Stress Space Research Articles

A CSS surface based THM bounding constitutive model for volumetric behavior of bentonite

Development of the constitutive model for bentonite under coupled thermo-hydro-mechanical (THM) condition is of great significance for the construction and safety assessment of deep geological disposal repositories for high-level radioactive waste (HLW). In this work, a new temperature-suction-mean net stress (T-s-p) space with the conception of critical saturated state (CSS) surface was defined to represent the actual stress state of bentonite under coupled THM condition. Then, based on the CSS surface, a THM constitutive model was proposed for describing the volumetric behavior of compacted bentonite. Under the THM model framework, two bounding surfaces were proposed to describe the elastoplastic volume changes induced by mechanical response of skeleton and hydration of montmorillonite, respectively. The model responses upon some typical THM paths were simulated and discussed to reveal the performance of the proposed constitutive model for bentonite. Finally, the proposed model was validated by simulating by several volume change tests carried out on different bentonites. The results confirmed that the proposed model shows more advantages in describing the THM volumetric behavior.

Phase-field anisotropic damage with bond-slip model for reinforced concrete beam under the service load

Concrete, as a quasi-brittle material, undergoes a latent damage accumulation preceding macroscopic crack formation, which is further complicated by the intricate interaction between steel reinforcements and concrete in reinforced concrete (RC) structures. Traditional approaches inadequately capture these nuances, especially when it comes to the seamless transition from numerous micro cracks to a visible macro cracks. Phase-field damage theory stands out as a sophisticated tool, integrating sharp cracks into a continuous damage field representation and detailing the entire process of micro-to-macroscopic cracking evolution. In this work, a phase-field damage model that accounts for bond-slip behavior is proposed, grounded in the principle of stress space decomposition to address the inherent tension–compression anisotropy. Newton’s method with a viscosity coefficient of 0.001 enhances simulation accuracy and robustness through optimal convergence. The comparison between rigid bond and bond slip mechanisms indicates a significant difference in their impact on crack modes, revealing the necessity of considering bond slip. As the steel reinforcement ratio increases, the RC beam’s load-bearing capacity increases incrementally, concurrently exhibiting a reduction in macroscopic cracks, steel reinforcement stress, and overall damage severity. However, the comparative advantage of rigid bond in improving RC beam’s resistance against cracking begins to wane as the reinforcement proportion rises. This study thus sheds light on the nuanced interplay between bond characteristics and the cracking behavior of RC beams, providing a comprehensive and advanced perspective.

A computed tomography-based limit analysis approach to investigate the mechanical behavior of the human femur prone to fracture

The paper proposes a refined CT-based FE modelling strategy that implements a limit analysis numerical procedure, namely the Elastic Compensation Method (ECM), to estimate a lower bound to the collapse load of a human femur. In particular, the model geometry was obtained from CT images by segmentation of a fresh-frozen human cadaveric femur that was discretized with second-order tetrahedral 3D finite elements. A yield criterion of Tsai–Wu-type, expressed in principal stress space, was adopted to model the bone tissues for which the strength limit values in tension, compression and shear are computed locally from the femoral density distribution also derived from CT images. The developed CT-based numerical technique showed the ability to predict, at least for the examined femur for which the experimental collapse load is available, a lower bound to the collapse load. The proposed approach seems a promising and effective tool that could be adopted into clinical practice to predict the fracture risk of human femur starting from patient-specific data given by medical imaging.

Experimental investigation on mechanical behavior of natural soft clay by true triaxial tests

Laboratory tests on undisturbed and remolded Shanghai clay were conducted with a novel mixed boundary true triaxial apparatus. The strength and deformation behaviors of the structured soft clay at different Lode angles were carefully investigated. The relationship between the shear stress ratio and the dilatancy ratio of the clay in three different stress spaces, that is p–q space, TS stress space and tij modified stress space, are discussed in detail. In particular, the influences of the stress path and the structure of non–disturbed clay on the strength, deformation and failure criterion of Shanghai clay were quantitatively evaluated. The shear strength and dilatancy of undisturbed /remolded clay decreases with the increase of the Lode angle. It is also found that the shear strength and dilatancy of the undisturbed clay are larger than those of the remolded clay; while the influence of the structure on the dilatancy decreases with an increase in the Lode angle. In the π–plane, the maximum strength of Shanghai clay under different stress paths generally obeys the SMP failure criterion. The coincidence of the stress–dilatancy relationship given by the TS and tij stress spaces with the test results is much better than that given by p–q stress space. Furthermore, the linearity of the plastic potential curves of the undisturbed/remolded clay is more evident in tij stress space.

