General Stress State Research Articles

On anisotropic local bifurcation based on hypoplastic model

The incipience of shear band in homogeneous granular materials is well captured by the bifurcation analysis. Most bifurcation analyses are based on isotropic plastic constitutive models. In this paper, a hypoplastic constitutive model is presented by considering a fabric tensor for inherent anisotropy. Based on this model, we carry out bifurcation analysis for the plane strain case, and then extend the analysis to consider general three-dimensional stress state. The theoretical results are compared with experiments on sand conducted using a plane strain device and a true triaxial device. It's indicated the salient features of stress-strain behaviour and shear band formation are well captured by our analyses.

Derivation, characterization, and application of complete orthonormal sequences for representing general three-dimensional states of residual stress

Residual stresses are self-equilibrated stresses on unloaded bodies. Owing to their complex origins, it is useful to develop functions that can be linearly combined to represent any sufficiently regular residual stress field. In this work, we develop orthonormal sequences that span the set of all square-integrable residual stress fields on a given three-dimensional region. These sequences are obtained by extremizing the most general quadratic, positive-definite functional of the stress gradient on the set of all sufficiently regular residual stress fields subject to a prescribed normalization condition; each such functional yields a sequence. For the special case where the sixth-order coefficient tensor in the functional is homogeneous and isotropic and the fourth-order coefficient tensor in the normalization condition is proportional to the identity tensor, we obtain a three-parameter subfamily of sequences. Upon a suitable parameter normalization, we find that the viable parameter space corresponds to a semi-infinite strip. For a further specialized spherically symmetric case, we obtain analytical expressions for the sequences and the associated Lagrange multipliers. Remarkably, these sequences change little across the entire parameter strip. To illustrate the applicability of our theoretical findings, we employ three such spherically symmetric sequences to accurately approximate two standard residual stress fields. Our work opens avenues for future exploration into the implications of different sequences, achieved by altering both the spatial distribution and the material symmetry class of the coefficient tensors, toward specific objectives.

A numerical method for calculating the long-term settlement of three-dimensional subgrade under numerous traffic loads

Settlement problems caused by various traffic loads significantly impact infrastructure sustainability. Accurately predicting the long-term settlement of subgrade is crucial for improving infrastructure resilience. This study determined the element strain of soil using an explicit strain model, based on the bounding surface model and associated flow rules. Using the method of generalized shear strain equivalent, a cyclic cumulative factor is proposed for determining the magnitude of cumulative strain increment. The direction of plastic strain increment was determined using the bounding surface model combined with associated flow rules. A cumulative strain calculation method integrating the bounding surface and explicit strain models under general stress states was established. This computational method, combined with equivalent finite elements, can be used for calculating the long-term settlement of three-dimensional subgrade under numerous cyclic loads at general stress states through a user-defined subroutine provided by the commercial finite element modeling (FEM) software. The reliability of the method was verified through unit tests.

Quantifying tidal versus non-tidal stresses in driving time-varying fluxes of Enceladus' plume eruptions

In this study we investigate the relative importance of endogenic vs. exogenic stresses in controlling the location and timing of active ice-shell deformation on Enceladus, which is expressed by cyclic plume eruptive flux along active fault zones (i.e., the tiger stripes). Although the variation of the eruption flux on Enceladus follows the periodicity of the diurnal tide, it remains unclear why there is a consistent phase delay of the observed peak eruption when compared to the predicted peak tidal stress. Here, we explore whether endogenic stresses in the ice shell are capable of explaining this observed phase delay. To achieve this goal, we performed geologic mapping along the tiger-stripe faults that host the erupting plumes. Using the fault kinematics established from our mapping, we determine the general stress state (i.e., the principal-stress directions) along the tiger-stripe faults. This knowledge in turn forms the basis for inferring the most likely plume-eruption mechanism. Our mapping shows that the tiger-stripe fractures are not tensile cracks but are instead left-slip fault zones locally displaying extensional fissures. This insight leads to a hypothesis that strike-slip faults and their local tensile cracks experience simultaneous shear and tensile failure, and that the tensional opening reaches maximum at the time of the peak plume flux. We quantified this hypothesis using a stress decomposition model that assesses (1) the relative importance in magnitude between the tectonic stress and tidal stress exerted on the tiger-stripe faults and (2) the role of ice shell properties such as the shear strengths, tensile strengths, and ice shell thickness in controlling the eruption phase delay. Using laboratory-determined ice strengths and the best estimate of the ice shell thickness at the South Polar Terrain of Enceladus, which hosts the tiger-stripe faults, our model results indicate that the endogenic tectonic stress is comparable in magnitude to the tidal stress. Although we cannot rule out warm-ice convection, true polar wander, and non-synchronous rotation as causes of endogenic stresses, the large variation in ice shell thickness makes the lateral gravitational-potential gradient the most plausible source of the endogenic stress required by our model results.

