Isotropic Stress Research Articles

A density functional theory perspective on the structural, elastic, thermal, and electronic properties of copper nitride doped with transition metal (Fe, Co, and Ni)

Abstract The present study demonstrates structural, elastic, thermal and electronic properties of transition metal M (M: Fe, Co and Ni) doped copper nitride (Cu3N) using pseudopotential based density functional calculations as implemented in Quantum ESPRESSO simulation code. The exchange-correlation is approximated by PBE-GGA functional. The doped matrices represented as Cu3NM are verified to be stable structures, both thermodynamically and mechanically. Tailoring of elastic properties and their anisotropy due to M doping has been successfully demonstrated through comprehensive analysis of the computed elastic stiffness coefficients, elastic moduli, elastic anisotropy factors and spatial variation of the elastic moduli, which were not explored yet. An increase in bulk modulus due to M doping ensures enhanced mechanical stability under isotropic stress. Conversely, while doping of Co and Ni enhances the shear resistance of the host material, Fe doping slightly reduces it. Superior ductile nature of all the studied systems predicts their suitability for application in flexible electronics. It is evident that doping of M substantially reduces the elastic anisotropy of Cu3N. Using the calculated elastic moduli, velocity of acoustic waves and its anisotropy for Cu3N and Cu3NM are also predicted. The anisotropy in the acoustic velocity of the studied materials recommends their potential application in acoustic devices with directional selectivity. It is also noticed that, while average acoustic velocity is reduced due to Fe doping, it increases for Co and Ni doping. Furthermore, analysis of computed Debye temperature and minimum thermal conductivity forecasts their employability as thermal barrier coatings. Finally, the calculations reveal ferromagnetic nature of Cu3NFe and Cu3NCo with respective induced magnetic moments of 2.71 and 1.47 μB/cell, recommending their potential application in spintronics. It is also proved that, the M-d ― Cu-d coupling stabilizes the ferromagnetic ordering in such magnetic systems. On the other hand, Cu3NNi is observed to be non-magnetic.

Chromatin-site-specific accessibility: A microtopography-regulated door into the stem cell fate.

Biomaterials that mimic extracellular matrix topography are crucial in tissue engineering. Previous research indicates that certain biomimetic topography can guide stem cells toward multiple specific lineages. However, the mechanisms by which topographic cues direct stem cell differentiation remain unclear. Here, we demonstrate that microtopography influences nuclear tension in mesenchymal stem cells (MSCs), shaping chromatin accessibility and determining lineage commitment. On aligned substrates, MSCs exhibit high cytoskeletal tension along the fiber direction, creating anisotropic nuclear stress that opens chromatin sites for neurogenic, myogenic, and tenogenic genes via transcription factors like Nuclear receptor TLX (TLX). In contrast, random substrates induce isotropic nuclear stress, promoting chromatin accessibility for osteogenic and chondrogenic genes through Runt-related transcription factors (RUNX). Our findings reveal that aligned and random microtopographies direct site-specific chromatin stretch and lineage-specific gene expression, priming MSCs for distinct lineages. This study introduces a novel framework for understanding how topographic cues govern cell fate in tissue repair and regeneration.

Polyaxial Stress-Dependent Tensorial Permeability Variations of a Columnar Jointed Rock Mass: Insights from 3D Distinct Element Method

AbstractStress-induced permeability changes in geological formations have implications for various geo-engineering applications. Fractures are the predominant fluid flow pathways within tight geological formations such as jointed basaltic rock mass. Three-dimensional permeability variations of a columnar jointed rock mass using the three-dimensional block distinct element method are investigated. First, a permeability tensor is constructed by simulating fluid flow through joint sets using cubic law and determining its principal components through eigenvector analysis. Subsequently, numerical simulations are conducted to gain insights into the impact of principal stresses on joint deformation and fluid flow. Joint deformation is controlled by the joint’s mechanical properties, contact models, and stress state. Different isotropic and anisotropic stress loading scenarios on the permeability tensor evolution are investigated. The research findings indicate that isotropic stress loading led to uniform normal compression on fractures, resulting in a monotonic reduction of all permeability tensor components and increased permeability anisotropy. Anisotropic stress loading, particularly the intermediate stress, often neglected, significantly influenced the rock’s overall permeability. While the directions of the principal components remained consistent during isotropic loading, they exhibited changes in both direction and magnitude during anisotropic loading. The relative angle between the joint plane and the principal stresses was crucial in controlling joint behavior, including normal compression, shear failure, and dilation. Additionally, data analysis revealed that the exponential empirical model provided an excellent fit for permeability–stress data.

