Constitutive Equation

Ductile fracture prediction is often considered as a challenging task in complex stress state applications, such as metal joining process. A systematic method for predicting the joint strength in the hot shear joining process is presented in this paper by considering two different ductile damage models, namely Johnson-Cook and modified Lemaitre damage models. Since the crack formation in metalworking is considered to be a combination of both load conditions and metallurgical properties, the microstructure evolution is taken into account by characterizing the considered material, AISI-1045, at different temperatures and for different strain rates and by testing different specimen shapes, namely round bar, joint bar, flat and notched specimens. The derived material properties have been inversely calibrated in order to be used in the developed numerical model. A shear joining process simulation has been implemented in DEFORM and have been validate with shear joining experiments carried out at 950°C, allowing to validate the accuracy of the proposed model in simulating the hot shear joining, both in terms of joining strength and identification of the damage locations. Thanks to a precise material characterization, and by utilizing the proposed numerical model, both the joining tool design and the process condition can be studied and improved.

In this work, we developed a bond-based cohesive peridynamics model (CPDM) and apply it to simulate inelastic fracture by using the meso-scale Xu-Needleman cohesive potential . By doing so, we have successfully developed a bond-based cohesive continuum mechanics model with intrinsic stress/strain measures as well as consistent and built-in macro-scale constitutive relations. The main novelties of this work are: (1) We have shown that the cohesive stress of the proposed nonlocal cohesive continuum mechanics model is exactly the same as the nonlocal peridynamic stress; (2) For the first time, we have applied an irreversible built-in cohesive stress-strain relation in a bond-based cohesive peridynamics to model inelastic material behaviors without prescribing phenomenological plasticity stress-strain relations; (3) The cohesive bond force possesses both axial and tangential components, and they contribute a nonlinear constitutive relation with variable Poisson's ratios; (4) The bond-based cohesive constitutive model is consistent with the cohesive fracture criterion, and (5) We have shown that the proposed method is able to model inelastic fracture and simulate ductile fracture of small scale yielding in the nonlocal cohesive continua. Several numerical examples have been presented to be compared with the finite element based continuum cohesive zone model, which shows that the proposed approach is a simple, efficient and effective method to model inelastic fracture in the nonlocal cohesive media.

Thermomechanical fatigue loadings (TMF) applied on components in a certain temperature range with a variable state of stress (tensile and/or compression) produce a localized concentration of plastic strains that results in crack initiation and propagation. The time evolution of plastic strains must be known a priori to predict the lifetime of a part submitted to TMF loadings, which requires an extensive campaign of mechanical characterization conducted at different temperatures and aging conditions. Such a campaign was proposed for the aluminum alloy AlSi7Cu3.5Mg0.15 (Mn, Zr, V), which is recognized as being creep resistant. Combined isothermal low-cycle fatigue and isothermal creep tests were performed on this alloy to determine the constitutive parameters based on the Lemaître and Chaboche (LM&C) viscoplastic model. These laws were implemented within the finite element simulation software (Z-set) to model the response of the alloy to a thermomechanical fatigue test. The results of TMF Z-Set simulations, using the LM&C model adapted for two aging conditions, were then compared with results obtained from "Out of Phase" thermomechanical fatigue testings (OP-TMF) performed on a Gleeble 3800 machine. The modelling of the OP-TMF test revealed the complexity of the mechanical behavior of the material induced by the temperature gradient prevailing along with the cylindrical specimen. It was found that a better prediction of the evolution of plastic strains requires taking into account a larger range of plastic strain rates conditions for the determination of the constitutive law and eventually includes the role of the microstructure in the evolution of the material behavior, starting first with the yield stress.

