element framework. We demonstrate the capability of the model to generate mesh-independent results and to follow the rupture process very close to failure. Rupture analysis of thin plates of different geometry is presented (symmetric double notch-edged specimen, asymmetric double notch-edged specimen, double notch-edged specimen containing a hole). Further modifications are outlined required to simulate crack growth and paths under the conditions of creep and fatigue.

The response to mechanical loading of the thermosetting resin system RTM-6 has been investigated experimentally as a function of strain rate and a constitutive model has been applied to describe the observed and quantified material behaviour. In order to determine strain rate effects and to draw conclusions about the hydrostatic stress dependency of the material, specimens were tested in compression and tension at strain rates from 10−3 to 104 s−1. A Standard screw-driven tensile machine was used for quasi-static testing, with an ‘in house’ hydraulic rig and Hopkinson bars for medium and high strain rates, respectively. At all rates appropriate photography and optical metrology have been used for direct strain measurement, observation of failure and validation of experimental procedures. In order to enable the experimental characterisation of this brittle material at very high rates in tension, a novel pulse shaping technique has been applied. With the help of this device, strain rates of up to 3800 s−1 have been achieved while maintaining homogeneous deformation state until specimen fracture in the gauge section of the tensile specimens. The yield stress and initial modulus increased with increasing strain rate for both compression and tension, while the strain to failure decreased with strain rate in tension. An existing constitutive model, the Goldberg model has been extended in order to take into account the nonlinear strain rate dependence of the elastic modulus. The model has been validated against 3-point impact bending tests of prismatic RTM-6 beams.