Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 19

Search results for: non-homogeneous

19 Nonhomogeneous Linear Second Order Differential Equations and Resonance through Geogebra Program

Authors: F. Maass, P. Martin, J. Olivares

Abstract:

The aim of this work is the application of the program GeoGebra in teaching the study of nonhomogeneous linear second order differential equations with constant coefficients. Different kind of functions or forces will be considered in the right hand side of the differential equations, in particular, the emphasis will be placed in the case of trigonometrical functions producing the resonance phenomena. In order to obtain this, the frequencies of the trigonometrical functions will be changed. Once the resonances appear, these have to be correlationated with the roots of the second order algebraic equation determined by the coefficients of the differential equation. In this way, the physics and engineering students will understand resonance effects and its consequences in the simplest way. A large variety of examples will be shown, using different kind of functions for the nonhomogeneous part of the differential equations.

Keywords: education, geogebra, ordinary differential equations, resonance

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18 Using Nonhomogeneous Poisson Process with Compound Distribution to Price Catastrophe Options

Authors: Rong-Tsorng Wang

Abstract:

In this paper, we derive a pricing formula for catastrophe equity put options (or CatEPut) with non-homogeneous loss and approximated compound distributions. We assume that the loss claims arrival process is a nonhomogeneous Poisson process (NHPP) representing the clustering occurrences of loss claims, the size of loss claims is a sequence of independent and identically distributed random variables, and the accumulated loss distribution forms a compound distribution and is approximated by a heavy-tailed distribution. A numerical example is given to calibrate parameters, and we discuss how the value of CatEPut is affected by the changes of parameters in the pricing model we provided.

Keywords: catastrophe equity put options, compound distributions, nonhomogeneous Poisson process, pricing model

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17 Flow Dynamics of Nanofluids in a Horizontal Cylindrical Annulus Using Nonhomogeneous Dynamic Model

Authors: M. J. Uddin, M. M. Rahman

Abstract:

Transient natural convective flow dynamics of nanofluids in a horizontal homocentric annulus using nonhomogeneous dynamic model has been experimented numerically. The simulation is carried out for four different shapes of the inner wall, which is either cylindrical, elliptical, square or triangular. The outer surface of the annulus is maintained at constant low temperature while the inner wall is maintained at a uniform temperature; higher than the outer one. The enclosure is permeated by a uniform magnetic field having variable orientation. The Brownian motion and thermophoretic deposition phenomena of the nanoparticles are taken into account in model construction. The governing nonlinear momentum, energy, and concentration equations are solved numerically using Galerkin weighted residual finite element method. To find the best performer, the local Nusselt number is demonstrated for different shapes of the inner wall. The heat transfer enhancement for different nanofluids for four different shapes of the inner wall is exhibited.

Keywords: nanofluids, annulus, nonhomogeneous dynamic model, heat transfer

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16 A Semi-Analytical Method for Analysis of the Axially Symmetric Problem on Indentation of a Hot Circular Punch into an Arbitrarily Nonhomogeneous Halfspace

Authors: S. Aizikovich, L. Krenev, Y. Tokovyy, Y. C. Wang

Abstract:

An approximate analytical-numerical solution to the axisymmetric problem on thermo-mechanical indentation of a flat cylindrical punch into an arbitrarily non-homogeneous elastic half-space is constructed by making use of the bilateral asymptotic method. The key point of this method lies in evaluation of the ker¬nels in the obtained integral equations by making use of a numerical technique. Once the structure of the kernel is defined, it then is approximated by an analytical expression of special kind so that the solution of the integral equation can be achieved analytically. This fact allows for construction of the solution in an analytical form, which is convenient for analysis of the mechanical effects concerned with arbitrarily presumed non-homogeneity of the material.

Keywords: contact problem, circular punch, arbitrarily-nonhomogeneous halfspace

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15 Modeling of Radiofrequency Nerve Lesioning in Inhomogeneous Media

Authors: Nour Ismail, Sahar El Kardawy, Bassant Badwy

Abstract:

Radiofrequency (RF) lesioning of nerves have been commonly used to alleviate chronic pain, where RF current preventing transmission of pain signals through the nerve by heating the nerve causing the pain. There are some factors that affect the temperature distribution and the nerve lesion size, one of these factors is the inhomogeneities in the tissue medium. Our objective is to calculate the temperature distribution and the nerve lesion size in a nonhomogenous medium surrounding the RF electrode. A two 3-D finite element models are used to compare the temperature distribution in the homogeneous and nonhomogeneous medium. Also the effect of temperature-dependent electric conductivity on maximum temperature and lesion size is observed. Results show that the presence of a nonhomogeneous medium around the RF electrode has a valuable effect on the temperature distribution and lesion size. The dependency of electric conductivity on tissue temperature increased lesion size.

