Search results for: elasto-plastic model

Authors: Nikolaos Reppas, Yilin Gui

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A dual-porosity finite element-code will be presented for the stability analysis of the wellbore during CO₂ injection. An elastoplastic damage response will be considered to the model. The Finite Element Method (FEM) will be validated using experimental results from literature or from experiments that are planned to be undertaken at Newcastle University. The main target of the research paper is to present a constitutive model that can help industries to safely store CO₂ in geological rock formations and forecast any changes on the surrounding rock of the wellbore. The fully coupled elastoplastic damage Thermo-Hydraulic-Mechanical (THM) model will determine the pressure and temperature of the injected CO₂ as well as the size of the radius of the wellbore that can make the Carbon Capture and Storage (CCS) procedure more efficient.

Keywords: carbon capture and storage, Wellbore stability, elastoplastic damage response for rock, constitutive THM model, fully coupled thermo-hydraulic-mechanical model

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Authors: Nikolaos Reppas, Yilin Gui, Ben Wetenhall, Colin Davie

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Injection of CO2 inside wellbore can induce different kind of loadings that can lead to thermal, hydraulic, and mechanical changes on the surrounding rock. A dual-porosity theoretical constitutive model will be presented for the stability analysis of the wellbore during CO2 injection. An elastoplastic damage response will be considered. A bounding yield surface will be presented considering damage effects on sandstone. The main target of the research paper is to present a theoretical constitutive model that can help industries to safely store CO2 in geological rock formations and forecast any changes on the surrounding rock of the wellbore. The fully coupled elasto-plastic damage Thermo-Hydraulic-Mechanical theoretical model will be validated from existing experimental data for sandstone after simulating some scenarios by using FEM on MATLAB software.

Keywords: carbon capture and storage, rock mechanics, THM effects on rock, constitutive model

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Authors: Leo Laine, Morgan Johansson

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To meet the civilizations future needs for safe living and low environmental footprint, the engineers designing the complex systems of tomorrow will need efficient ways to model and optimize these systems for their intended purpose. For example, a civil defence shelter and its subsystem components needs to withstand, e.g. airblast and ground shock from decided design level explosion which detonates with a certain distance from the structure. In addition, the complex civil defence shelter needs to have functioning air filter systems to protect from toxic gases and provide clean air, clean water, heat, and electricity needs to also be available through shock and vibration safe fixtures and connections. Similar complex building systems can be found in any concentrated living or office area. In this paper, the authors use a multidomain modelling language called Modelica to model a concrete wall as a single degree of freedom (SDOF) system with elastoplastic properties with the implemented option of plastic hardening. The elastoplastic model was developed and implemented in the open source tool OpenModelica. The simulation model was tested on the case with a transient equivalent reflected pressure time history representing an airblast from 100 kg TNT detonating 15 meters from the wall. The concrete wall is approximately regarded as a concrete strip of 1.0 m width. This load represents a realistic threat on any building in a city like area. The OpenModelica model results were compared with an Excel implementation of a SDOF model with an elastic-plastic spring using simple fixed timestep central difference solver. The structural displacement results agreed very well with each other when it comes to plastic displacement magnitude, elastic oscillation displacement, and response times.

Keywords: airblast from explosives, elastoplastic spring model, Modelica modelling language, SDOF, structural response of concrete structure

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Authors: Huijuan Liu, Fukun Li, Hao Yuan

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The bolted spherical node is a common type of joint in space steel structures. The bolt-sphere joint portion almost always controls the bearing capacity of the bolted spherical node. The investigation of the bearing performance and progressive failure in service often requires high-fidelity numerical models. This paper focuses on the constitutive models of bolt steel and sphere steel used in China’s space structure construction. The elastoplastic model is determined by a standard tensile test and calibrated Voce saturated hardening rule. The ductile damage is found dominant based on the fractography analysis. Then Rice-Tracey ductile fracture rule is selected and the model parameters are calibrated based on tensile tests of notched specimens. These calibrated material models can benefit research or engineering work in similar fields.

Keywords: bolt-sphere joint, steel, constitutive model, ductile damage, model calibration

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Authors: Azher Jameel, Ghulam Ashraf Harmain

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In the recent years, the enriched techniques like the extended finite element method, the element free Galerkin method, and the Coupled finite element-element free Galerkin method have found wide application in modeling different types of discontinuities produced by cracks, contact surfaces, and bi-material interfaces. The extended finite element method faces severe mesh distortion issues while modeling large deformation problems. The element free Galerkin method does not have mesh distortion issues, but it is computationally more demanding than the finite element method. The coupled FE-EFGM proves to be an efficient numerical tool for modeling large deformation problems as it exploits the advantages of both FEM and EFGM. The present paper employs the coupled FE-EFGM to model large elastoplastic deformations in bi-material engineering components. The large deformation occurring in the domain has been modeled by using the total Lagrangian approach. The non-linear elastoplastic behavior of the material has been represented by the Ramberg-Osgood model. The elastic predictor-plastic corrector algorithms are used for the evaluation stresses during large deformation. Finally, several numerical problems are solved by the coupled FE-EFGM to illustrate its applicability, efficiency and accuracy in modeling large elastoplastic deformations in bi-material samples. The results obtained by the proposed technique are compared with the results obtained by XFEM and EFGM. A remarkable agreement was observed between the results obtained by the three techniques.