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In this paper we devise and analyze a pressure-robust and superconvergent HDG method in stress-velocity formulation for the Stokes equations and the Navier–Stokes equations with strongly symmetric stress. The stress and velocity are approximated using piecewise polynomial space of order k and H(div;Ω)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$H(\ extrm{div};\\Omega )$$\\end{document}-conforming space of order k+1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$k+1$$\\end{document}, respectively, where k is the polynomial order. In contrast, the tangential trace of the velocity is approximated using piecewise polynomials of order k. Moreover, the characterization of the proposed schemes shows that the globally coupled unknowns are the normal trace and the tangential trace of velocity, and the piecewise constant approximation for the trace of the stress. The discrete H1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$H^1$$\\end{document}-stability is established for the discrete solution. The proposed formulation yields divergence-free velocity, but causes difficulties for the derivation of the pressure-independent error estimate given that the pressure variable is not employed explicitly in the discrete formulation. This difficulty can be overcome by observing that the L2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L^2$$\\end{document} projection to the stress space has a nice commuting property. Moreover, superconvergence for velocity in discrete H1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$H^1$$\\end{document}-norm is obtained, with regard to the degrees of freedom of the globally coupled unknowns. Then the convergence of the discrete solution to the weak solution for the Navier–Stokes equations via the compactness argument is rigorously analyzed under minimal regularity assumption. The strong convergence for velocity and stress is proved. Importantly, the strong convergence for velocity in discrete H1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$H^1$$\\end{document}-norm is achieved. Several numerical experiments are carried out to confirm the proposed theories.

A size‐dependent energy‐based strain burst criterion

AbstractThis paper presents a size‐dependent energy‐based strain burst criterion linking strength, elasticity, fracture energies and specimen size effect with stress state due to changes in boundary conditions. It proposes the concept of a ‘Burst Envelope’, a surface in three‐dimensional principal stress space derived based on energy storing and dissipation characteristics of a rock sample, taking into account the size of the specimen and potential localised failure pattern. A scalar burst index is also proposed to quantify the bursting scale. To illustrate and verify its functioning, a numerical modelling framework based on the distinct element method and employing a new cohesive‐frictional contact model is used to perform virtual strain burst experiments under different polyaxial loading‐unloading scenarios, mimicking various underground excavation scenarios. The obtained results are in good agreement with the theoretical prediction of burst occurrence. On that basis, the variation of burst possibility and magnitude are investigated with key factors, including confinement level and the material's elastic, strength and fracture properties. The effect of the specimen's aspect ratio and size on the rock burst potential is elaborated and verified using virtual strain burst experiments, facilitating the linking of the proposed theoretical framework with the evaluation of in‐situ strain bursts in rock masses around underground openings.

Prediction of Short- to Long-Term Cyclic Deformation Behavior and Fatigue Life of Polymers.

The prediction of mechanical behavior and fatigue life is of major importance for design and for replacing costly and time-consuming tests. The proposed approach for polymers is a combination of a fatigue model and a governing constitutive model, which is formulated using the Haward-Thackray viscoplastic model (1968) and is capable of capturing large deformations. The fatigue model integrates high- and low-cycle fatigue and is based on the concept of damage evolution and a moving endurance surface in the stress space, therefore memorizing the load history without requesting vague cycle-counting approaches. The proposed approach is applicable for materials in which the fatigue development is ductile, i.e., damage during the formation of microcracks controls most of the fatigue life (up to 90%). Moreover, damage evolution shows a certain asymptote at the ultimate of the low-cycle fatigue, a second asymptote at the ultimate of the high-cycle fatigue (which is near zero), and a curvature of how rapidly the transition between the asymptotes is reached. An interesting matter is that similar to metals, many polymers satisfy these constraints. Therefore, all the model parameters for fatigue can be given in terms of the Basquin and Coffin-Manson model parameters, i.e., satisfying well-defined parameters.