Keywords: finite element model, nerve lesioning, pain relief, radiofrequency lesion

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14 Numerical Simulation of Convective Flow of Nanofluids with an Oriented Magnetic Field in a Half Circular-Annulus

Authors: M. J. Uddin, M. M. Rahman

Abstract:

The unsteady convective heat transfer flow of nanofluids in a half circular-annulus shape enclosure using nonhomogeneous dynamic model has been investigated numerically. The round upper wall of the enclosure is maintained at constant low temperature whereas the bottom wall is heated by three different thermal conditions. The enclosure is permeated by a uniform magnetic field having variable orientation. The Brownian motion and thermophoretic phenomena of the nanoparticles are taken into account in model construction. The governing nonlinear momentum, energy, and concentration equations are solved numerically using Galerkin weighted residual finite element method. To discover the best performer, the average Nusselt number is demonstrated for different types of nanofluids. The heat transfer rate for different flow parameters, positions of the annulus, thicknesses of the half circular-annulus and thermal conditions is also exhibited.

Keywords: nanofluid, convection, semicircular-annulus, nonhomogeneous dynamic model, finite element method

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13 Nonhomogeneous Linear Fractional Differential Equations Will Bessel Functions of the First Kind Giving Hypergeometric Functions Solutions

Authors: Fernando Maass, Pablo Martin, Jorge Olivares

Abstract:

Fractional derivatives have become very important in several areas of Engineering, however, the solutions of simple differential equations are not known. Here we are considering the simplest first order nonhomogeneous differential equations with Bessel regular functions of the first kind, in this way the solutions have been found which are hypergeometric solutions for any fractional derivative of order α, where α is rational number α=m/p, between zero and one. The way to find this result is by using Laplace transform and the Caputo definitions of fractional derivatives. This method is for values longer than one. However for α entire number the hypergeometric functions are Kumer type, no integer values of alpha, the hypergeometric function is more complicated is type ₂F₃(a,b,c, t2/2). The argument of the hypergeometric changes sign when we go from the regular Bessel functions to the modified Bessel functions of the first kind, however it integer seems that using precise values of α and considering no integers values of α, a solution can be obtained in terms of two hypergeometric functions. Further research is required for future papers in order to obtain the general solution for any rational value of α.

Keywords: Caputo, fractional calculation, hypergeometric, linear differential equations

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12 Further Results on Modified Variational Iteration Method for the Analytical Solution of Nonlinear Advection Equations

Authors: A. W. Gbolagade, M. O. Olayiwola, K. O. Kareem

Abstract:

In this paper, further to our result on recent paper on the solution of nonlinear advection equations, we present further results on the nonlinear nonhomogeneous advection equations using a modified variational iteration method.

Keywords: lagrange multiplier, non-homogeneous equations, advection equations, mathematics

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11 Strength Analysis of RCC Dams Subject to the Layer-by-Layer Construction Method

Authors: Archil Motsonelidze, Vitaly Dvalishvili

Abstract:

Existing roller compacted concrete (RCC) dams indicate that the layer-by-layer construction method gives considerable economies as compared with the conventional methods. RCC dams have also gained acceptance in the regions of high seismic activity. Earthquake resistance analysis of RCC gravity dams based on nonlinear finite element technique is presented. An elastic-plastic approach is used to describe the material of a dam while it is under static conditions (period of construction). Seismic force, as an acceleration equivalent to that produced by a real earthquake, is supposed to act when the dam is completed. The materials of the dam and foundation may be nonhomogeneous and anisotropic. The “dam-foundation” system is idealized as a plain strain problem.

Keywords: finite element method, layer-by-layer construction, RCC dams, strength analysis

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10 Hypergeometric Solutions to Linear Nonhomogeneous Fractional Equations with Spherical Bessel Functions of the First Kind

Authors: Pablo Martin, Jorge Olivares, Fernando Maass

Abstract:

The use of fractional derivatives to different problems in Engineering and Physics has been increasing in the last decade. For this reason, we have here considered partial derivatives when the integral is a spherical Bessel function of the first kind in both regular and modified ones simple initial conditions have been also considered. In this way, the solution has been found as a combination of hypergeometric functions. The case of a general rational value for α of the fractional derivative α has been solved in a general way for alpha between zero and two. The modified spherical Bessel functions of the first kind have been also considered and how to go from the regular case to the modified one will be also shown.