A state-dependent non-orthogonal elastoplastic constitutive model for sand

The state-dependent deformation behavior of sand is reinterpreted from the perspective of strain increment magnitude and direction by analyzing the existing test data. A state-dependent non-orthogonal elastoplastic constitutive model for sand is established by incorporating the state variable into plastic strain increment magnitude and direction, respectively. For the magnitude of plastic strain increment, an S-type isotropic compression hardening rule applicable in large stress ranges is proposed, which is extended into a new hardening parameter for general stress states. Furthermore, the state variable is introduced into the newly proposed hardening parameter to consider the state dependence. On the other hand, the non-orthogonal plastic flow rule is employed to determine the plastic strain increment direction. To consider its state dependence, the relationship between the state variable and the parameter controlling the plastic flow direction is established. The comparison with the test results of four types of sand demonstrates that the proposed model can reasonably capture the state-dependent deformation behaviors of plastic strain increment magnitude and direction of sand.

A conceptual three-dimensional frictional model to predict the effect of the intermediate principal stress based on the Mohr-Coulomb and Hoek-Brown failure criteria

The intermediate effective principal stress has a considerable influence on rock strength as shown by true-triaxial data on intact rock. Therefore, a failure criterion that incorporates all three principal stresses may provide an improved prediction of failure than one that considers only the major and minor effective principal stresses. This study introduces a generalisation method, which converts two-dimensional failure criteria (i.e., Mohr-Coulomb and Hoek-Brown failure criteria) to three-dimensional failure criteria, for the prediction of this true-triaxial data. This method is based on a physical mechanism, and it assumes that the potential failure surface of a material has roughness, which provides additional frictional resistance when the intermediate effective principal stress is greater than the minor effective principal stress. This roughness is introduced theoretically by assuming a repeating diamond-shaped element over the failure surface. These roughness elements have the same dip as predicted by the Mohr-Coulomb and Hoek-Brown failure criteria but are offset by the dip direction angle which is assumed similar to that calculated traditionally from the major effective principal stress direction to the failure surface. With this roughness, it is shown that the major effective principal stress at failure can be predicted using an explicit solution that uses the intermediate and minor effective principal stresses and the Mohr-Coulomb or Hoek-Brown parameters as inputs. This generalisation predicts the same strength as the Mohr-Coulomb or Hoek-Brown failure criteria under conventional triaxial loading conditions, when the intermediate and minor effective principal stresses are equal. Under general stress conditions, this generalisation produces results that are aligned closely with the true-triaxial data as well as other previous theoretical predictions. This method importantly gives a possible physical mechanism for the strengthening influence of the intermediate effective principal stress. This may lead to a more accurate prediction of the rock strength under general stress conditions.

Elastic stability of a lattice of cross-braced shear deformable beams

A plane metamaterial made up of a periodic square grid of shear deformable beams has been braced by crossing cables. This coupling, widely adopted in structural engineering, is here applied with the aim of enhancing the stability performance of a periodic material. Under suitable assumptions, analytical solutions for a rich variety of critical modes and the stability domain are determined by the Bloch wave approach and the effectiveness of our analytical results has been verified by numerical simulations. Furthermore, the experimental response of a specimen, in which hierarchical beams composed by lower order elements are modeled as equivalent shear deformable beams, has shown a satisfactory agreement with our analytical solutions. We argue that our analytical model can be efficiently used to tailor the buckling response of various new metamaterials under general plane stress states.