Recent environmental restrictions constrained car manufacturers to promote cast aluminum alloys working at high temperatures (180 • C-300 • C). The development of new alloys permits the fabrication of higher-strength components in engine downsizing. Those technologies increase internal loadings and specific power and stretch current materials to their limits. Transition metals in aluminum alloys are good candidates to improve physical, mechanical, and thermodynamic properties with the aim of increasing service life of parts. This study is focused on the modified AlSi7Cu3.5Mg0.15 alloy where Mn, Zr, and V have been added as alloying elements for high-temperature applications. The characterization of the cast alloy in this study helps to evaluate and understand its performance according to their physical state: As-cast, as-quenched, or artificially aged. The precipitation kinetics of the AlSi7Cu3.5Mg0.15 (Mn, Zr, V) alloy has been characterized by differential scanning calorimetry (DSC), transmission electron microscopy (TEM) observations, and micro-hardness testing. The Kissinger analysis was applied to extract activation energies from non-isothermal DSC runs conducted at different stationary heating rates. Finally, first-order evaluations of the interfacial mobility of precipitates were obtained.

Thermomechanical fatigue loadings (TMF) applied on components in a certain temperature range with a variable state of stress (tensile and/or compression) produce a localized concentration of plastic strains that results in crack initiation and propagation. The time evolution of plastic strains must be known a priori to predict the lifetime of a part submitted to TMF loadings, which requires an extensive campaign of mechanical characterization conducted at different temperatures and aging conditions. Such a campaign was proposed for the aluminum alloy AlSi7Cu3.5Mg0.15 (Mn, Zr, V), which is recognized as being creep resistant. Combined isothermal low-cycle fatigue and isothermal creep tests were performed on this alloy to determine the constitutive parameters based on the Lemaître and Chaboche (LM&C) viscoplastic model. These laws were implemented within the finite element simulation software (Z-set) to model the response of the alloy to a thermomechanical fatigue test. The results of...

The coolant channel of Indian Pressurized Heavy Water Reactor (PHWR)[1] is having two concentric tubes, the Pressure Tube (PT) and Calandria Tube (CT). There are four spacer rings known as Garter spring between these two tubes. At operating conditions, the PT is at high temperature of around 300°C while the CT is at a low temperature of around 50°C. Heavy water flows in pressure tube at high pressure and it takes away the heat generated due to fission reaction in fuel bundles. Thus during operation, pressure tubes are subjected to high pressure, temperature and radiation. In these operating conditions pressure tube expands in both axial and radial direction due to creep phenomena. The tube also sags in downward direction. Thus with time, the annular space between PT and CT reduces and they may come in contact with each other. If contact condition remains for a long time it is postulated that PT may fail in brittle mode. Hence it is important to periodically measure annular gap betwe...

Visual examination is the first and most important stage in the examination of a component. It is one of the simplest methods used for the inspection of defects / discontinuities open to the surface. The flaws present on the surface are very detrimental, as surface is the part directly connected to environment. Hostile environment may introduce corrosion, erosion etc. Thus visual inspection plays a major role in assessing the condition of component. When it comes to visual inspection of components in very high radiation field, it becomes a big challenge as the area is mostly inaccessible due to high radiation and contamination. Remote inspection using commercially available camera is difficult because Charge Coupled Devices (CCD) have limited radiation life. Exposure to high radiation fields causes browning of optics and failure of camera electronics including the CCD sensors. Hence for visual inspection of components in high radiation environment we need specialized cameras. DRHR, ...

In Portugal, steel fibres are the most used for concrete reinforcement, and flooring and tunnelling are the main applications of fibre reinforced concrete (FRC). In last years the prefabrication industry is showing more interest in collaborating in FRC research projects. The research carried out in consortium by University of Minho (UM) and two private companies for the development of self-compacting steel fibre reinforced concrete (SCSFRC) is an example of this new strategy. This research has the following main tasks: conceive a rational mix design method; evaluate the most relevant material properties and the structural behaviour of laminar elements; develop numerical tools. This paper intends to show the research strategy adopted in the SCSFRC project, since it is a typical example of the methodology followed by the UM research group, the most active in Portugal, in the FRC domain.