Keywords: caputo fractional derivatives, hypergeometric functions, linear differential equations, spherical Bessel functions

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9 Assessment of Residual Stress on HDPE Pipe Wall Thickness

Authors: D. Sersab, M. Aberkane

Abstract:

Residual stresses, in high-density polyethylene (HDPE) pipes, result from a nonhomogeneous cooling rate that occurs between the inner and outer surfaces during the extrusion process in manufacture. Most known methods of measurements to determine the magnitude and profile of the residual stresses in the pipe wall thickness are layer removal and ring slitting method. The combined layer removal and ring slitting methods described in this paper involves measurement of the circumferential residual stresses with minimal local disturbance. The existing methods used for pipe geometry (ring slitting method) gives a single residual stress value at the bore. The layer removal method which is used more in flat plate specimen is implemented with ring slitting method. The method permits stress measurements to be made directly at different depth in the pipe wall and a well-defined residual stress profile was consequently obtained.

Keywords: residual stress, layer removal, ring splitting, HDPE, wall thickness

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8 Torsional Rigidities of Reinforced Concrete Beams Subjected to Elastic Lateral Torsional Buckling

Authors: Ilker Kalkan, Saruhan Kartal

Abstract:

Reinforced concrete (RC) beams rarely undergo lateral-torsional buckling (LTB), since these beams possess large lateral bending and torsional rigidities owing to their stocky cross-sections, unlike steel beams. However, the problem of LTB is becoming more and more pronounced in the last decades as the span lengths of concrete beams increase and the cross-sections become more slender with the use of pre-stressed concrete. The buckling moment of a beam mainly depends on its lateral bending rigidity and torsional rigidity. The nonhomogeneous and elastic-inelastic nature of RC complicates estimation of the buckling moments of concrete beams. Furthermore, the lateral bending and torsional rigidities of RC beams and the buckling moments are affected from different forms of concrete cracking, including flexural, torsional and restrained shrinkage cracking. The present study pertains to the effects of concrete cracking on the torsional rigidities of RC beams prone to elastic LTB. A series of tests on rather slender RC beams indicated that torsional cracking does not initiate until buckling in elastic LTB, while flexural cracking associated with lateral bending takes place even at the initial stages of loading. Hence, the present study clearly indicated that the un-cracked torsional rigidity needs to be used for estimating the buckling moments of RC beams liable to elastic LTB.

Keywords: lateral stability, post-cracking torsional rigidity, uncracked torsional rigidity, critical moment

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7 Full-Field Estimation of Cyclic Threshold Shear Strain

Authors: E. E. S. Uy, T. Noda, K. Nakai, J. R. Dungca

Abstract:

Cyclic threshold shear strain is the cyclic shear strain amplitude that serves as the indicator of the development of pore water pressure. The parameter can be obtained by performing either cyclic triaxial test, shaking table test, cyclic simple shear or resonant column. In a cyclic triaxial test, other researchers install measuring devices in close proximity of the soil to measure the parameter. In this study, an attempt was made to estimate the cyclic threshold shear strain parameter using full-field measurement technique. The technique uses a camera to monitor and measure the movement of the soil. For this study, the technique was incorporated in a strain-controlled consolidated undrained cyclic triaxial test. Calibration of the camera was first performed to ensure that the camera can properly measure the deformation under cyclic loading. Its capacity to measure deformation was also investigated using a cylindrical rubber dummy. Two-dimensional image processing was implemented. Lucas and Kanade optical flow algorithm was applied to track the movement of the soil particles. Results from the full-field measurement technique were compared with the results from the linear variable displacement transducer. A range of values was determined from the estimation. This was due to the nonhomogeneous deformation of the soil observed during the cyclic loading. The minimum values were in the order of 10-2% in some areas of the specimen.

Keywords: cyclic loading, cyclic threshold shear strain, full-field measurement, optical flow

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6 Influences of Slope Inclination on the Storage Capacity and Stability of Municipal Solid Waste Landfills

Authors: Feten Chihi, Gabriella Varga

Abstract:

The world's most prevalent waste management strategy is landfills. However, it grew more difficult due to a lack of acceptable waste sites. In order to develop larger landfills and extend their lifespan, the purpose of this article is to expand the capacity of the construction by varying the slope's inclination and to examine its effect on the safety factor. The capacity change with tilt is mathematically determined. Using a new probabilistic calculation method that takes into account the heterogeneity of waste layers, the safety factor for various slope angles is examined. To assess the effect of slope variation on the overall safety of landfills, over a hundred computations were performed for each angle. It has been shown that capacity increases significantly with increasing inclination. Passing from 1:3 to 2:3 slope angles and from 1:3 to 1:2 slope angles, the volume of garbage that can be deposited increases by 40 percent and 25 percent, respectively, of the initial volume. The results of the safety factor indicate that slopes of 1:3 and 1:2 are safe when the standard method (homogenous waste) is used for computation. Using the new approaches, a slope with an inclination of 2:3 can be deemed safe, despite the fact that the calculation does not account for the safety-enhancing effect of daily cover layers. Based on the study reported in this paper, the malty layered nonhomogeneous calculating technique better characterizes the safety factor. As it more closely resembles the actual state of landfills, the employed technique allows for more flexibility in design parameters. This work represents a substantial advance in limiting both safe and economical landfills.