Composite ellipsoids to model charge anisotropy in particle-scale simulations of kaolinite

This paper outlines a new approach to use coarse-grained molecular dynamics (CGMD) and the Gay–Berne (GB) potential to simulate the compression of kaolinite saturated with water at an acidic pH ( = 4) in a low (1 mM) ion concentration solution. To overcome the limitations of the standard GB potential and capture the charge heterogeneity on the surface of kaolinite particles under acidic pH conditions, each clay platelet is modelled using a two-ellipsoid composite particle. The molecular dynamics software Large-scale Atomic/Molecular Massively Parallel Software was employed to generate virtual monodisperse samples containing 1000 composite particles and to simulate isotropic compression at 100 kPa. The observed macro-scale response in void ratio–effective stress space lay above the response obtained in a simulation that used an equivalent CGMD model developed to simulate alkaline (pH = 8) pore water conditions. This is in qualitative agreement with available experimental data for one-dimensional compression. A post-compression qualitative observation of two virtual samples revealed a book-house-type fabric in the sample with acidic pore fluid, whereas a turbostatic-type fabric was observed when an alkaline pore fluid was simulated. These observations are also in qualitative agreement with scanning electron microscopy data reported in the literature.

Biaxial tensile behavior of CoCrFeNi high-entropy alloy under dynamic and proportional loadings

The dynamic failure behavior of CoCrFeNi High-Entropy Alloy (HEA) under plane biaxial stress was investigated in detail. The dynamic biaxial tensile tests were conducted using an Electromagnetic Biaxial Split Hopkinson Tensile Bar (EBSHTB) system. For comparison, the quasi-static uniaxial and biaxial tensile tests, as well as dynamic uniaxial tensile tests, were performed respectively. A cruciform specimen suitable for large plastic deformation was designed and employed in the experiments. The Finite Element Method (FEM) verified that the improved cruciform specimen could satisfy the basic requirements. The feasibility of the proposed specimen was further confirmed through loading tests. Finally, the quasi-static and dynamic yield loci of the HEA in the first quadrant of the principal stress space were plotted. The results indicate that the alloy exhibits obvious strain hardening effect and strain rate strengthening effect, the yield locus and plastic work contours can be accurately described by Hill’48 criterion.

Maternal perceived stress and green spaces during pregnancy are associated with adult offspring gene (NR3C1 and IGF2/H19) methylation patterns in adulthood: A pilot study

BackgroundChanges in NR3C1 and IGF2/H19 methylation patterns have been associated with behavioural and psychiatric outcomes. Maternal mental state has been associated with offspring NR3C1 promotor and IGF2/H19 imprinting control region (ICR) methylation patterns. However, there is a lack of prospective studies with long-term follow-up. Methods52 mother-offspring pairs were studied from 12 to 22 weeks of pregnancy and offspring was followed-up until 28–29 years-of-age. During pregnancy, mothers filled in a Life Event Scale and a Daily Hassles Scale measuring perceived stress; i.e., appraisal or subjectively experienced severity of impact of important life events and of daily hassles in several life domains during pregnancy, respectively. Green space was quantified around the residence, using high-resolution (1 m2) map data. Saliva and blood samples were obtained from the adult offspring. Absolute DNA methylation levels were determined in blood and saliva on four NR3C1 amplicons, and one IGF2/H19 ICR amplicon using a bisulfite PCR and sequencing method. Linear mixed effect models were used to test the associations between perceived stress and green spaces during pregnancy, and adult offspring methylation patterns. ResultsWe found associations between maternal perceived stress during pregnancy and methylation patterns on two out of the four NR3C1 amplicons, measured in blood, from offspring in adulthood, but not with IGF2/H19 methylation. For an interquartile-range (IQR) increase in maternal perceived life event or daily hassles stress scores, absolute methylation levels on several NR3C1 CpG sites were significantly changed (-1.62 % to +5.89 %, p<0.05). Maternal perceived stress scores were not associated with IGF2/H19 methylation, neither in blood nor in saliva. Maternal exposure to green spaces surrounding the residence during the pregnancy was associated with IGF2/H19 ICR methylation (-0.80 % to −1.04 %, p<0.05) in saliva, but not with NR3C1 promotor methylation. ConclusionWe observed significant long-term effects of maternal perceived stress during pregnancy on the methylation patterns of the NR3C1 promotor in offspring well into adulthood. This may imply that maternal psychological distress during pregnancy may influence the regulation of the HPA-axis well into adulthood. Additionally, maternal proximity to green spaces was associated with IGF2/H19 ICR methylation patterns, which is a novel finding.