Time domain analytical bounds to the homogenized viscous kernels of linear viscoelastic composites

New extremum principles in linear viscoelasticity are derived from general stationarity ones proposed in Carini and Mattei (2015), exploiting suitable selections of the admissible fields in the associated convolutive functionals. These new extremum principles have therefore a restricted validity. Analytical bounds to the homogenized viscous kernels of linear viscoelastic composites are derived in the time domain. In the restricted case of macroscopically isotropic composite materials, six new bounds are obtained from the new extremum principles. These bounds can be derived exploiting the choice of Representative Volume Elements (RVEs) loaded in a purely deviatoric way only. Two strict lower bounds to the homogenized viscous kernels, of the Reuss type, are also derived. One of these was already proposed in Huet (1995), and is valid for generic linear viscoelastic composites under general stress and strain states. The other Reuss-type strict lower bound is new, but has the same limited validity as the first six ones. The new upper bounds for isotropic composites, obtained both in terms of viscous kernels and of their time rates, as well as the strict lower bounds, are extensions to viscoelasticity of the Voigt and Reuss bounds for linear elastic composites. The performance of the obtained bounds is checked by comparison with numerical solutions. It is worth remarking that the use of the new extremum theorems for the purpose of deriving bounds is not possible in a general RVE stress case, i.e., deviatoric plus volumetric. As a consequence, the non-strict bounds holding for the case of deviatoric RVE loading are not valid for the volumetric case. The reason for this difference is not yet fully understood.

Tetrandrine Derivatives as Promising Antibacterial Agents.

This work reports on the antibacterial activity of two tetrandrine derivatives, with acridine (MAcT) and anthracene (MAnT) units, against Gram-positive and Gram-negative bacteria of clinical importance by the broth microdilution method as well as their antioxidant activity against ABTS•+ and DPPH•+ radicals. Unlike natural tetrandrine, its derivatives inhibited bacterial growth, showing selectivity against Staphylococcus aureus with notable activity of MAnT (MIC = 0.035 μg/mL); this compound also has good activity against the ABTS•+ radical (IC50 = 4.59 μg/mL). Cell membrane integrity studies and reactive oxygen species (ROS) detection by fluorescent stains helped to understand possible mechanisms related to antibacterial activity, while electrophoretic mobility assays showed that the derivatives can bind to bacterial DNA plasmid. The results indicate that MAnT can induce a general state of oxidative stress in S. aureus and Escherichia coli, while MAcT induces an oxidative response in S. aureus. Complementary electrochemical studies were included.

DEM Analysis of Fabric Evolution and Behavior of Granular Geomaterials in True Triaxial Test with Flexible Boundary

The fabric of granular geomaterials used in roads and embankments is related to properties such as shear strength, permeability and liquefaction resistance. To evaluate the fabric evolution and behavior of geomaterials, a series of the true triaxial test simulations with flexible boundaries under general stress states in this study were performed using the three-dimensional discrete element method (DEM). First, the stress states at the axial strain of 20%, which indicates that the stress under the critical state conforms to the Matsuoka-Nakai criterion, were examined. Then the uniqueness of the coordination number and non-uniqueness of void ratio and invariant of anisotropic fabric tensor under the critical state were investigated based on the contact density, which indicates the relative number of contacts in different orientations. In particular, the contact density at the critical state under different mean effective principal stresses with its effects on the invariant of anisotropic fabric tensor were discussed. It was found that the contribution of the contact density to the fabric anisotropy decreased as the mean effective principal stress increased due to geometric limitations.

A thermal elastic visco-plastic model for soft clayey soils

It is frequently observed that the stress–strain behaviour of soft clayey soils is affected by temperature changes. Development and verification of a reliable constitutive model with consideration of variable temperature conditions are necessary. Due to the significant rheological and other nonlinear properties of clayey soils, the coupled effects of temperature, time dependency, structuration, nonlinear creep, and anisotropy should be considered in the constitutive model. In this study, a new three-dimensional (3D) thermal elastic visco-plastic model is established and verified for the time-dependent stress–strain behaviour of clayey soils considering temperature changes. The model is developed based on the existing elastic visco-plastic models with the equivalent time concept, the overstress theory, and the critical state model. The thermal elastic line and virgin heating line are introduced and generalized to construct constitutive equations for both thermal elastic and thermal visco-plastic behaviour of clayey soils in general stress conditions. After establishing the 3D basic model, further refinement is introduced to consider the nonlinear creep behaviour and structuration for natural and reconstituted clayey soils. Finally, the model is successfully validated by a series of laboratory test data on different clayey soils under variable temperature paths with reasonably good accuracy.