A novel tube law analysis under anisotropic external load

Mathematical and physical modeling of flows in collapsible pipes often relates the flow area to the difference between the internal and the external pressures (i.e. the transmural pressure). The relation is used to model the conduits of the human body transporting biological fluids, is called tube law and usually considers the transmural pressure resulting from isotropic external pressure only. We provide a new empirical tube law considering anisotropic conditions of the external load; our formulation is based on the hypothesis, supported by clinical and experimental findings, that in physiological conditions both isotropic and anisotropic stresses are combined in the external load acting on vessels. The proposed mathematical model was validated through laboratory experiments reproducing the flow through a collapsible tube representing the physiological conditions of male urethra during micturition. The proposed tube law better agrees with the experimental observations, in comparison to classic formulations available in literature, thus showing that the proposed model better describes the physiological condition of flow in collapsible tubes subjected to anisotropic external load. The application of our model can be readily extended to several types of vessels.

Local Stress in Cylindrically Curved Lipid Membrane: Insights into Local Versus Global Lateral Fluidity Models.

Lipid membranes, which are fundamental to cellular function, undergo various mechanical deformations. Accurate modeling of these processes necessitates a thorough understanding of membrane elasticity. The lateral shear modulus, a critical parameter describing membrane resistance to lateral stresses, remains elusive due to the membrane's fluid nature. Two contrasting hypotheses, local fluidity and global fluidity, have been proposed. While the former suggests a zero local lateral shear modulus anywhere within lipid monolayers, the latter posits that only the integral of this modulus over the monolayer thickness vanishes. These differing models lead to distinct estimations of other elastic moduli and affect the modeling of biological processes, such as membrane fusion/fission and membrane-mediated interactions. Notably, they predict distinct local stress distributions in cylindrically curved membranes. The local fluidity model proposes isotropic local lateral stress, whereas the global fluidity model predicts anisotropy due to anisotropic local lateral stretching of lipid monolayers. Using molecular dynamics simulations, this study directly investigates these models by analyzing local stress in a cylindrically curved membrane. The results conclusively demonstrate the existence of static local lateral shear stress and anisotropy in local lateral stress within the monolayers of the cylindrical membrane, strongly supporting the global fluidity model. These findings have significant implications for the calculation of surface elastic moduli and offer novel insights into the fundamental principles governing lipid membrane elasticity.

Data‐Driven Tools to Evaluate Support Pressure, Radial Displacements, and Face Extrusion for Tunnels Excavated in Elastoplastic Grounds

ABSTRACTTwo‐dimensional analysis of tunnel design based on the convergence–confinement method, although commonly used in tunnel design, may not always be applied. For example, in squeezing grounds, if the support is installed very close to the tunnel face, three‐dimensional numerical modeling is required but is computationally expensive. Therefore, it is usually performed before or after tunnel excavation. A machine learning approach is presented here as an alternative to costly computations. Two surrogate models are developed based on synthetic data. The first model aims to assess the support pressure and the radial displacement at equilibrium in the lining and the radial displacement occurring close to the face at the installation distance of the support. The second model is intended to compute the extrusion of the core considering an unlined gallery. It is assumed a circular tunnel excavated in a Mohr–Coulomb elastoplastic perfectly plastic ground under an initial isotropic stress state. In particular, the bagging method is applied to neural networks to enhance the generalization capability of the models. A good performance is obtained using relatively scarce datasets. The modeling of the surrogate models is explained from the creation of the synthetic datasets to the evaluation of their performance. Their limitations are discussed. In practice, these two machine learning tools should be helpful in the field during the excavation phase.