Multiaxial yield behavior of 2D re-entrant auxetic cellular materials

A series of re-entrant honeycombs (RH) with different off-axis angles and perturbation parameters are constructed and utilized to numerically explore the multiaxial yield behavior for 2D auxetic cellular materials. The off-axis angle significantly affects the anisotropic properties and Poisson's ratio of RH. The effects of microstructural irregularity on the multiaxial yield surfaces are also evaluated for all of the topologies. Simulation results under principal stress space, mean stress-effective stress space and normal stress-shear stress space reveal that the unique microstructure of auxetic cellular materials makes its mechanical properties significantly different from conventional cellular materials with positive Poisson's ratio. Furthermore, a pressure-dependent anisotropic phenomenological yield criterion is proposed for 2D auxetic cellular materials, which can effectively capture the multiaxial yield behavior of RH with different topologies in principal stress space. The present conclusions provide fresh insights into the microstructural design of auxetic cellular materials and pave the way for their future engineering applications.

A multiscale bifurcation analysis using micromechanical-based constitutive tensor for granular material

The current study presents a multiscale approach that investigates material instability and localization phenomena in plastic granular materials and the discrete-continuum duality. A bifurcation and stability analysis in continuum mechanics usually requires the material’s tangent (stiffness) operator, the computation of which in a micromechanical approach such as Discrete Element Modeling (DEM) requires specific treatment. To bridge the discrete and continuum worlds, a new computational approach incorporating strain probing is proposed to reconstruct the elastoplastic constitutive tensor and its spectral characteristics from DEM simulations. The probing technique permits the computation of the tangent operator that inherits microstructural information from the discrete world to analyze bifurcation in elastoplasticity at the macro level. An incrementally linear constitutive tensor is computed, distinct for each of the ensemble of probing directions belonging to a particular tensorial zone or sector of incremental stress or strain space, thus making it directionally non-linear. Following such an approach, material instability can be evaluated from the spectral characteristics of the tangent constitutive tensor deduced from DEM probing calculations belonging to an identified tensorial zone. A meso-scale analysis is finally offered to detect shear band localization through the well-known Rice’s criterion as a continuum-based concept extended to a micromechanical discrete modeling framework. These new numerical results show that the multiscale proposed approach, which allows access to microstructural information, is consistent with a continuum one such as when predicting the localization angle during shear banding in a granular specimen in DEM.

Implementation of modified cam–clay model using closest point projection method under Cartesian coordinate system

The modified Cam–Clay model is an elastoplastic soil model that holds a prominent position in civil engineering for its precise depiction of varied soil behaviors. Despite extensive examination of its numerical processes, the predominant focus on stress integration algorithms within the triaxial stress space presents challenges for individuals less acquainted with geotechnical science. In response to this, the present study derived the stress integration equations for the modified Cam–Clay model within the Cartesian coordinate system employing the closest point projection method. Subsequently, a finite element program was developed incorporating the derived integration process. This study computed and compared the consolidation processes under both drained and undrained conditions for cubic soil samples with various over-consolidation ratios using the developed program, ABAQUS, and analytical formulas. The findings demonstrate that equations integrated within the Cartesian coordinate system offer ease of understanding and programming. The feasibility, accuracy, and stability of the closest point projection method have been validated. Comparative analysis of soil samples across various over-consolidation ratios indicated a reduction in failure stress with an increase in over-consolidation ratio, indicating a higher propensity for failure under undrained conditions than under the drained conditions.

Volume change characteristic of compacted bentonite during hydration upon high suction change: Experimental study and constitutive simulation