Large diameter welded pipes are amongst the most cost effective transportation means for oil and gas. In general, one can differentiate between longitudinally (LSAW) and spirally welded (HSAW) pipes, whereby LSAW pipes are produced from plate and HSAW pipes from coil. Pipe forming involves several cold forming steps, such as (cyclic) bending and (mechanical) expansion. Obviously, the mechanical properties on pipe differ from those of the base material. Detailed understanding of how the mechanical properties evolve during pipe forming would help steel mills to target specific base material properties to ensure the final pipe strength. Therefore, an FE (Finite Element) model, capable of simulating different pipe forming processes, was developed using the commercial FE software Abaqus. Thereby, an advanced constitutive model, accounting for isotropic, kinematic and distortional hardening was implemented via a UMAT user subroutine. A reverse engineering strategy was applied to calibrate the constitutive model. The model was then used to simulate spiral pipe forming of a 28" x 16mm HSAW pipe.

In this work, a one-dimensional constitutive model is used to study rotary bending fatigue in shape memory alloy beams. The stress and strain distributions in a beam section are driven numerically for both pure bending and rotary bending to show the basic differences between these two loading types. In order to verify the numerical results, experiments are performed on NiTi specimens with an imposed bending angle using a bending apparatus. Since the specimens show significant stress plateau for forward and backward transformation in their stress–strain response, an enhanced stress–temperature phase diagram is proposed in which different slopes are considered for the start and finish of each transformation strip. In order to study low cycle fatigue of shape memory alloys during rotary bending, the stabilized dissipated energy is calculated from numerical solution. A power law for variations of the fatigue life with the stabilized dissipated energy is obtained for the studied specimen...

In this work, a one-dimensional constitutive model is used to study rotary bending fatigue in shape memory alloy beams. The stress and strain distributions in a beam section are driven numerically for both pure bending and rotary bending to show the basic differences between these two loading types. In order to verify the numerical results, experiments are performed on NiTi specimens with an imposed bending angle using a bending apparatus. Since the specimens show significant stress plateau for forward and backward transformation in their stress–strain response, an enhanced stress–temperature phase diagram is proposed in which different slopes are considered for the start and finish of each transformation strip. In order to study low cycle fatigue of shape memory alloys during rotary bending, the stabilized dissipated energy is calculated from numerical solution. A power law for variations of the fatigue life with the stabilized dissipated energy is obtained for the studied specimen...

The vast expanse of coasts in iran is affected by many faults and has a high seismic potential. Most of coastal lands consist of very loose soils with the risk of liquefaction. In the present study, the seismic behavior of the anchored sheet pile quay wall, which regardless of the risk of liquefaction, is buried in the loose liquefiable layer, has been numerically analyzed using PLAXIS software and the PM4Sand constitutive model. The soil in front of the root of the sheet pile (sea side) is the most prone area for liquefaction due to the low initial vertical effective stress level. The presence of a loose layer around the root of the sheet pile, due to the liquefaction of the soil in front of the root and the lateral pressure of the soil behind the sheet pile, leads to the rupture of the buried part. Soil-cement is one of the methods of improving loose coastal soils, which increases adhesion and reduces the liquefaction potential of saturated loose soils. Improving the soil around the root of the sheet pile on the sea side using the soil-cement method greatly reduces the proportion of excess pore water pressure, displacement and bending anchor of the sheet pile. The comparison made with the corresponding past research shows that soil-cement improvement with less time and volume of execution than the compaction method has a better performance in stabilizing anchored sheet pile quay wall affected by the loose liquifiable layer.

Incremental forming is a rather innovative process in which sheet metal is formed into complex shapes by stretching the sheet with forming tool whose path is controlled by a computer numerical control machine, this kind of process is suitable for low patch production and customized parts. The blank is fully clamped at its perimeter, so there is no any drawing operation occurs to sheet blank during forming process, therefore an excessive thinning would appear along the wall of the formed parts. Study the influence of some process parameters on the thinning ratio, find suitable parameters to minimize the thinning in single point incremental forming and find some methods to reduce it that is the aim of this research. Ansys workbench software based on finite element method is used to simulate the forming process and analyze the thickness reduction along the wall parts, numerical results are verified experimentally. The results showed the forming angle has great effect while the feed speed has the little effect on the thinning ratio on the formed parts.