A state-dependent bimodal soil water retention model considering evolutions of pore-scale soil–water interaction

Existing soil water retention models can capture the effects of void ratio and/or net mean stress on the changes in soil water retention curve (SWRC). However, most of them, especially those for bimodal soil that is composed of macro- and micro-pore systems, do not consider the simultaneous evolutions of pore structure and particle contacts, and neglected the drainage processes of bulk water and meniscus water when subjected to any external hydro-mechanical loading condition. This paper proposes a state-dependent bimodal SWRC model considering pore structure evolution and pore-scale water drainage. In this model, an elastoplastic relationship is introduced to describe the variations of void ratio with net mean stress and suction, whilst the corresponding changes in the pore structure are modelled by the shift and scaling of the pore-size distribution and the volumetric proportion between the macro- and micro-pore systems. By relating stress-induced changes in void ratio and coordination number to the mean pore radius and total meniscus water volume, respectively, the soil water content at different stages of water drainage can be determined. The model is validated against existing and new data, and can capture the effects of void ratio, isotropic stress, and K0 stress for unimodal and bimodal soils.

Analytical solutions considering face advance and time-dependent behavior for back-analysis of convergence measurements in deep circular tunnels under isotropic initial stress state

A methodology is presented for the back-analysis of convergence measurements in deep tunnels to determine the constitutive parameters of the surrounding rock mass. Since increasing deformations and stresses with time are due to both the face advance and the time-dependent behavior of the ground, the two effects must be considered during the excavations. To that end, an analytical solution assuming an unlined circular tunnel excavated in a homogeneous isotropic ground under an initial isotropic stress field and assuming a fractional viscoelastic plastic behavior is developed. A second closed-form solution is also derived assuming an instantaneous excavation. Additionally, combining the developed analytical solution that takes into account the progressive face advance and an empirical approach, convergences are back-analyzed based on a least-squares optimization method to calibrate the constitutive parameters of the ground. The presented methodology aims to characterize the long-term behavior of tunnels and offers the advantage of being directly applicable during the excavation phase as soon as convergence measurements are available. Finally, the method is illustrated by two case studies related to the Fréjus road tunnel and the Saint-Martin-la-Porte access gallery (SMP2).

Insight into the electronic, elastic, structural, thermal, and optical characteristics of potassium magnesium fluoride KMgF3 with isotropic external stress

The demand for increasingly fine detail in optical lithography for semiconductors necessitates the use of lower-wavelength lithographic light. This drives the need for lenses in optical lithography steppers made of vacuum ultraviolet-transparent (VUV-transparent) materials. In this work, the density functional theory (DFT) study of potassium magnesium fluoride KMgF3 is presented. Total energy was calculated with correlation functional generalized gradient approximation (GGA). The ground state quantities such as bulk modulus and lattice parameters have been evaluated. The material's cubic structure is scrutinized under various stress levels (0–100 GPa), revealing that KMgF3 starts to deform at 128 GPa. The C11, C12, and C44 independent elastic constants were used to analyze the structural stability of the KMgF3. The densities of states and electronic band structures have also been computed. According to electronic calculations, when stress is applied to KMgF3, the band gap increases for all values of stress (0–100 GPa). Mechanical parameters, including elastic constants and ratios, indicate the material's remarkable ductility and stability. Phonon density of states and thermal characteristics exhibit shifts and variations with increasing stress, providing insights into the material's behaviour below its melting point. The thermodynamic properties of KMgF3, such as enthalpy, free energy, entropy, heat capacity, and Debye temperatures at various temperatures ranging from 0 K to 1000 K, have also been examined to explore their basic properties. These findings contribute to a comprehensive understanding of KMgF3, opening avenues for its application in advanced technologies, particularly in the realms of semiconductors and optoelectronics.

Effect of stress conditions on concentrated leak erosion resistant of fine-grained soils with different characteristics

Internal erosion is one of the most important factors that cause earth structures that retain water, such as embankment dams, to collapse. Concentrated leak erosion, one of the forms of internal erosion, occurs in cracked fine-grained soils and pressurized flow conditions. To evaluate the concentrated leak erosion risk of cracks/voids, it is necessary to ascertain the erosion resistance of these materials. The erosion rate and critical shear stresses determine internal erosion resistance in concentrated leak erosion. This study determined soil’s concentrated leak erosion resistance using test equipment that allowed the flow to pass through a hole with stress-free (no loading), anisotropic-compression stress, anisotropic-expansion stress, and isotropic stress conditions. The stresses that developed in the samples’ hole wall where erosion occurred were determined with numerical modeling as pre-experimental stress conditions. The experiments were performed under a single hydraulic head on four selected cohesive soils with different erosion sensitivity. Time-dependent flow rates obtained from the test system can be used to determine hydraulic parameters, such as energy grade lines, with the help of basic theorems of pipe hydraulics in theoretical hydraulic models. Moreover, the erosion rates were quantitatively determined using the continuity equation, while critical shear stresses were qualitatively compared for concentrated leak erosion developed by the dispersion mechanism. As a result of the experiments, stress conditions influence the concentrated leak erosion resistance in the soil samples with dispersive erosion. Moreover, the shear strength in the Mohr–Coulomb hypothesis can explain the erosion resistance in these soils under stress conditions depending on the sand/clay ratio.