The assessment and predicting of volume change characteristic in compacted bentonite during hydration upon high suction change are crucial considerations in the design and construction of geological repositories. However, the mechanism for volume change behavior of bentonite upon suction change path is not yet well understood. Existing elastoplastic models show some limitations for describing hydration deformation of compacted bentonite upon high suction change path. In this work, suction-controlled hydration deformation tests were conducted on compacted GMZ01 bentonite under constant vertical stresses. The various forms of void ratio-suction curves observed suggested that the swelling-collapse behavior during hydration was influenced by the over-consolidation ratio (OCR). Furthermore, it was observed that each hydration deformation curve (e-lns) exhibited a saturation suction value. When the suction decreased to the saturation suction, the bentonite reached a state where further hydration was no longer possible, resulting in the absence of additional swelling or collapse deformation. The unique relationship between saturation suction and stress applied, i.e. critical saturated state (CSS) curve was proved to existed, which dividing the stress space (s-p plane) into unsaturated and saturated zones. A model framework with the concept of CSS curve was introduced and the suction-induced volume change equation was determined based on the tests results. The simulation results of hydration deformation tests demonstrated excellent agreement with the experimental data. The test results in this work provide the important mechanical parameters for the design and construction of geological repositories. Meanwhile, the proposed model could describe volume change characteristic of compacted bentonite during hydration upon high suction change, showing great significance for the safety assessment of repositories.

On the energy decomposition in variational phase-field models for brittle fracture under multi-axial stress states

Phase-field models of brittle fracture are typically endowed with a decomposition of the elastic strain energy density in order to realistically describe fracture under multi-axial stress states. In this contribution, we identify the essential requirements for this decomposition to correctly describe both nucleation and propagation of cracks. Discussing the evolution of the elastic domains in the strain and stress spaces as damage evolves, we highlight the links between the nucleation and propagation conditions and the modulation of the elastic energy with the phase-field variable. In light of the identified requirements, we review some of the existing energy decompositions, showcasing their merits and limitations, and conclude that none of them is able to fulfil all requirements. As a partial remedy to this outcome, we propose a new energy decomposition, denoted as star-convex model, which involves a minimal modification of the volumetric-deviatoric decomposition. Predictions of the star-convex model are compared with those of the existing models with different numerical tests encompassing both nucleation and propagation.

Tension-shear characteristics, cost and environmental impact of polyethylene fiber reinforced engineered cementitious composites: The role of fiber content

Engineered cementitious composites (ECC) tailored with fibers is famous for distinguished tensile ductility and tight crack width control capacity. The ECC material of the structural members may be in the state of tension-shear stress, e.g. ECC in the shear span of beams. Accordingly, this research focuses on the characteristics of ECC with diverse polyethylene (PE) fiber contents (0.5%, 1.0%, 1.5% and 2.0%) under tension-shear loading. The basic characteristics of PE-ECC subjected to uniaxial tension, uniaxial compression and pure shear were tested. The tension-shear behaviors of PE-ECC subjected to various loading angles were investigated by an elaborately designed test fixture. PE-ECC with the fiber content of over 1% exhibited obvious multiple-cracking phenomenon when subjected to tension-shear loading, and crack number decreased as loading angle continued to raise. The tension-shear strength for PE-ECC was enhanced by increasing fiber content. The failure criteria stemmed from the octahedral stress space (linear function) or stress invariant can be applied for depicting the failure laws of PE-ECC. Additionally, cost comparison and environmental impact evaluation indicated that fiber cost accounted for a significant higher proportion of the total cost (over 36%), while the proportion of fiber carbon footprint to the entire carbon footprint was low (less than 12%). This research will provide a useful assistance in understanding the tension-shear behaviors of PE-ECC and further facilitating its structural applications.

Modified cam clay bounding surface hyper-viscoplastic model

Clays exhibit complex mechanical behaviour with significant viscous, nonlinear, and hysteric characteristics, beyond the prediction capacity of the well-known modified cam clay (MCC) model. This paper extends the MCC model to address these important limitations. The proposed family of models is constructed entirely within the hyperplasticity framework deduced from thermodynamic extremal principles. More specifically, the previously developed MCC hyper-viscoplastic model based on the isotache concept is extended to incorporate multiple internal variables and to capture recent loading history, hysteresis, and smooth response of the material. This is achieved by defining an inelastic free energy and an element that implements a bounding surface within hyperplasticity, resulting in pressure dependency in both reversible and irreversible processes with a unique critical state envelope, and only eight material parameters with a readily measurable viscous parameter. A kinematic hardening in the logistic differential form in stress space is derived that enables the proposed model to function effectively across a wide range of stresses. Based on this kinematic hardening rule, the current stress state acts as an asymptotic attractor for the back/shift stresses whose evolution rates are proportional to their current state.