This work addresses the formulation of a new mixed-mode cohesive model, able to handle the transition from small to large openings: the proposed model is an extension of the isotropic damage model formulated in [Confalonieri and Perego, JSSCM, 11-2, 2017] for the simulation of mixed-mode delamination with variable mode-ratio, under the assumption of small relative displacements.

Every day billions of tiny meteoroids impact the Earth's atmosphere at hypersonic speeds, creating dense plasmas between 80 and 130 km altitude. In this part of the E-region ionosphere electrons are magnetized by the geomagnetic field while ions are largely unmagnetized due to their frequent collisions with neutral atmosphere. This discrepancy leads to a variety of inhomogeneous, unstable, and nonlinear plasma phenomena. Among them is the formation of field-aligned irregularities in the slowly diffusing dense meteor plasma trails which are important for radar observations of mostly optically invisible meteors. We will present a quantitative model of the evolution of a plasma trail density and its ambipolar electric fields. Our theory predicts that plasma trail diffusion induces electric currents through a large volume of the background ionosphere with important consequences for plasma trail diffusion. Also, strong electric fields propagate long distances along the magnetic field...

Some aspects of numerical analysis of problems related to high strain rates with thermal effects are considered. The attention is focused on constitutive modelling that describes the accompanied phenomena like plastic strain localization and softening. The importance of proper formulation of failure criteria is stressed. Also the complexity of computations is discussed.

The behaviour of concrete under quasi-static loadings for uniaxial compression, tension and plane stress conditions is studied. The failure criteria of concrete are discussed as well as the methods of constitutive parameters identification are elaborated. The attention is focus on an energetic interpretation of selected failure criteria. The numerical example with concrete damage plasticity material model is shown

We obtain in this article a new formulation of the generalizations of the Cahn-Hilliard equation based on constitutive equations proposed by Gurtin. This formulation, which can be seen as a compatibility equation, is obtained by making a suitable change of function. The interest is that it allows, once this equation is solved, to obtain the order parameter and the chemical potential by simple explicit expressions. Indeed, we can note that, in the original setting, once the order parameter is known (by solving the (generalized) Cahn-Hilliard equation), then, the expressions giving the chemical potential in terms of the order parameter are, for nonisotropic materials, intricate and not convenient (in view of numerical simulations for instance); in the classical Cahn-Hilliard theory, the chemical potential is given, constitutively, as a function of the order parameter. We then study the existence and uniqueness of solutions.

Most constitutive models can only simulate cumulative deformation after a limited number of cycles. However, railroad ballast usually experiences a large number of train passages that cause history-dependent long-term deformation. Fractional calculus is an efficient tool for modelling this phenomenon and therefore is incorporated into a constitutive model for predicting the cumulative deformation. The proposed model is further validated by comparing the model predictions with a series of corresponding experimental results. It is observed that the proposed model can realistically simulate the cumulative deformation of ballast from the onset of loading up to a large number of load cycles.

We consider stagnation point flow away from a wall for creeping flow of dilute polymer solutions. For a simplified flow geometry, we explicitly show that a narrow region of strong polymer extension (a birefringent strand) forms downstream of the stagnation point in the UCM model and extensions, like the FENE-P model. These strands are associated with the existence of an essential singularity in the stresses, which is induced by the fact that the stagnation point makes the convective term in the constitutive equation into a singular point. We argue that the mechanism is quite general, so that all flows that have a separatrix going away from the stagnation point exhibit some singular behaviour. These findings are the counterpart for wall stagnation points of the recently discovered singular behaviour in purely elongational flows: the underlying mechanism is the same while the different nature of the singular stress behaviour reflects the different form of the velocity expansion close to the stagnation point.