Keywords: XFEM, EFGM, coupled FE-EFGM, level sets, large deformation

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Authors: Martin Cermak, Stanislav Sysala

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In this paper we present the efficient parallel implementation of elastoplastic problems based on the TFETI (Total Finite Element Tearing and Interconnecting) domain decomposition method. This approach allow us to use parallel solution and compute this nonlinear problem on the supercomputers and decrease the solution time and compute problems with millions of DOFs. In our approach we consider an associated elastoplastic model with the von Mises plastic criterion and the combination of linear isotropic-kinematic hardening law. This model is discretized by the implicit Euler method in time and by the finite element method in space. We consider the system of nonlinear equations with a strongly semismooth and strongly monotone operator. The semismooth Newton method is applied to solve this nonlinear system. Corresponding linearized problems arising in the Newton iterations are solved in parallel by the above mentioned TFETI. The implementation of this problem is realized in our in-house MatSol packages developed in MATLAB.

Keywords: isotropic-kinematic hardening, TFETI, domain decomposition, parallel solution

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Authors: Joseph Marae Djouda, Ashraf Kasmi, François Hild

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Fused filament fabrication is one of the most widespread additive manufacturing techniques because of its low-cost implementation. Its initial development was based on part fabrication with thermoplastic materials. The influence of the manufacturing parameters such as the filament orientation through the nozzle, the deposited layer thickness, or the speed deposition on the mechanical properties of the parts has been widely experimentally investigated. It has been recorded the remarkable variations of the anisotropy in the function of the filament path during the fabrication process. However, there is a lack in the development of constitutive models describing the mechanical properties. In this study, integrated digital image correlation (I-DIC) is used for the identification of mechanical constitutive parameters of two configurations of ABS samples: +/-45° and so-called “oriented deposition.” In this last, the filament was deposited in order to follow the principal strain of the sample. The identification scheme based on the gap reduction between simulation and the experiment directly from images recorded from a single sample (single edge notched tension specimen) is developed. The macroscopic and mesoscopic analysis are conducted from images recorded in both sample surfaces during the tensile test. The elastic and elastoplastic models in isotropic and orthotropic frameworks have been established. It appears that independently of the sample configurations (filament orientation during the fabrication), the elastoplastic isotropic model gives the correct description of the behavior of samples. It is worth noting that in this model, the number of constitutive parameters is limited to the one considered in the elastoplastic orthotropic model. This leads to the fact that the anisotropy of the architectured 3D printed ABS parts can be neglected in the establishment of the macroscopic behavior description.

Keywords: elastic anisotropy, fused filament fabrication, Acrylonitrile butadiene styrene, I-DIC identification

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Authors: M. Palizvan, M. H. Sadr, M. T. Abadi

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The representative volume element (RVE) plays a central role in the mechanics of random heterogeneous materials with a view to predicting their effective properties. In this paper, a computational homogenization methodology, developed to determine effective linear elastic properties of composite materials, is extended to predict the effective nonlinear elastoplastic response of long fiber reinforced composite. Finite element simulations of volumes of different sizes and fiber volume fractures are performed for calculation of the overall response RVE. The dependencies of the overall stress-strain curves on the number of fibers inside the RVE are studied in the 2D cases. Volume averaged stress-strain responses are generated from RVEs and compared with the finite element calculations available in the literature at moderate and high fiber volume fractions. For these materials, the existence of an RVE is demonstrated for the sizes of RVE corresponding to 10–100 times the diameter of the fibers. In addition, the response of small size RVE is found anisotropic, whereas the average of all large ones leads to recover the isotropic material properties.

Keywords: homogenization, periodic boundary condition, elastoplastic properties, RVE

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Authors: Dina Kon Mushid, Kabutakapua Kakanda, Dibu Dave Mbako

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The failure of material usually involves elastoplastic deformation and fracturing. Continuum mechanics can effectively deal with plastic deformation by using a yield function and the flow rule. At the same time, it has some limitations in dealing with the fracture problem since it is a theory based on the continuous field hypothesis. The lattice model can simulate the fracture problem very well, but it is inadequate for dealing with plastic deformation. Based on the discretized virtual internal bond model (DVIB), this paper proposes a lattice model that can account for plasticity. DVIB is a lattice method that considers material to comprise bond cells. Each bond cell may have any geometry with a finite number of bonds. The two-body or multi-body potential can characterize the strain energy of a bond cell. The two-body potential leads to the fixed Poisson ratio, while the multi-body potential can overcome the limitation of the fixed Poisson ratio. In the present paper, the modified Stillinger-Weber (SW), a multi-body potential, is employed to characterize the bond cell energy. The SW potential is composed of two parts. One part is the two-body potential that describes the interatomic interactions between particles. Another is the three-body potential that represents the bond angle interactions between particles. Because the SW interaction can represent the bond stretch and bond angle contribution, the SW potential-based DVIB (SW-DVIB) can represent the various Poisson ratios. To embed the plasticity in the SW-DVIB, the plasticity is considered in the two-body part of the SW potential. It is done by reducing the bond stiffness to a lower level once the bond reaches the yielding point. While before the bond reaches the yielding point, the bond is elastic. When the bond deformation exceeds the yielding point, the bond stiffness is softened to a lower value. When unloaded, irreversible deformation occurs. With the bond length increasing to a critical value, termed the failure bond length, the bond fails. The critical failure bond length is related to the cell size and the macro fracture energy. By this means, the fracture energy is conserved so that the cell size sensitivity problem is relieved to a great extent. In addition, the plasticity and the fracture are also unified at the bond level. To make the DVIB able to simulate different Poisson ratios, the three-body part of the SW potential is kept elasto-brittle. The bond angle can bear the moment before the bond angle increment is smaller than a critical value. By this method, the SW-DVIB can simulate the plastic deformation and the fracturing process of material with various Poisson ratios. The elastoplastic SW-DVIB is used to simulate the plastic deformation of a material, the plastic fracturing process, and the tunnel plastic deformation. It has been shown that the current SW-DVIB method is straightforward in simulating both elastoplastic deformation and plastic fracture.