A Three-Dimensional Elastoplastic Constitutive Model for Geomaterials

The Mohr-Coulomb (M-C) failure criterion has been a popular choice for geotechnical analysis because of its simplicity and ease of use. The fact that the M-C criterion disregards the intermediate principal stress’s impact is a significant drawback. As a result, the M-C criterion is only applied to materials under biaxial stress. This paper presents a three-dimensional version of the M-C criterion. The proposed criterion, called the Generalized Mohr-Coulomb (GMC) criterion, considers the intermediate principal stress’s effect, in addition to inheriting the original M-C criterion’s benefits. We obtained the conditions that the strength parameters must satisfy when the GMC criterion fulfills the π plane’s convexity. The GMC criterion can better describe geotechnical materials’ strengths under general stress conditions. Based on an implicit algorithm, the user material subroutine (UMAT) of the three-dimensional GMC model was developed in ABAQUS using the Fortran programming language. The established elastoplastic model’s validity and the program’s accuracy were examined using numerical simulation. Finally, a numerical simulation of a three-dimensional tunnel excavation under various working conditions was performed. The calculation results from the GMC model are precise and have some engineering-related practical significance.

Positive Psychology as a Tool for Staff Motivation

Abstract. Introduction. In the conditions of martial law in Ukraine, the problem of effective application of positive psychology as a tool for motivating the personnel of enterprises is relevant and important. The general state of stress from the existence of a constant threat to the national security and territorial integrity of Ukraine affects the psychological state of enterprise personnel, in particular, the motivation to work. The use of positive psychology as a tool for motivating staff can contribute to raising the morale of employees, strengthen their faith in their own strength and the positive result of their work, and reduce the risk of burnout at work in this difficult period for the country. In these conditions, the problem of effective application of positive psychology as a tool for motivating the personnel of enterprises is important and meets the current needs of society. Purpose. The purpose of the article is to substantiate the theoretical and methodological principles and practical approaches to the application of positive psychology as a tool for motivating the personnel of enterprises. Results. The main principles of applying positive psychology as a tool for motivating the personnel of enterprises are systematized. The global experience of the effective application of positive psychology as a tool for motivating the personnel of enterprises has been studied, namely: the «Googliness» program and the principle of «20% time on one's own project» of the Google company; positive psychology programs to increase staff motivation and Zappos' «responsible leisure» practices; Marriott International's «Positive Workplace» program aimed at improving the working environment and increasing staff satisfaction; Adobe Systems' Check-In program. The main techniques of positive thinking and optimism, which can be useful for increasing staff motivation, are summarized. Conclusions. It is concluded that the application of elements of positive psychology in the personnel policy of the enterprise can help to increase the motivation of employees, improve productivity and ensure job satisfaction.

In Vitro Nano-Polystyrene Toxicity: Metabolic Dysfunctions and Cytoprotective Responses of Human Spermatozoa.

The ubiquitous spread of Polystyrene nanoplastics (PS-NPs) has rendered chronic human exposure an unavoidable phenomenon. The biodistribution of such particles leads to bioaccumulation in target organs including the testis, the site of sperm maturation. The purpose of this research has been to estimate the impact of PS-NPs (50 and 100 nm) on the metabolism of mature spermatozoa. The analysis of the semen parameters has revealed a higher toxicity of the smaller sized PS-NPs, which have negatively affected major organelles, leading to increased acrosomal damage, oxidative stress with the production of ROS, DNA fragmentation, and decreased mitochondrial activity. PS-NPs of 100 nm, on the other hand, have mainly affected the acrosome and induced a general state of stress. An attempt has also been made to highlight possible protective mechanisms such as the expression of HSP70s and their correlation among various parameters. The results have evinced a marked production of HSP70s in the samples exposed to the smaller PS-NPs, negatively correlated with the worsening in oxidative stress, DNA fragmentation, and mitochondrial anomalies. In conclusion, our results have confirmed the toxicity of PS-NPs on human spermatozoa but have also demonstrated the presence of mechanisms capable of counteracting at least in part these injuries.