Current needs in the design and optimization of complex protective structures lead to the development of more accurate numerical modelling of impact loadings. The aim of developing such a tool is to be able to predict the protection performance of structures using fewer experiments. Considering only the numerical approach, the most important issue to have a reliable simulation is to focus on the material behavior description in terms of constitutive relations and failure model for high strain rates, large field of temperatures and complex stress states. In this context, the present study deals with the dynamic thermo-mechanical behavior of a high strength steel (HSS) close to the Mars ® 190 (Industeel France, Le Creusot, France). For the considered application, the material can undergo both quasi-static and dynamic loadings. Thus, the studied strain rate range is varying from 10 -3 -10 4 s -1 . Due to the fast loading time, the local temperature increase during dynamic loading induces a thermal softening. The temperature sensitivity has been studied up to 473 K under quasi-static and dynamic conditions. Low temperature measurements (lower than the room temperature) are also reported in term of σ -ε| ε,T curves. Experimental results are then used to identify the parameters of several constitutive relations, such as the model developed initially by Johnson and Cook; Voyiadjis and Abed; and Rusinek and Klepaczko respectively termed Johnson-Cook (JC), Voyiadjis-Abed (VA), and Rusinek-Klepaczko (RK). Finally, comparisons between experimental results and model predictions are reported and compared.

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.

Recently, there has been a burgeoning interest in developing constitutive soil models from the laws of thermodynamics, mainly due to the benefits that these models automatically obey them and the approach provides a well-established structure and reduces the need for 'ad hoc' postulates. A thermodynamic framework, also known as thermo-mechanical framework, has the capability to predict the behaviour of geotechnical materials, which requires the anticipated incorporation of nonassociated flow rules. As it is very challenging to achieve acceptable accuracy in plasticity modelling of granular materials, this paper aims to review this framework not only to discuss the details of the major components but also to highlight the capability of generating non-associated flow rules in a natural way from thermo-mechanical principles. This approach introduces the use of internal variables to develop the two thermodynamic potentials (the free energy and the rate of dissipation functions), sufficient to derive the corresponding yield function, flow rule, isotropic and kinematic hardening rules as well as the basic elasticity law. It is shown that the non-associated flow rule can be derived naturally from the postulated stress-dependent dissipation increment function. Comparison has been made with stress-independent dissipation to demonstrate that the approach can also successfully explain the behaviour of standard materials with associated flow rules. The basic steps for the thermomechanical formulation for developing a constitutive model are also reviewed and summarised. Furthermore, the power of conventional mathematical technique, Legendre transformation, in the derivation of constitutive equations has been highlighted.

This Note lays out the specialization of the two-potential constitutive framework -also known as the "generalized standard materials" framework -to rubber viscoelasticity. Inter alia, it is shown that a number of popular rubber viscoelasticity formulations, introduced over the years following different approaches, are special cases of this framework. As a first application of practical relevance, the framework is utilized to put forth a new objective and thermodynamically consistent rubber viscoelastic model for incompressible isotropic elastomers. The model accounts for the non-Gaussian elasticity of elastomers, as well as for the deformation-enhanced shear thinning of their viscous dissipation governed by reptation dynamics. The descriptive and predictive capabilities of the model are illustrated via comparisons with experimental data available from the literature for two commercially significant elastomers.

If the modeling approach for strain localization with softening does not contain a material length-scale parameter, the numerical simulation suffers from the excessive mesh dependence. This paper presented the extended finite element (XFEM) method combined with new integral type nonlocal model for numerical simulation of strain localization with softening. The XFEM method was employed for simulation of high strain gradient in the localization band. The governing differential equations were regularized by nonlocal continuum theory, including the material length-scale parameter. For nonlocal plasticity, element size has a critical effect on the solution. Sufficiently refined meshes are required for an accurate solution without mesh dependency. It was shown that an extended finite element method can be applied to the problem to decrease the required mesh density close to the localization band. A new method based on the local bifurcation theory was proposed for the initiation and growth criterion of the strain localization interface. When using this method, the softening zone initiation locus did not need to be known in advance. Finally, several numerical examples were used to demonstrate the efficiency of the mixed XFEM-integral type nonlocal model in shear band localization modeling without mesh dependency.