Keywords: lattice model, discretized virtual internal bond, elastoplastic deformation, fracture, modified stillinger-weber potential

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Authors: Xuejiao Shao, Jianguo Chen, Xiaolong Fu

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In this paper, the elastoplastic strain correction factor computed by software of ANSYS was modified, and the fatigue usage factor in air was also corrected considering in water under reactor operating condition. The fatigue of key parts on control rod drive mechanisms was analyzed considering the influence of environmental fatigue caused by the coolant in the react pressure vessel. The elastoplastic strain correction factor was modified by analyzing thermal and mechanical loads separately referring the rules of RCC-M 2002. The new elastoplastic strain correction factor Ke(mix) is computed to replace the original Ke computed by the software of ANSYS when evaluating the fatigue produced by thermal and mechanical loads together. Based on the Ke(mix) and the usage cycle and fatigue design curves, the new range of primary plus secondary stresses was evaluated to obtain the final fatigue usage factor. The results show that the precision of fatigue usage factor can be elevated by using modified Ke when the amplify of the primary and secondary stress is large to some extent. One approach has been proposed for incorporating the environmental effects considering the effects of reactor coolant environments on fatigue life in terms of an environmental correction factor Fen, which is the ratio of fatigue life in air at room. To incorporate environmental effects into the RCCM Code fatigue evaluations, the fatigue usage factor based on the current Code design curves is multiplied by the correction factor. The contribution of environmental effects to results is discussed. Fatigue life decreases logarithmically with decreasing strain rate below 10%/s, which is insensitive to strain rate when temperatures below 100°C.

Keywords: environmental fatigue, usage factor, elastoplastic strain correction factor, environmental correction

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Authors: Andres Nieto-Leal, Victor N. Kaliakin, Tania P. Molina

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The nature of most engineering materials is quite complex. It is, therefore, difficult to devise a general mathematical model that will cover all possible ranges and types of excitation and behavior of a given material. As a result, the development of mathematical models is based upon simplifying assumptions regarding material behavior. Such simplifications result in some material idealization; for example, one of the simplest material idealization is to assume that the material behavior obeys the elasticity. However, soils are nonhomogeneous, anisotropic, path-dependent materials that exhibit nonlinear stress-strain relationships, changes in volume under shear, dilatancy, as well as time-, rate- and temperature-dependent behavior. Over the years, many constitutive models, possessing different levels of sophistication, have been developed to simulate the behavior geomaterials, particularly cohesive soils. Early in the development of constitutive models, it became evident that elastic or standard elastoplastic formulations, employing purely isotropic hardening and predicated in the existence of a yield surface surrounding a purely elastic domain, were incapable of realistically simulating the behavior of geomaterials. Accordingly, more sophisticated constitutive models have been developed; for example, the bounding surface elastoplasticity. The essence of the bounding surface concept is the hypothesis that plastic deformations can occur for stress states either within or on the bounding surface. Thus, unlike classical yield surface elastoplasticity, the plastic states are not restricted only to those lying on a surface. Elastoplastic bounding surface models have been improved; however, there is still need to improve their capabilities in simulating the response of anisotropically consolidated cohesive soils, especially the response in extension tests. Thus, in this work an improved constitutive model that can more accurately predict diverse stress-strain phenomena exhibited by cohesive soils was developed. Particularly, an improved rotational hardening rule that better simulate the response of cohesive soils in extension. The generalized definition of the bounding surface model provides a convenient and elegant framework for unifying various previous versions of the model for anisotropically consolidated cohesive soils. The Generalized Bounding Surface Model for cohesive soils is a fully three-dimensional, time-dependent model that accounts for both inherent and stress induced anisotropy employing a non-associative flow rule. The model numerical implementation in a computer code followed an adaptive multistep integration scheme in conjunction with local iteration and radial return. The one-step trapezoidal rule was used to get the stiffness matrix that defines the relationship between the stress increment and the strain increment. After testing the model in simulating the response of cohesive soils through extensive comparisons of model simulations to experimental data, it has been shown to give quite good simulations. The new model successfully simulates the response of different cohesive soils; for example, Cardiff Kaolin, Spestone Kaolin, and Lower Cromer Till. The simulated undrained stress paths, stress-strain response, and excess pore pressures are in very good agreement with the experimental values, especially in extension.