Keywords: landfill, municipal solid waste, slope inclination, capacity, safety factor

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5 The Effect of Discontinued Water Spray Cooling on the Heat Transfer Coefficient

Authors: J. Hrabovský, M. Chabičovský, J. Horský

Abstract:

Water spray cooling is a technique typically used in heat treatment and other metallurgical processes where controlled temperature regimes are required. Water spray cooling is used in static (without movement) or dynamic (with movement of the steel plate) regimes. The static regime is notable for the fixed position of the hot steel plate and fixed spray nozzle. This regime is typical for quenching systems focused on heat treatment of the steel plate. The second application of spray cooling is the dynamic regime. The dynamic regime is notable for its static section cooling system and moving steel plate. This regime is used in rolling and finishing mills. The fixed position of cooling sections with nozzles and the movement of the steel plate produce nonhomogeneous water distribution on the steel plate. The length of cooling sections and placement of water nozzles in combination with the nonhomogeneity of water distribution leads to discontinued or interrupted cooling conditions. The impact of static and dynamic regimes on cooling intensity and the heat transfer coefficient during the cooling process of steel plates is an important issue. Heat treatment of steel is accompanied by oxide scale growth. The oxide scale layers can significantly modify the cooling properties and intensity during the cooling. The combination of the static and dynamic (section) regimes with the variable thickness of the oxide scale layer on the steel surface impact the final cooling intensity. The study of the influence of the oxide scale layers with different cooling regimes was carried out using experimental measurements and numerical analysis. The experimental measurements compared both types of cooling regimes and the cooling of scale-free surfaces and oxidized surfaces. A numerical analysis was prepared to simulate the cooling process with different conditions of the section and samples with different oxide scale layers.

Keywords: heat transfer coefficient, numerical analysis, oxide layer, spray cooling

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4 Multicellular Cancer Spheroids as an in Vitro Model for Localized Hyperthermia Study

Authors: Kamila Dus-Szachniewicz, Artur Bednarkiewicz, Katarzyna Gdesz-Birula, Slawomir Drobczynski

Abstract:

In modern oncology hyperthermia (HT) is defined as a controlled tumor heating. HT treatment temperatures range between 40–48 °C and can selectively damage heat-sensitive cancer cells or limit their further growth, usually with minimal injury to healthy tissues. Despite many advantages, conventional whole-body and regional hyperthermia have clinically relevant side effects, including cardiac and vascular disorders. Additionally, the lack of accessibility of deep-seated tumor sites and impaired targeting micrometastases renders HT less effective. It is believed that above disadvantages can significantly overcome by the application of biofunctionalized microparticles, which can specifically target tumor sites and become activated by an external stimulus to provide a sufficient cellular response. In our research, the unique optical tweezers system have enabled capturing the silica microparticles, primary cells and tumor spheroids in highly controllable and reproducible environment to study the impact of localized heat stimulation on normal and pathological cell and within multicellular tumor spheroid. High throughput spheroid model was introduced to better mimic the response to HT treatment on tumors in vivo. Additionally, application of local heating of tumor spheroids was performed in strictly controlled conditions resembling tumor microenvironment (temperature, pH, hypoxia, etc.), in response to localized and nonhomogeneous hyperthermia in the extracellular matrix, which promotes tumor progression and metastatic spread. The lack of precise control over these well- defined parameters in basic research leads to discrepancies in the response of tumor cells to the new treatment strategy in preclinical animal testing. The developed approach enables also sorting out subclasses of cells, which exhibit partial or total resistance to therapy, in order to understand fundamental aspects of the resistance shown by given tumor cells in response to given therapy mode and conditions. This work was funded by the National Science Centre (NCN, Poland) under grant no. UMO-2017/27/B/ST7/01255.