The Influence of the COVID-19 Pandemic Emergency on Alcohol Use: A Focus on a Cohort of Sicilian Workers.

The period between the beginning and the end of the COVID-19 pandemic emergency generated a general state of stress, affecting both the mental state and physical well-being of the general population. Stress is the body's reaction to events or stimuli perceived as potentially harmful or distressing. Particularly when prolonged over time, it can promote the consumption of different psychotropic substances such as alcohol, and thus the genesis of various pathologies. Therefore, our research aimed to evaluate the differences in alcohol consumption in a cohort of 640 video workers who carried out activities in smart working, subjects particularly exposed to stressful situations due to the stringent rules of protection and prevention implemented during the pandemic. Furthermore, based on the results obtained from the administration of the AUDIT-C, we wanted to analyse the different modes of alcohol consumption (low, moderate, high, severe) to understand whether there is a difference in the amount of alcohol consumed that could predispose individuals to health problems. To this end, we administered the AUDIT-C questionnaire in two periods (T0 and T1), coinciding with annual occupational health specialist visits. The results of the present research showed an increase in the number of subjects consuming alcohol (p = 0.0005) and in their AUDIT-C scores (p < 0.0001) over the period considered. A significant decrease in subgroups who drink in a low-risk (p = 0.0049) mode and an increase in those with high (p = 0.00012) and severe risk (p = 0.0002) were also detected. In addition, comparing the male and female populations, it emerged that males have drinking patterns that lead to a higher (p = 0.0067) health risk of experiencing alcohol-related diseases than female drinking patterns. Although this study provides further evidence of the negative impact of the stress generated by the pandemic emergency on alcohol consumption, the influence of many other factors cannot be ruled out. Further research is needed to better understand the relationship between the pandemic and alcohol consumption, including the underlying factors and mechanisms driving changes in drinking behaviour, as well as potential interventions and support strategies to address alcohol-related harm during and after the pandemic.

Non-linear elastic tension–compression asymmetric anisotropic model for fibre-reinforced composite materials

We present a novel constitutive model capable of describing non-linear anisotropic fibre-reinforced materials with different responses in tension and compression under a general stress state. The model is based on the original one-dimensional Ramberg–Osgood model, which is generalized to a multiaxial stress state and anisotropic material behaviour under thermodynamic requirements. To account for tension–compression asymmetry under a multiaxial stress state, the model is extended by the use of the stress triaxiality invariant as an indicator of stress state type, e.g. shear, uniaxial or biaxial tension, compression, etc. The model is implemented in ABAQUS/Explicit via the VUMAT subroutine and verified on two material datasets, which are an S2-glass/E773-epoxy and a reinforced polyester composite material. In comparison with other models, the proposed model provides an elegant formulation for the description of all the aforementioned phenomena, resulting in a simple calibration procedure based on uniaxial tensile and compressive tests.

The change of glass transition temperature under general stress state in amorphous materials

The phenomenon of the change in glass transition temperature (Tg) upon externally applied stresses in amorphous materials has been known for a long time. However, most of the existing works focus on the effects of hydrostatic stress state, while the effect of a general stress state on glass transition behaviors remains largely unknown. In this work, molecular dynamics (MD) simulations are first performed on typical amorphous polymers and alloys to probe the change of Tg under different stress states. It is found that Tg changes linearly with pure hydrostatic stress, while under shear stress, Tg changes nonlinearly with the stress magnitude. This further leads to an asymmetric change in Tg under uniaxial tension and compression loading conditions. Based on the above observations, a theoretical model based on the free volume theory and Eyring model is proposed to quantify the change of Tg under general stress states. Comparison with simulation results and existing experimental data reported in the literature demonstrate that the theoretical model can capture the stress dependence of Tg in amorphous materials. Potential applications in tuning Tg through external stress and the sensitivity of Tg to hydrostatic and shear stresses for different amorphous materials are subsequently discussed. The current work reveals the dependence of Tg on general stress states, pointing out potential routes to tune the mechanical properties of amorphous materials.