Keywords: bounding surface elastoplasticity, cohesive soils, constitutive model, modeling of geomaterials

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Authors: Fangyuan Shao, Wei Liu, Deli Gao

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Polycrystalline diamond compact (PDC) bits have occupied a large market of unconventional oil and gas drilling. The application of PDC bits benefits from the efficient rock breaking of PDC cutters. In response to increasingly complex formations, many shaped cutters have been invited, but many of them have not been solved by the mechanism of rock breaking. In this paper, two kinds of PDC cutters: a new axe-shaped (NAS) cutter and cylindrical cutter (benchmark) were studied by laboratory experiments. NAS cutter is obtained by optimizing two sides of axe-shaped cutter with curved surfaces. All the cutters were put on a vertical turret lathe (VTL) in the laboratory for cutting tests. According to the cutting distance, the VTL tests can be divided into two modes: single-turn rotary cutting and continuous cutting. The cutting depth of cutting (DOC) was set at 1.0 mm and 2.0 mm in the former mode. The later mode includes a dry VTL test for thermal stability and a wet VTL test for wear resistance. Load cell and 3D optical profiler were used to obtain the value of cutting forces and wear area, respectively. Based on the findings of the single-turn rotary cutting VTL tests, the performance of A NAS cutter was better than the benchmark cutter on elastoplastic material cutting. The cutting forces (normal forces, tangential force, and radial force) and special mechanical energy (MSE) of a NAS cutter were lower than that of the benchmark cutter under the same condition. It meant that a NAS cutter was more efficient on elastoplastic material breaking. However, the wear resistance of a new axe-shaped cutter was higher than that of a benchmark cutter. The results of the dry VTL test showed that the thermal stability of a NAS cutter was higher than that of a benchmark cutter. The cutting efficiency can be improved by optimizing the geometric structure of the PDC cutter. The change of thermal stability may be caused by the decrease of the contact area between cutter and rock at given DOC. The conclusions of this paper can be used as an important reference for PDC cutters designers.

Keywords: axe-shaped cutter, PDC cutter, rotary cutting test, vertical turret lathe

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Authors: Ravi Raj, Louis Chiu, Deepak Marla, Aijun Huang

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Hybridization of the directed laser deposition (DLD) process using an in-situ micro-roller to impart a vertical compressive load on the deposited bead at elevated temperatures can relieve tensile residual stresses incurred in the process. To investigate this stress relief mechanism and its relationship with the in-situ rolling parameters, a fully coupled dynamic thermo-mechanical model is presented in this study. A single bead deposition of Ti-6Al-4V alloy with an in-situ roller made of mild steel moving at a constant speed with a fixed nominal bead reduction is simulated using the explicit solver of the finite element software, Abaqus. The thermal model includes laser heating during the deposition process and the heat transfer between the roller and the deposited bead. The laser heating is modeled using a moving heat source with a Gaussian distribution, applied along the pre-formed bead’s surface using the VDFLUX Fortran subroutine. The bead’s cross-section is assumed to be semi-elliptical. The interfacial heat transfer between the roller and the bead is considered in the model. Besides, the roller is cooled internally using axial water flow, considered in the model using convective heat transfer. The mechanical model for the bead and substrate includes the effects of rolling along with the deposition process, and their elastoplastic material behavior is captured using the J2 plasticity theory. The model accounts for strain, strain rate, and temperature effects on the yield stress based on Johnson-Cook’s theory. Various aspects of this material behavior are captured in the FE software using the subroutines -VUMAT for elastoplastic behavior, VUHARD for yield stress, and VUEXPAN for thermal strain. The roller is assumed to be elastic and does not undergo any plastic deformation. Also, contact friction at the roller-bead interface is considered in the model. Based on the thermal results of the bead, the distance between the roller and the deposition nozzle (roller o set) can be determined to ensure rolling occurs around the beta-transus temperature for the Ti-6Al-4V alloy. It is identified that roller offset and the nominal bead height reduction are crucial parameters that influence the residual stresses in the hybrid process. The results obtained from a simulation at roller offset of 20 mm and nominal bead height reduction of 7% reveal that the tensile residual stresses decrease to about 52% due to in-situ rolling throughout the deposited bead. This model can be used to optimize the rolling parameters to minimize the residual stresses in the hybrid DLD process with in-situ micro-rolling.

Keywords: directed laser deposition, finite element analysis, hybrid in-situ rolling, thermo-mechanical model

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Authors: Shigeyuki Haruyama, Oke Oktavianty, Zefry Darmawan, Tadayuki Kyoutani, Ken Kaminishi

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Cab’s frame strength is considered as an important factor in excavator’s operator safety, especially during roll-over. In this study, we use a model of cab frame with different thicknesses and perform elastoplastic numerical analysis by using Finite Element Method (FEM). Deformation mode and energy absorption's of cab’s frame part are investigated on two conditions, with wrinkle and without wrinkle. The occurrence of wrinkle when deforming cab frame can reduce energy absorption, and among 4 parts with wrinkle, the energy absorption significantly decreases in part C. Residual stress that generated upon the bending process of part C is analyzed to confirm it possibility in increasing the energy absorption.