Deficiencies of constitutive models in prediction of dilatancy are often attributed to simplifications associated with flow rules such as assumptions of isotropy and coaxiality. It is thus proposed here to develop a comprehensive flow rule for granular materials by including the effect of fabric and without the assumption of coaxiality. A secondorder tensor is introduced as a fabric for the distribution of contact normals and contact forces. By using the energy principle in micro-mechanical scale and a suitable dissipation mechanism in granular materials, a stress-dilatancy relation is obtained. Fabric plays a "bridge-like" role in the dilatancy and non-coaxiality. Non-coaxialities between stress-strainfabric are attributed to the non-coaxiality between stressfabric and strain-fabric. In this formulation the constants for modeling fabric depend on non-coaxiality of the system rather than the history that determines such a state. Ability of this stress-fabric-dilatancy for modeling the non-coaxiality shows that this relation can predict the behavior of granular materials in the presence of the rotation of principal stress axes.

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 [

This work addresses the formulation of a new mixed-mode cohesive model, able to handle the transition from small to large openings: the proposed model is an extension of the isotropic damage model formulated in [Confalonieri and Perego, JSSCM, 11-2, 2017] for the simulation of mixed-mode delamination with variable mode-ratio, under the assumption of small relative displacements.

In this work, a fully adaptive 2D numerical methodology is proposed in order to simulate with accuracy various metal forming processes. The methodology is based on fully coupled advanced finite strain constitutive equations accounting for the main physical phenomena such as large plastic deformation, non-linear isotropic and kinematic hardening, ductile isotropic damage and contact with friction. The adaptivity concerns the space discretization using FEM as well as the applied loading sequences. Mesh size distribution is based on various error indicators making use of the hessian of the plastic strain rate combined with a specific damage error function and a specific local curvature error function evaluated at contact boundaries. 2D mesh size can be refined or coarsened when necessary according to these error indicators. Particularely, the smallest size is found to be inside the zones where the damage is highly active. The applied loading paths are also adaptively decomposed into various sequences depending on both number and size of the fully damaged elements. The adaptive procedure is validated through various sheet and bulk metal forming examples. In this paper, a plane stress tensile test, an axisymmetric blanking process of two materials with different ductilities and a cold extrusion process are presented.

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The springback phenomenon is a significant concern in manufacturing processes, particularly in metal component forming, as it directly affects dimensional control and the shape of formed parts. Accurate prediction and analysis of springback are crucial for achieving precise dimensional control and ensuring the desired final shape. Therefore, this study focuses on analyzing the springback phenomenon using finite element method. The primary objective is to develop a Matlab program for analyzing three-dimensional springback problems. Throughout the research process, the understanding of the phenomenon has been enhanced. The developed program has been successfully implemented to model and simulate the forming process, considering various aspects of the problem. The results of the solutions have been compared and evaluated, leading to important conclusions. The research also outlines future developments in this field. It is hoped that the results and understanding of this research will contribute to the field of computational mechanics and inspire further research.

The coupled damage/plasticity model for meso-level which is plylevel in case of Uni-Directional (UD) Fiber Reinforced Polymers (FRPs) is implemented. The mathematical formulations, particularly the plasticity part, are discussed in a comprehensive manner. The plastic potential is defined in effective stress space and the damage evolution is based on the theory of irreversible thermodynamics. The model which is illustrated here has been implemented by different authors previously but, the complete prerequisite algorithm ingredients used in the implicit scheme implementation are not available in the literature. This leads to the complexity in its implementation. Furthermore, this model is not available as a built-in material constitutive law in the commercial Finite Element Method (FEM) softwares. To facilitate the implementation and understanding, all the mathematical formulations are presented in great detail. In addition, the elastoplastic consistent operator needed for implementation in the implicit solution scheme is also derived. The model is formularized in incremental form to be used in the Return Mapping Algorithm (RMA). The quasi-static load carrying capability and non-linearity caused by the collaborative effect of damage and plasticity is predicted with User MATerial (UMAT) subroutine which solves the FEM problem with implicit techniques in ABAQUS.