Study of Energy Dissipation in a Two-Phase Soil System

The dependence of energy dissipation coefficient on filtration properties and on creep characteristics of soil skeleton is examined. The study was carried out on the basis of the general solution of the joint task of creep and consolidation theory for a two-phase soil system obtained on the basis of the generalized model of bulk forces, taking into account the interaction of soil phases, changes over time in the general stress state at any point of the soil and additional pressures in pore water, and incomplete transfer of external pressure to the pore water. Interactions between phases are taken into account in the solution of the one-dimensional joint task of the theory of creep and consolidation, and the creep kernel is taken in the form of an exponential function. The formula for the deformation of two-phase soils is presented as the sum of two syllables due to primary and secondary consolidation of the soil. The strain formula uses experimentally obtained values of filtration characteristics and creep parameters of the soil skeleton. Using the formulas obtained, hysteresis loops under sinusoidal stress changes can be plotted and the energy expended per deformation cycle and the dissipation coefficient for two-phase soil can be obtained.

Cyclic stress–dilatancy relations and plastic flow potentials for soils based on hypothesis of complementarity of stress–dilatancy conjugates

Soil, rocks and rock masses dilate or compact when sheared, i.e., distortion necessitates volume change. This coupling between distortional strains and volumetric strains, described by stress–dilatancy theories, endows soils with manifestation of peculiar characteristics when they are subjected to shear. Stress–dilatancy theories have become central in describing the mechanical energy dissipation mechanism and further establishing flow rules in constitutive modelling of soils. The classical stress–dilatancy theories, such as Taylor's and Rowe's, are endowed with simplicity and descriptive power, but they were developed for describing the dilatancy behaviour of soils subjected to loading in shear (mobilizing away from isotropic stress state) and needed to be extended for describing plastic dissipation and shear-induced volumetric changes when soils are subjected to cyclic shear. In this paper, hypothesis of complementarity of stress–dilatancy conjugates is proposed as a unifying hypothesis for deriving stress–dilatancy relations for both loading in shear and unloading in shear. Then, plastic potential functions are derived based on the resulting stress–dilatancy relations. In so doing, the resulting stress–dilatancy relations and plastic potential functions are rendered with a quality to be used for the modelling of deformation behavior of soils subjected to both monotonic and cyclic shearing. The theoretical framework is applied first for plane strain and axisymmetric stress–strain conditions; and then extended for the general stress condition considering the Lode angle dependency of the shear strength of soils, using the multilaminate framework and applying the Matsuoka–Nakai spatial mobilized plane.

Multi-scale analysis of shear behaviour of crushable granular sand under general stress conditions

Grain crushing underpins key mechanical behaviours of granular materials. A variety of factors, including grading, particle shapes and loading conditions, have been recognised to affect the crushability of grains and the overall behaviour of a granular material. Among them, the role of intermediate principal stress in a general stress condition on the shear behaviour of crushable granular sand remains less understood, owing to the scarcity of experimental data and analytical tools available. In this paper, a multi-scale computational approach is employed to investigate the shear behaviour of crushable granular sand under general stress conditions with varying intermediate principal stresses and confining pressures. The computational approach features multi-scale coupling between non-smooth contact dynamics and peridynamics, and offers a rigorous way to consider the intertwined evolution of particle size and shape during the process of grain crushing. The numerical study helps to quantify comprehensively and analyse the grain crushing-induced changes of macro- and micro-scale material behaviours including strength, deformability, particle size and shape evolution, particle-scale forces and contact conditions, and the development of anisotropy. The competition between a void-filling mechanism due to grain size change and enhanced friction and interlocking due to grain shape change in dictating the deformation of crushable sand is further discussed. The findings offer insights into the complex behaviours of crushable granular materials under general stress conditions and facilitate future development of physics-based constitutive theories on crushable sand.