Keywords: ROPS, FEM, hydraulic excavator, cab frame

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Authors: Zerarka Hizia, Akchiche Mustapha, Prunier Florent

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The landslide of Ain El Hammam (AEH) is characterized by a complex geology and a high hydrogeology hazard. AEH's perpetual reactivation compels us to look closely at its triggers and to better understand the mechanisms of its evolution in mass and in depth. This study builds a numerical model to simulate the influencing factors such as precipitation, non-saturation, and pore pressure fluctuations, using Plaxis software. For a finer analysis of instabilities, we use Hill's criterion, based on the sign of the second order work, which is the most appropriate material stability criterion for non-associated elastoplastic materials. The results of this type of calculation allow us, in theory, to predict the shape and position of the slip surface(s) which are liable to ground movements of the slope, before reaching the rupture given by the plastic limit of Mohr Coulomb. To validate the numerical model, an analysis of inclinometer measures is performed to confirm the direction of movement and kinematic of the sliding mechanism of AEH’s slope.

Keywords: landslide, second order work, precipitation, inclinometers

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Authors: Maria Lazari, Lorenzo Sanavia

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Mechanics of unsaturated soils has been an active field of research in the last decades. Efficient constitutive models that take into account the partial saturation of soil are necessary to solve a number of engineering problems e.g. instability of slopes and cuts due to heavy rainfalls. A large number of constitutive models can now be found in the literature that considers fundamental issues associated with the unsaturated soil behaviour, like the volume change and shear strength behaviour with suction or saturation changes. Partially saturated soils may either expand or collapse upon wetting depending on the stress level, and it is also possible that a soil might experience a reversal in the volumetric behaviour during wetting. Shear strength of soils also changes dramatically with changes in the degree of saturation, and a related engineering problem is slope failures caused by rainfall. There are several states of the art reviews over the last years for studying the topic, usually providing a thorough discussion of the stress state, the advantages, and disadvantages of specific constitutive models as well as the latest developments in the area of unsaturated soil modelling. However, only a few studies focused on the coupling between partial saturation states and time effects on the behaviour of geomaterials. Rate dependency is experimentally observed in the mechanical response of granular materials, and a viscoplastic constitutive model is capable of reproducing creep and relaxation processes. Therefore, in this work an elasto-viscoplastic constitutive model for unsaturated soils is proposed and validated on the basis of experimental data. The model constitutes an extension of an existing elastoplastic strain-hardening constitutive model capable of capturing the behaviour of variably saturated soils, based on energy conjugated stress variables in the framework of superposed continua. The purpose was to develop a model able to deal with possible mechanical instabilities within a consistent energy framework. The model shares the same conceptual structure of the elastoplastic laws proposed to deal with bonded geomaterials subject to weathering or diagenesis and is capable of modelling several kinds of instabilities induced by the loss of hydraulic bonding contributions. The novelty of the proposed formulation is enhanced with the incorporation of density dependent stiffness and hardening coefficients in order to allow the modeling of the pycnotropy behaviour of granular materials with a single set of material constants. The model has been implemented in the commercial FE platform PLAXIS, widely used in Europe for advanced geotechnical design. The algorithmic strategies adopted for the stress-point algorithm had to be revised to take into account the different approach adopted by PLAXIS developers in the solution of the discrete non-linear equilibrium equations. An extensive comparison between models with a series of experimental data reported by different authors is presented to validate the model and illustrate the capability of the newly developed model. After the validation, the effectiveness of the viscoplastic model is displayed by numerical simulations of a partially saturated slope failure of the laboratory scale and the effect of viscosity and degree of saturation on slope’s stability is discussed.

Keywords: PLAXIS software, slope, unsaturated soils, Viscoplasticity

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Authors: Ladislav Écsi, Roland Jančo

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Contemporary multiplicative plasticity models assume that the body's intermediate configuration consists of an assembly of locally unloaded neighbourhoods of material particles that cannot be reassembled together to give the overall stress-free intermediate configuration since the neighbourhoods are not necessarily compatible with each other. As a result, the plastic deformation gradient, an inelastic component in the multiplicative split of the deformation gradient, cannot be integrated, and the material particle moves from the initial configuration to the intermediate configuration without a position vector and a plastic displacement field when plastic flow occurs. Such behaviour is incompatible with the continuum theory and the continuum physics of elastoplastic deformations, and the related material models can hardly be denoted as truly continuum-based. The paper presents a proper continuum-based reformulation of current problems in finite strain plasticity. It will be shown that the incompatible neighbourhoods in real material are modelled by the product of the plastic multiplier and the yield surface normal when the plastic flow is defined in the current configuration. The incompatible plastic factor can also model the neighbourhoods as the solution of the system of differential equations whose coefficient matrix is the above product when the plastic flow is defined in the intermediate configuration. The incompatible tensors replace the compatible spatial plastic velocity gradient in the former case or the compatible plastic deformation gradient in the latter case in the definition of the plastic flow rule. They act as local imperfections but have the same position vector as the compatible plastic velocity gradient or the compatible plastic deformation gradient in the definitions of the related plastic flow rules. The unstressed intermediate configuration, the unloaded configuration after the plastic flow, where the residual stresses have been removed, can always be calculated by integrating either the compatible plastic velocity gradient or the compatible plastic deformation gradient. However, the corresponding plastic displacement field becomes permanent with both elastic and plastic components. The residual strains and stresses originate from the difference between the compatible plastic/permanent displacement field gradient and the prescribed incompatible second-order tensor characterizing the plastic flow in the definition of the plastic flow rule, which becomes an assignment statement rather than an equilibrium equation. The above also means that the elastic and plastic factors in the multiplicative split of the deformation gradient are, in reality, gradients and that there is no problem with the continuum physics of elastoplastic deformations. The formulation is demonstrated in a numerical example using the regularized Mooney-Rivlin material model and modified equilibrium statements where the intermediate configuration is calculated, whose analysis results are compared with the identical material model using the current equilibrium statements. The advantages and disadvantages of each formulation, including their relationship with multiplicative plasticity, are also discussed.