In mine ventilation, the head loss due to friction is usually calculated using Atkinson's equation. But only in an ideal case is this equation valid. In the present analysis a power law constitutive relation based on Atkinson's equation is introduced and a differential equation for the head loss gradient is derived. The constitutive law proposed here provides a more general description of air flow characteristics in mine ventilation.

Computational mechanics has been advanced in every area of orthopedic biomechanics. The objective of this paper is to provide a general review of the computational models used in the analysis of the mechanical function of the knee joint in different loading and pathological conditions. Major review articles published in related areas are summarized first. The constitutive models for soft tissues of the knee are briefly discussed to facilitate understanding the joint modeling. A detailed review of the tibiofemoral joint models is presented thereafter. The geometry reconstruction procedures as well as some critical issues in finite element modeling are also discussed. Computational modeling can be a reliable and effective method for the study of mechanical behavior of the knee joint, if the model is constructed correctly. Single-phase material models have been used to predict the instantaneous load response for the healthy knees and repaired joints, such as total and partial meniscect...

SummaryIn the context of eigenfracture scheme, the work at hand introduces a variational eigenerosion approach for inelastic materials. The theory seizes situations where the material accumulates large amounts of plastic deformations. For these cases, the surface energy entering the energy balance equation is rescaled to favor fracture, thus energy minimization delivers automatically the crack‐tracking solution also for inelastic cases. The minimization approach is sound and preserves the mathematical properties necessary for the Γ‐limit proof, thus the existence of (local) minimizers is guaranteed by the Γ‐convergence theory. Although it is not possible to demonstrate that the obtained minimizers are global, satisfactory results are obtained with the local minimizers provided by the method. Furthermore, with the goal of addressing the constitutive behavior of concrete, a Drucker‐Prager viscoplastic consistency model is introduced in the microplane setting. The model delivers a rate...

L’indentation instrumentee est une technique repandue et tres puissante utilisee pour l’etude des proprietes mecaniques des materiaux, principalement la durete et le module d’elasticite. Cependant, l’analyse des resultats est une procedure complexe faisant intervenir le type d’appareil utilise, les conditions experimentales et le mode d’interpretation des resultats. Ces parametres ont un impact important sur la determination de proprietes mecaniques recherchees et sont plus ou moins influents selon les dispositifs experimentaux utilises et les domaines de force et de profondeur de penetration appliques [1], [2], [3]. Dans cette etude nous utilisons trois appareils d’indentation instrumentee : le nanoindenteur MTS XP (methode standard ou Continuous Stiffness Measurement), le microindenteur CSM Instruments (methode standard ou indentation repetee) et le macroindenteur Zwick ZHU 2.5, avec deux types d’indenteurs pyramidaux, Berkovich et Vickers. La gamme de charge etudiee varie entre 2...

To gain a better insight into the failure mechanism of reinforced sand, a FEM simulation of plane strain compression tests of dense Toyoura sand reinforced with planar reinforcement having a wide range of stiffness was performed. A new elastoplastic constitutive model for sand, having a stress path-independent work-hardening parameter based on modified plastic strain energy, is applied. The constitutive model of sand is capable of simulating the effects on the deformation characteristics of stress history, stress path and pressure level, taking into account inherent anisotropy in the elastic and plastic properties and work-softening associated with strain localization into a shear band. The FEM code incorporating the above-mentioned new constitutive model is validated by a direct comparison between results from the physical experiments and the numerical simulation for sand specimens reinforced by using relatively flexible and rigid reinforcement as well as an unreinlorced sand specimen. The comparison was made in terms of global stress-strain relationships and local strain fields showing the generation and development of shear band. It was found that the FEM code incorporating the proposed model workhardening model simulates the experimental results much better than one with the previous shear strain-hardening model.

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.