Keywords: cancer spheroids, hyperthermia, microparticles, optical tweezers

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3 Fracture Behaviour of Functionally Graded Materials Using Graded Finite Elements

Authors: Mohamad Molavi Nojumi, Xiaodong Wang

Abstract:

In this research fracture behaviour of linear elastic isotropic functionally graded materials (FGMs) are investigated using modified finite element method (FEM). FGMs are advantageous because they enhance the bonding strength of two incompatible materials, and reduce the residual stress and thermal stress. Ceramic/metals are a main type of FGMs. Ceramic materials are brittle. So, there is high possibility of crack existence during fabrication or in-service loading. In addition, damage analysis is necessary for a safe and efficient design. FEM is a strong numerical tool for analyzing complicated problems. Thus, FEM is used to investigate the fracture behaviour of FGMs. Here an accurate 9-node biquadratic quadrilateral graded element is proposed in which the influence of the variation of material properties is considered at the element level. The stiffness matrix of graded elements is obtained using the principle of minimum potential energy. The implementation of graded elements prevents the forced sudden jump of material properties in traditional finite elements for modelling FGMs. Numerical results are verified with existing solutions. Different numerical simulations are carried out to model stationary crack problems in nonhomogeneous plates. In these simulations, material variation is supposed to happen in directions perpendicular and parallel to the crack line. Two special linear and exponential functions have been utilized to model the material gradient as they are mostly discussed in literature. Also, various sizes of the crack length are considered. A major difference in the fracture behaviour of FGMs and homogeneous materials is related to the break of material symmetry. For example, when the material gradation direction is normal to the crack line, even under applying the mode I loading there exists coupled modes I and II of fracture which originates from the induced shear in the model. Therefore, the necessity of the proper modelling of the material variation should be considered in capturing the fracture behaviour of FGMs specially, when the material gradient index is high. Fracture properties such as mode I and mode II stress intensity factors (SIFs), energy release rates, and field variables near the crack tip are investigated and compared with results obtained using conventional homogeneous elements. It is revealed that graded elements provide higher accuracy with less effort in comparison with conventional homogeneous elements.

Keywords: finite element, fracture mechanics, functionally graded materials, graded element

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2 Wound Healing Process Studied on DC Non-Homogeneous Electric Fields

Authors: Marisa Rio, Sharanya Bola, Richard H. W. Funk, Gerald Gerlach

Abstract:

Cell migration, wound healing and regeneration are some of the physiological phenomena in which electric fields (EFs) have proven to have an important function. Physiologically, cells experience electrical signals in the form of transmembrane potentials, ion fluxes through protein channels as well as electric fields at their surface. As soon as a wound is created, the disruption of the epithelial layers generates an electric field of ca. 40-200 mV/mm, directing cell migration towards the wound site, starting the healing process. In vitro electrotaxis, experiments have shown cells respond to DC EFs polarizing and migrating towards one of the poles (cathode or anode). A standard electrotaxis experiment consists of an electrotaxis chamber where cells are cultured, a DC power source and agar salt bridges that help delaying toxic products from the electrodes to attain the cell surface. The electric field strengths used in such an experiment are uniform and homogeneous. In contrast, the endogenous electric field strength around a wound tend to be multi-field and non-homogeneous. In this study, we present a custom device that enables electrotaxis experiments in non-homogeneous DC electric fields. Its main feature involves the replacement of conventional metallic electrodes, separated from the electrotaxis channel by agarose gel bridges, through electrolyte-filled microchannels. The connection to the DC source is made by Ag/AgCl electrodes, incased in agarose gel and placed at the end of each microfluidic channel. An SU-8 membrane closes the fluidic channels and simultaneously serves as the single connection from each of them to the central electrotaxis chamber. The electric field distribution and current density were numerically simulated with the steady-state electric conduction module from ANSYS 16.0. Simulation data confirms the application of nonhomogeneous EF of physiological strength. To validate the biocompatibility of the device cellular viability of the photoreceptor-derived 661W cell line was accessed. The cells have not shown any signs of apoptosis, damage or detachment during stimulation. Furthermore, immunofluorescence staining, namely by vinculin and actin labelling, allowed the assessment of adhesion efficiency and orientation of the cytoskeleton, respectively. Cellular motility in the presence and absence of applied DC EFs was verified. The movement of individual cells was tracked for the duration of the experiments, confirming the EF-induced, cathodal-directed motility of the studied cell line. The in vitro monolayer wound assay, or “scratch assay” is a standard protocol to quantitatively access cell migration in vitro. It encompasses the growth of a confluent cell monolayer followed by the mechanic creation of a scratch, representing a wound. Hence, wound dynamics was monitored over time and compared for control and applied the electric field to quantify cellular population motility.

Keywords: DC non-homogeneous electric fields, electrotaxis, microfluidic biochip, wound healing

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1 Improved Elastoplastic Bounding Surface Model for the Mathematical Modeling of Geomaterials

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

Abstract:

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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