Hydrostatic pressure drives sprouting angiogenesis via adherens junction remodelling and YAP signalling

Endothelial cell physiology is governed by its unique microenvironment at the interface between blood and tissue. A major contributor to the endothelial biophysical environment is blood hydrostatic pressure, which in mechanical terms applies isotropic compressive stress on the cells. While other mechanical factors, such as shear stress and circumferential stretch, have been extensively studied, little is known about the role of hydrostatic pressure in the regulation of endothelial cell behavior. Here we show that hydrostatic pressure triggers partial and transient endothelial-to-mesenchymal transition in endothelial monolayers of different vascular beds. Values mimicking microvascular pressure environments promote proliferative and migratory behavior and impair barrier properties that are characteristic of a mesenchymal transition, resulting in increased sprouting angiogenesis in 3D organotypic model systems ex vivo and in vitro. Mechanistically, this response is linked to differential cadherin expression at the adherens junctions, and to an increased YAP expression, nuclear localization, and transcriptional activity. Inhibition of YAP transcriptional activity prevents pressure-induced sprouting angiogenesis. Together, this work establishes hydrostatic pressure as a key modulator of endothelial homeostasis and as a crucial component of the endothelial mechanical niche.

How Energy Dissipation Mode Controls the Evolution of Multiple Plane‐Strain Hydraulic Fractures Under Isotropic Stresses

AbstractThe geometrical prediction of multiple hydraulic fractures fed from a single fluid source is a major challenge due to transient stress interference among fractures and nonlinear coupling between rock deformation and fluid flow. Here we find that the evolution of multiple hydraulic fractures under isotropic stresses is controlled by a dimensionless toughness, which measures the ratio of the energy dissipated in rock fracturing to that dissipated in viscous fluid flow. The existence of a relation between the dimensionless toughness and the dimensionless length of the arrested fractures is demonstrated by using a bifurcation analysis. The numerical results show that the fractures tend to grow simultaneously in the viscosity‐dominated regime, and the scaling remains effective when the number of fractures varies. This study provides a quantitative and efficient tool for predicting the fracture pattern in engineered and natural fracture systems.

Impact of scan strategy on principal stresses in laser powder bed fusion

Additive manufacturing techniques, such as laser powder bed fusion (PBF-LB), are well known for their exceptional freedom in part design. However, these techniques are also characterized by the development of large thermal gradients during production and thus residual stress (RS) formation in produced parts. In this context, neutron diffraction enables the non-destructive characterization of the bulk RS distribution. By control of the thermal gradients in the powder-bed plane by scan strategy variation we study the impact of in-process scan strategy variations on the microstructure and the three-dimensional distribution of RS. Microstructural analysis by means of electron backscatter diffraction reveals sharp microstructure transitions at the interfaces ranging from 100-200 µm. The components of the RS tensor are determined by means of neutron diffraction and the principal stress directions and magnitudes are determined by eigenvalue decomposition. We find that the distribution of RS in the powder-bed plane corresponds to the underlying scan strategy. When the alternating scan vectors align with the x- and y sample coordinate axes, the principal stress directions co-align. In the present geometry, nearly transverse isotropic stress states develop when the scan vectors are either aligned 45° between x and y or continuously rotated by 67° between each layer.