We investigate the transient viscoelastic response of weakly strain-hardening fluids to imposed elongational deformation in filament stretching devices. We combine timedependent finite-element simulations with quantitative experimental measurements on a rheologically well-characterized test fluid to investigate how well the device reproduces the ideal transient uniaxial extensional viscosity predicted theoretically. A concentrated polymer solution containing 5.0 wt.% monodisperse polystyrene is used as the test fluid and the experiments are conducted using the filament stretching rheometer developed by Spiegelberg et al. The axisymmetric numerical simulations incorporate the effects of viscoelasticity, surface tension, fluid inertia and a deformable free surface. Single and multi-mode versions of the Giesekus constitutive equation are used to model the rheology of the shear-thinning test fluid. Excellent agreement between the measured transient Trouton ratio and the numerical predictions over a range of deformation rates is reported. The numerical simulations also reveal some important aspects of the fluid kinematics exhibited by weakly strain-hardening fluids during stretching; including a rapid necking of the filament diameter near the axial mid-plane of the fluid column, and an associated elastic recoil phenomenon near the rigid end-plates. This necking instability of a viscoelastic filament can be understood through a generalized Considère criterion, as recently documented by Hassager et al. As a consequence of this necking, spatial and temporal homogeneity in the extensional deformation of the filament is never achieved, even at large Hencky strains. This is in sharp contrast to the numerical and experimental studies for strongly strain-hardening dilute polymer solutions that have been reported to date. Nonetheless, the present computational rheology study shows that filament stretching devices can still be used to accurately extract the transient extensional viscosity function for weakly strain-hardening fluids, provided that the evolution history of the tensile force at the end-plate and the filament radius at the mid-plane are carefully measured and that the experimental data are correctly processed.

The application of hyperbolic sine equation and Artificial Neural Network(ANN) model to predict high temperature flow behaviour of Ti-6Al-4V preform is assessed for development of a constitutive equation to model ring rolling process. Uniaxial compression specimens were obtained from a specific location and direction, where the radial deformation is the major deformation location, to study the ring rolling process. The adiabatic temperature corrected data was used to find constants for hyperbolic sine equation and train the ANN model. The ANN model used normalised strain, strain rate and temperature as input variables and the output parameter was the flow stress. Comparison of the predicting capability of both models showed that the predictions of ANN were better. The hyperbolic sine equation was integrated in a user subroutine and finite element-based simulations of isothermal uniaxial compression were carried out for validation.

During the last decade, finite element (FE) modelling has become ubiquitous in understanding complex mechanobiological phenomena, e.g. bone-implant interactions. The extensive computational effort required to achieve biorealistic results when modelling the post-yield behaviour of microstructures like cancellous bone is a major limitation of these techniques. This study describes the anisotropic biomechanical response of cancellous bone through stress-strain curves of equivalent bulk geometries. A cancellous bone segment, reverse engineered by micro computed tomography, was subjected to uniaxial compression. The material's constitutive law, obtained by nano-indentations, was considered during the simulation of the experimental process. A homodimensionally bulk geometry was employed to determine equivalent properties, resulting in a similar anisotropic response to the trabecular structure. The experimental verification of our model sustained that the obtained stress-strain curves can adequately reflect the post-yield behaviour of the sample. The introduced approach facilitates the consideration of nonlinearity and anisotropy of the tissue, while reducing the geometrical complexity of the model to a minimum.

A theory is presented to simulate the consolidation of elastic porous media saturated by two immiscible Newtonian fluids. The macroscopic equations, including mass and momentum balance equations and constitutive relations, are obtained by volume averaging the microscale equations. The theory is based on the small deformation assumption. In the microscale, the grains are assumed to be linearly elastic and the fluids are Newtonian. The bulk and shear moduli of the solid matrix are introduced to obtain the macroscopic constitutive equations. Momentum transfer terms are expressed in terms of intrinsic and relative permeabilities assuming the validity of Darcy's law. In one dimension, the governing equations reduce to two coupled diffusion equations in terms of the pore pressures of the fluid phases. An analytical solution is obtained for a column with a fixed impervious base and a free drainage surface. Results are presented for cases of practical interest, Le., columns saturated by oil-water and air-water phases. Results indicate that the presence of a second fluid phase affects pore water pressure and total settlement.