Keywords: finite strain plasticity, continuum formulation, regularized Mooney-Rivlin material model, compatibility

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Authors: M. Khaing, A. V. Tkacheva

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The work is devoted to solving the problem of temperature stresses, caused by the heating point of the round plate. The plate is made of elastoplastic material, so the Prandtl-Reis model is used. A piecewise-linear condition of the Ishlinsky-Ivlev flow is taken as the loading surface, in which the yield stress depends on the temperature. Piecewise-linear conditions (Treska or Ishlinsky-Ivlev), in contrast to the Mises condition, make it possible to obtain solutions of the equilibrium equation in an analytical form. In the problem under consideration, using the conditions of Tresca, it is impossible to obtain a solution. This is due to the fact that the equation of equilibrium ceases to be satisfied when the two Tresca conditions are fulfilled at once. Using the conditions of plastic flow Ishlinsky-Ivlev allows one to solve the problem. At the same time, there are also no solutions on the edge of the Ishlinsky-Ivlev hexagon in the plane-stressed state. Therefore, the authors of the article propose to jump from the edge to the edge of the mine edge, which gives an opportunity to obtain an analytical solution. At the same time, there is also no solution on the edge of the Ishlinsky-Ivlev hexagon in a plane stressed state; therefore, in this paper, the authors of the article propose to jump from the side to the side of the mine edge, which gives an opportunity to receive an analytical solution. The paper compares solutions of the problem of plate thermal deformation. One of the solutions was obtained under the condition that the elastic moduli (Young's modulus, Poisson's ratio) which depend on temperature. The yield point is assumed to be parabolically temperature dependent. The main results of the comparisons are that the region of irreversible deformation is larger in the calculations obtained for solving the problem with constant elastic moduli. There is no repeated plastic flow in the solution of the problem with elastic moduli depending on temperature. The absolute value of the irreversible deformations is higher for the solution of the problem in which the elastic moduli are constant; there are also insignificant differences in the distribution of the residual stresses.

Keywords: temperature stresses, elasticity, plasticity, Ishlinsky-Ivlev condition, plate, annular heating, elastic moduli

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Authors: Akm Badrul Alam, Yoshiaki Fujii, Nahid Hasan Dipu, Shakil Ahmed Razo

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Shale rockmasses often include silt layers, impacting slope stability in construction and mining. Analyzing their interaction is crucial for long-term stability. A study used an elastoplastic model, incorporating the stress transfer method and Coulomb's criterion, to assess a shale rock mass with silt layers. It computed stress distribution, assessed failure potential, and identified vulnerable regions where nodal forces were calculated for a comprehensive analysis. A shale rock mass ranging from 14.75 to 16.75 meters thick, with silt layers varying from 0.36 to 0.5 meters, was considered in the model. It examined four silt layer conditions: horizontal (SiHL), vertical (SiVL), inclined against slope (SiIincAGS), and along slope (SilincALO). Mechanical parameters like uniaxial compressive strength (UCS), tensile strength (TS), Young’s modulus (E), Poisson’s ratio, and density were adjusted for varied scenarios: UCS (0.5 to 5 MPa), TS (0.1 to 1 MPa), and E (6 to 60 MPa). In elastic analysis of shale rock masses, stress distributions vary based on layer properties. When shale and silt layers have the same elasticity modulus (E), stress concentrates at corners. If the silt layer has a lower E than shale, marginal changes in maximum stress (σmax) occur for SilHL. A decrease in σmax is evident at SilVL. Slight variations in σmax are observed for SilincAGS and SilincALO. In the elastoplastic analysis, the overall decrease of 20%, 40%, 60%, 80%, and 90% was considered. For SilHL:(i) Same E, UCS, and TS for silt layer and shale, UCS/TS ratio 5: strength decrease led to shear (S), tension then shear (T then S) failure; noticeable failure at 60% decrease, significant at 80%, collapse at 90%. (ii) Lower E for silt layer, same strength as shale: No significant differences. (iii) Lower E and UCS, silt layer strength 1/10: No significant differences. For SilVL: (i) Same E, UCS, and TS for silt layer and shale, UCS/TS ratio 5: Similar effects as SilHL. (ii) Lower E for silt layer, same strength as shale: Slip occurred. (iii) Lower E and UCS, silt layer strength 1/10: Bitension failure also observed with larger slip. For SilincAGS: (i) Same E, UCS, and TS for silt layer and shale, UCS/TS ratio 5: Effects similar to SilHL. (ii) Lower E for silt layer, same strength as shale: Slip occurred. (iii) Lower E and UCS, silt layer strength 1/10: Tension failure also observed with larger slip. For SilincALO: (i) Same E, UCS, and TS for silt layer and shale, UCS/TS ratio 5: Similar to SilHL with tension failure. (ii) Lower E for silt layer, same strength as shale: No significant differences; failure diverged. (iii) Lower E and UCS, silt layer strength 1/10: Bitension failure also observed with larger slip; failure diverged. Toppling failure was observed for lower E cases of SilVL and SilincAGS. The presence of silt interlayers in shale greatly impacts slope stability. Designing slopes requires careful consideration of both the silt and shale's mechanical properties. The temporal degradation of strength in these layers is a major concern. Thus, slope design must comprehensively analyze the immediate and long-term mechanical behavior of interlayer silt and shale to effectively mitigate instability.