A modified constitutive model for whole-life thermal-mechanical fatigue incorporating dynamic strain aging in 316LN stainless steel

A comprehensive analysis of experimental data is presented for 316LN stainless steel subjected to isothermal and thermal-mechanical fatigue loading conditions within the temperature range of 350–600 °C. The study aims to provide a thorough understanding of the cyclic behavior through meticulous data integration, supplementation, and the use of stress decomposition methods combined with a classical damage evolution definition. The modeling approach employed in this study is based on the classical AF-OW-Kang model, with the incorporation of the Arrhenius term in the plastic flow rate equation. Furthermore, to consider the effect of dynamic strain aging at varying temperatures, temperature-dependent terms are introduced into the equations that govern the evolution of isotropic stress and backstress, resulting in enhanced accuracy in describing cyclic hardening behavior. Additionally, a modified damage evolution equation is utilized, along with equations for isotropic stress and backstress evolution, to address cyclic softening. Simulation results confirm the effectiveness of the modified model in capturing the cyclic hardening/softening behavior of 316LN stainless steel throughout the whole-life time, under both isothermal and thermal-mechanical fatigue loading conditions.

Control of Modular Tissue Flows Shaping the Embryo in Avian Gastrulation.

Avian gastrulation requires coordinated flows of thousands of cells to form the body plan. We quantified these flows using their fundamental kinematic units: one attractor and two repellers constituting its Dynamic Morphoskeleton (DM). We have also elucidated the mechanistic origin of the attractor, marking the primitive streak (PS), and controlled its shape, inducing gastrulation flows in the chick embryo that are typical of other vertebrates. However, the origins of repellers and dynamic embryo shape remain unclear. Here, we address these questions using active matter physics and experiments. Repeller 1, separating the embryo proper (EP) from extraembryonic (EE) tissues, arises from the tug-of-war between EE epiboly and EP isotropic myosin-induced active stress. Repeller 2, bisecting the anterior and posterior PS and associated with embryo shape change, arises from anisotropic myosin-induced active intercalation in the mesendoderm. Combining mechanical confinement with inhibition of mesendoderm induction, we eliminated either one or both repellers, as predicted by our model. Our results reveal a remarkable modularity of avian gastrulation flows delineated by the DM, uncovering the mechanistic roles of EE epiboly, EP active constriction, mesendoderm intercalation and ingression. These findings offer a new perspective for deconstructing morphogenetic flows, uncovering their modular origin, and aiding synthetic morphogenesis.

Effects of isotropic stress on the band structure elastic, optical, thermal, and x-ray diffraction properties of TiSnO3.

Cubic perovskite titanium stannous oxide (TiSnO3) is a promising material for various applications due to its functional properties. However, understanding how these properties change under external stress is crucial for its development and optimization. This study employed density functional theory calculations to investigate the structural, electronic, optical, thermal, and mechanical properties of TiSnO3 under varying degrees of external static isotropic stress (0-120 GPa). The study reveals a significant decrease in the bandgap of TiSnO3 with increasing stress due to lattice modifications and the formation of delocalized electrons. Partial density of states analysis indicates that Sn and O states play a key role in shaping the electronic band structure. TiSnO3 exhibits increased light absorption with stress, accompanied by a blue shift in absorption peaks, whereas, both polarizability and refractive index decrease with increasing stress. Mechanically, all elastic moduli (bulk, shear, and Young's) show an increase under stress, signifying a stiffening response of the material under stress. Similarly, the Pugh ratio suggests a transition from ductile to brittle behaviour at elevated stress levels. Phonon dispersion calculations indicate the instability of the cubic phase at 0 K. However, a phonon gap emerges at 30 GPa and widens with increasing stress. X-ray diffraction further supports these findings by demonstrating a shift in diffraction peaks towards higher angles with increasing stress, consistent with the applied stress. In conclusion, this computational study offers a thorough understanding of how external stress influences the properties of TiSnO3, providing valuable insights for potential applications in various fields.

An Innovative Experimental Methodology for Testing Anisotropic Permeabilities of Formation Rocks

Abstract The permeability of reservoir rocks is a typical anisotropic property. Accurate testing and characterization of reservoir in situ anisotropic permeability is crucial for geo-energy applications including geothermal energy extraction, hydrocarbon reservoir development, coalbed methane production, and carbon dioxide geological sequestration. In this work, a novel experimental apparatus was designed to more precisely determine the permeability tensor of reservoir rocks. The device can independently apply stresses in different directions to simulate in situ reservoir stress conditions and reservoir temperatures. The experiment can accurately measure the principal components of the permeability tensor in three directions for rock samples while effectively avoiding experimental errors caused by internal structure damage during disassembly. Using the self-developed apparatus, anisotropic permeability tests were conducted on sandstone, shale, and coal samples. The results show that the three-dimensional permeability of rock samples under in situ reservoir stress conditions is lower than under isotropic stress conditions. However, the variation magnitude of the three-dimensional permeability differs between the three rock types because of lithological differences. This confirms the difference in data between the proposed anisotropic permeability test method and other traditional methods. We also observed that for rocks without distinct oriented internal structures like sandstone, anisotropic permeability is more sensitive to (normal) stress changes. In contrast, for rocks with oriented pore structures such as shale and coal, the degree of anisotropic permeability is less sensitive to (normal) stress changes. The proposed novel anisotropic permeability test method obtains more accurate and realistic data under simulated in situ stress conditions compared with existing methods. It can evaluate rock properties and optimize geothermal or hydrocarbon production well designs to improve production efficiency.