A machine learning constitutive model for plasticity and strain hardening of polycrystalline metals based on data from micromechanical simulations

Machine learning (ML) methods have emerged as promising tools for generating constitutive models directly from mechanical data. Constitutive models are fundamental in describing and predicting the mechanical behavior of materials under arbitrary loading conditions. In recent approaches, the yield function, central to constitutive models, has been formulated in a data-oriented manner using ML. Many ML approaches have primarily focused on initial yielding, and the effect of strain hardening has not been widely considered. However, taking strain hardening into account is crucial for accurately describing the deformation behavior of polycrystalline metals. To address this problem, the present study introduces an ML-based yield function formulated as a support vector classification model, which encompasses strain hardening. This function was trained using a 12-dimensional feature vector that includes stress and plastic strain components resulting from crystal plasticity finite element method (CPFEM) simulations on a 3-dimensional RVE with 343 grains with a random crystallographic texture. These simulations were carried out to mimic multi-axial mechanical testing of the polycrystal under proportional loading in 300 different directions, which were selected to ensure proper coverage of the full stress space. The training data were directly taken from the stress–strain results obtained for the 300 multi-axial load cases. It is shown that the ML yield function trained on these data describes not only the initial yield behavior but also the flow stresses in the plastic regime with a very high accuracy and robustness. The workflow introduced in this work to generate synthetic mechanical data based on realistic CPFEM simulations and to train an ML yield function, including strain hardening, will open new possibilities in microstructure-sensitive materials modeling and thus pave the way for obtaining digital material twins.

A novel method for imitating true-triaxial stress path with conventional triaxial apparatus

The stress paths of the cylindrical specimen in the p–q stress space by controlling the ratio of the axial and the radial loading is guaranteed to be consistent with the cuboid specimen, a novel method for imitating true-triaxial stress path by conventional triaxial apparatus was presented. Under the condition that p and q were variables and b was constant, the true-triaxial stress paths were realized by conventional triaxial apparatus strictly and easily. Under the condition that b and p were invariants, the b was used to control the ratio of axial and radial loading to ensure p constant, the method can be used to measure the strength on the π plane. If the tests were conducted at the different p with the same b, the critical state line of different b could be obtained. Under the condition that p and q were constant, the proposed method of nonlinear loading with b as a parameter could be used to design the various stress paths of true-triaxial under the condition of deviatoric stress consolidation, and which could be used to determine the deformation and the plastic flow of soil in 3D space. The proposed method could be used to achieve the equivalent stress path in the p–q stress space to obtain the 3D mechanical properties, and the stress path controlled by stress, strain, and a hybrid of stress and strain. Once the software of conventional triaxial apparatus was developed by the novel method, the measuring range of stress paths could be expanded greatly.

Impact of Climate on Stress Ultrasound Findings of the Elbow Ulnar Collateral Ligament in Professional Baseball Pitchers: An 18-Year Study.

The ulnar collateral ligament (UCL) is the primary soft tissue stabilizer to valgus stress in the elbow and is placed under this valgus stress during the throwing motion. Although there are known risk factors for UCL injury, it is unknown whether the UCL undergoes adaptive changes in athletes from different climates. To compare elbow stress ultrasound (SUS) findings between professional baseball pitchers from warm climates versus cold climates and assess significant differences in adaptive and morphologic changes in the UCL. Cross-sectional study; Level of evidence, 3. Dynamic SUS evaluations were performed over 18 years on the dominant and nondominant arms of 643 professional pitchers from warm and cold climates as determined by the player's country/state of origin. Studies were compared with respect to relative UCL thickness (dominant arm vs nondominant arm), relative glenohumeral joint laxity (joint space distance under stress vs joint space distance at rest), and the presence of morphologic changes such as tears or calcifications. In addition, a subgroup analysis was performed to compare the progression of SUS findings over 3 years in players with sequential yearly data. Players from warmer climates had significantly greater relative UCL thicknesses than players from colder climates (1.75 vs 1.50 mm, respectively; P = .047). There were no differences between these 2 groups in terms of relative ulnohumeral joint laxity (P = .201), presence of morphologic changes (P = .433), 3-year progression of relative UCL thickness (P = .748), or relative joint laxity (P = .904). Professional pitchers from warm climates had a greater side-to-side difference in UCL thickness between the dominant and nondominant arms. This may be due to the potential for year-round throwing among baseball players from warm climates. There was no difference in laxity, thickness progression, laxity progression, or the presence of additional morphologic changes.