Keywords: shale rock masses, silt layers, slope stability, elasto-plastic model, temporal degradation

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Authors: Juan Huang, Hugo Ninanya

Abstract:

Oil has been used as a source of energy and supply to make materials, such as asphalt or rubber for many years. This is the reason why new technologies have been implemented through time. However, research still needs to continue increasing due to new challenges engineers face every day, just like unconventional reservoirs. Various numerical methodologies have been applied in petroleum engineering as tools in order to optimize the production of reservoirs before drilling a wellbore, although not all of these have the same efficiency when talking about studying fracture propagation. Analytical methods like those based on linear elastic fractures mechanics fail to give a reasonable prediction when simulating fracture propagation in ductile materials whereas numerical methods based on the cohesive zone method (CZM) allow to represent the elastoplastic behavior in a reservoir based on a constitutive model; therefore, predictions in terms of displacements and pressure will be more reliable. In this work, a hydro-geomechanical coupled model of horizontal wells in fractured rock was developed using ABAQUS; both extended element method and cohesive elements were used to represent predefined fractures in a model (2-D). A power law for representing the rheological behavior of fluid (shear-thinning, power index <1) through fractures and leak-off rate permeating to the matrix was considered. Results have been showed in terms of aperture and length of the fracture, pressure within fracture and fluid loss. It was showed a high infiltration rate to the matrix as power index decreases. A sensitivity analysis is conclusively performed to identify the most influential factor of fluid loss.

Keywords: fracture, hydro-geomechanical model, non-Newtonian fluid, numerical analysis, sensitivity analysis

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Authors: Tawanda Mushiri, Charles Mbohwa

Abstract:

When an external load is applied to one of its ends, a pipe’s bends cross section tends to deform significantly both in and out of its end plane. This shell type behaviour characteristic of pipe bends and mainly due to their curves geometry accounts for their greater flexibility. This added flexibility is also accompanied by stressed and strains that are much higher than those present in a straight pipe. The primary goal of this research is to study the elastic-plastic behaviour of pipe bends under out of plane moment loading. It is also required to study the effects of changing the value of the pipe bend factor and the value of the internal pressure on that behaviour and to determine the value of the limit moments in each case. The results of these analyses are presented in the form of load deflection plots for each load case belonging to each model. From the load deflection curves, the limit moments of each case are obtained. The limit loads are then compared to those computed using some of the analytical and empirical equation available in the literature. The effects of modelling parameters are also studied. The results obtained from small displacement and large displacement analyses are compared and the effects of using a strain hardened material model are also investigated. To better understand the behaviour of pipe elbows under out of plane bending and internal pressure, it was deemed important to know how the cross section deforms and to study the distribution of stresses that cause it to deform in a particular manner. An elbow with pipe bend factor h=0.1 to h=1 is considered and the results of the detailed analysis are thereof examined.

Keywords: elasto-plastic, finite element analysis, pipe bends, simulation

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Authors: Chinh Phuong Do

Abstract:

Dynamic analysis of slope under seismic condition requires the elimination of spurious reflection at the bounded domain. This paper studies the performances of wave transmitting boundaries, including the standard viscous boundary and the viscoelastic boundary to the material point method (MPM) framework. First, analytical derivations of these non-reflecting conditions particularly to the implicit MPM are presented. Then, a number of benchmark and geotechnical examples will be shown. Overall, the results agree well with analytical solutions, indicating the ability to accurately simulate the radiation at the bounded domain.

Keywords: dynamic analysis, implicit, MPM, non-reflecting boundary

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Authors: Abdullah Eqal Al Mazrooei

Abstract:

In this work, a new nonlinear model will be introduced. The model is in the state-space form. The nonlinearity of this model is in the state equation where the state vector is multiplied by its self. This technique makes our model generalizes many famous models as Lotka-Volterra model and Lorenz model which have many applications in the real life. We will apply our new model to estimate the wind speed by using a new nonlinear estimator which suitable to work with our model.

Keywords: nonlinear systems, state-space model, Kronecker product, nonlinear estimator

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Authors: Abdul Qader Melhem, Hacene Badache

Abstract:

This paper deals with the theoretical and experimental study of shear connection via simple steel reinforcement shear connectors, which are steel reinforcing bars bent into L-shapes, instead of commonly used headed studs. This suggested L-shape connectors are readily available construction material in steel reinforcement. The composite section, therefore, consists of steel inverted T-section being embedded within a lightly reinforced concrete flange at the top slab as a unit. It should be noted that the cross section of these composite models involves steel inverted T-beam, replacing the steel top flange of a standard commonly employed I-beam section. The paper concentrates on the elastic and elastic-plastic behavior of these composite models. Failure modes either by cracking of concrete or shear connection be investigated in details. Elastic and elastoplastic formulas of the composite model have been computed for different locations of NA. Deflection formula has been derived, its value was close to the test value. With a supportive designing curve, this curve is valuable for both designing engineers and researchers. Finally, suggested designing curves and valuable equations will be presented. A check is made between theoretical and experimental outcomes.