A Volterra edge dislocation problem in second-order elasticity theory

A displacement function technique has been developed to study plane strain problems in second-order elasticity theory for incompressible elastic materials. The formulation culminates in the development of a single inhomogeneous biharmonic equation of the form ∇ 4 Ψ 2 ( x ) = f ( x ) for the second-order displacement function Ψ 2 ( x ) . In the second-order, the isotropic stress associated with constitutive behaviour is governed by an inhomogeneous harmonic equation of the form ∇ 2 p 2 ( x ) = g ( x ) . Both functions f ( x ) and g ( x ) depend only on the solution to the analogous problem in classical elasticity. While there are similarities to the Airy stress function, the displacement function approach enables the evaluation of the first- and second-order displacement fields purely through its derivatives, thus eliminating the introduction of arbitrary rigid body terms normally associated with formulations where the strains derived from a stress function approach need to be integrated. The displacement function approach is applied to develop a second-order elasticity solution to the problem of a Volterra edge dislocation.

Cyclic cumulative strain of coarse-grained soil under large cyclic stress amplitude

The deformation behavior of coarse-grained soil under large cyclic stresses, such as those induced by strong earthquakes, has received limited attention. This study aims to investigate the cyclic accumulation behaviors and hysteresis loops of coarse-grained soil during drained cyclic triaxial tests, spanning a range from small to large cyclic stresses. The cyclic triaxial tests were primarily conducted under anisotropic consolidation conditions, with an axial-to-radial stress ratio of 2.0, confining pressures ranging from 100 to 500 kPa, and cyclic stresses varying from 0.01 to 1.85 times the confining pressure. Additionally, cyclic triaxial tests under isotropic consolidation conditions and constant mean stress conditions were performed for comparison and validation. The test results reveal that the properties of the hysteresis loops exhibit significant nonlinear behavior as cyclic stress increases, particularly concerning their shape, symmetry, degree of closure, and initial tangent modulus of elasticity. The cumulative axial strain displays three stages: strain increases slightly and gently at small cyclic stress, increases rapidly and substantially at medium cyclic stress, and decreases at large cyclic stress. The delineation of these phases is largely governed by the behaviors observed during the first cycle. Moreover, the cumulative volumetric strain increases monotonically with the increase of cyclic stress, with a more rapid increase at large cyclic stress. This study provides valuable insights into the cyclic deformation and constitutive modeling of coarse-grained soil under significant cyclic stress.

An effective stress-based DSC model for predicting hydromechanical shear behavior of unsaturated collapsible soils subjected to initial shear stress

Evaluation of hydromechanical shear behavior of unsaturated soils is still a challenging issue. The time and cost needed for conducting precise experimental investigation on shear behavior of unsaturated soils have encouraged several investigators to develop analytical, empirical, or semi-empirical models for predicting the shear behavior of unsaturated soils. However, most of the previously proposed models are for specimens subjected to the isotropic state of stress, without considering the effect of initial shear stress. In this study, a hydromechanical constitutive model is proposed for unsaturated collapsible soils during shearing, with consideration of the effect of the initial shear stress. The model implements an effective stress-based disturbed state concept (DSC) to predict the stress-strain behavior of the soil. Accordingly, material/state variables were defined for both the start of the shearing stage and the critical state of the soil. A series of laboratory tests was performed using a fully automated unsaturated triaxial device to verify the proposed model. The experimental program included 23 suction-controlled unsaturated triaxial shear tests on reconstituted specimens of Gorgan clayey loess wetted to different levels of suctions under both isotropic and anisotropic stress states. The results show excellent agreement between the prediction by the proposed model and the experimental results.