Keywords: composite, elastic-plastic, failure, inverted T-section, L-Shape connectors

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Authors: Mengxiao Li, Johnson Zhang

Abstract:

Currently, topology optimization technique is widely used to define the layout design of structures that are presented as truss-like topologies. However, due to the difficulty in combining optimization technique with more realistic material models where their nonlinear properties should be considered, the achieved optimized topologies are commonly unable to apply straight towards the practical design problems. This study presented an optimization procedure of composite structures where different elastic stiffness, yield criteria, and hardening models are assumed for the candidate materials. From the results, it can be concluded that a more explicit modeling has the significant influence on the resulting topologies. Also, the isotropic or kinematic hardening is important for elastoplastic structural optimization design. The capability of the proposed optimization procedure is shown through several cases.

Keywords: topology optimization, material composition, nonlinear modeling, hardening rules

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Authors: Entisar A. Elgmati

Abstract:

Recurrent infant diarrhea is studied using daily data collected in Salvador, Brazil over one year and three months. A logistic regression model is fitted instead of Aalen's additive model using the same covariates that were used in the analysis with the additive model. The model gives reasonably similar results to that using additive regression model. In addition, the problem with the estimated conditional probabilities not being constrained between zero and one in additive model is solved here. Also martingale residuals that have been used to judge the goodness of fit for the additive model are shown to be useful for judging the goodness of fit of the logistic model.

Keywords: additive model, cumulative probabilities, infant diarrhoea, recurrent event

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Authors: S. Ansari Sadrabadi, G. H. Rahimi

Abstract:

In this paper, thick walled Cylindrical tanks or tubes made of functionally graded material under internal pressure and temperature gradient are studied. Material parameters have been considered as power functions. They play important role in the elastoplastic behavior of these materials. To clarify their role, different materials with different parameters have been used under temperature gradient. Finally, their effect and loading effect have been determined in first yield point. Also, the important role of temperature gradient was also shown. At the end the study has been results obtained from changes in the elastic modulus and yield stress. Also special attention is also given to the effects of this internal pressure and temperature gradient in the creation of tensile and compressive stresses.

Keywords: FGM, cylindrical pressure tubes, small deformation theory, yield onset, thermal loading

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Authors: Sendi Zohra, Belhadjsalah Hedi, Labergere Carl, Saanouni Khemais

Abstract:

The modeling of mechanical problems including both material and geometric nonlinearities with Finite Element Method (FEM) remains challenging. Meshless methods offer special properties to get rid of well-known drawbacks of the FEM. The main objective of Meshless Methods is to eliminate the difficulty of meshing and remeshing the entire structure by simply insertion or deletion of nodes, and alleviate other problems associated with the FEM, such as element distortion, locking and others. In this study, a robust numerical implementation of an Element Free Galerkin Method for an elastoplastic coupled to damage problem is presented. Several results issued from the numerical simulations by a DynamicExplicit resolution scheme are analyzed and critically compared with Element Finite Method results. Finally, different numerical examples are carried out to demonstrate the efficiency of this method.

Keywords: damage, dynamic explicit, elastoplasticity, isotropic hardening, meshless

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Authors: João Paulo Pascon

Abstract:

In this work, a mixed 3D finite element formulation is proposed in order to analyze thermoviscoplastic materials under large strain levels and ductile damage. To this end, a tetrahedral element of linear order is employed, considering a thermoviscoplastic constitutive law together with the neo-Hookean hyperelastic relationship and a nonlocal Gurson`s porous plasticity theory The material model is capable of reproducing finite deformations, elastoplastic behavior, void growth, nucleation and coalescence, thermal effects such as plastic work heating and conductivity, strain hardening and strain-rate dependence. The nonlocal character is introduced by means of a nonlocal parameter applied to the Laplacian of the porosity field. The element degrees of freedom are the nodal values of the deformed position, the temperature and the nonlocal porosity field. The internal variables are updated at the Gauss points according to the yield criterion and the evolution laws, including the yield stress of matrix, the equivalent plastic strain, the local porosity and the plastic components of the Cauchy-Green stretch tensor. Two problems involving 3D specimens and ductile damage are numerically analyzed with the developed computational code: the necking problem and a notched sample. The effect of the nonlocal parameter and the mesh refinement is investigated in detail. Results indicate the need of a proper nonlocal parameter. In addition, the numerical formulation can predict ductile fracture, based on the evolution of the fully damaged zone.

Keywords: mixed finite element, large strains, ductile damage, thermoviscoplasticity

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Authors: Mechlouch Ridha Fethi

Abstract:

This paper presents a recent mathematical model in political sciences concerning democracy. The model is represented by a logarithmic equation linking the Relative Index of Democracy (RID) to Participation Ratio (PR). Firstly the meanings of the different parameters of the model were presented; and the variation curve of the RID according to PR with different critical areas was discussed. Secondly, the model was applied to a virtual group where we show that the model can be applied depending on the gender. Thirdly, it was observed that the model can be extended to different language models of democracy and that little use to assess the state of democracy for some International organizations like UNO.

Keywords: democracy, mathematic, modelization, quantification

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