Spatial Stress Distribution Research Articles

States of stress and slip partitioning in a continental scale strike-slip duplex: Tectonic and magmatic implications by means of finite element modeling

Orogenic belts at oblique convergent subduction margins accommodate deformation in several trench-parallel domains, one of which is the magmatic arc, commonly regarded as taking up the margin-parallel, strike-slip component. However, the stress state and kinematics of volcanic arcs is more complex than usually recognized, involving first- and second-order faults with distinctive slip senses and mutual interaction. These are usually organized into regional scale strike-slip duplexes, associated with both long-term and short-term heterogeneous deformation and magmatic activity. This is the case of the 1100 km-long Liquiñe–Ofqui Fault System in the Southern Andes, made up of two overlapping margin-parallel master faults joined by several NE-striking second-order faults. We present a finite element model addressing the nature and spatial distribution of stress across and along the volcanic arc in the Southern Andes to understand slip partitioning and the connection between tectonics and magmatism, particularly during the interseismic phase of the subduction earthquake cycle. We correlate the dynamics of the strike-slip duplex with geological, seismic and magma transport evidence documented by previous work, showing consistency between the model and the inferred fault system behavior. Our results show that maximum principal stress orientations are heterogeneously distributed within the continental margin, ranging from 15° to 25° counter-clockwise (with respect to the convergence vector) in the master faults and 10–19° clockwise in the forearc and backarc domains. We calculate the stress tensor ellipticity, indicating simple shearing in the eastern master fault and transpressional stress in the western master fault. Subsidiary faults undergo transtensional-to-extensional stress states. The eastern master fault displays slip rates of 5 to 10 mm/yr, whereas the western and subsidiary faults show slips rates of 1 to 5 mm/yr. Our results endorse that favorably oriented subsidiary faults serve as magma pathways, particularly where they are close to the intersection with a master fault. Also, the slip of a fault segment is enhanced when an adjacent fault kinematics is superimposed on the regional tectonic loading. Hence, finite element models help to understand coupled tectonics and volcanic processes, demonstrating that geological and geophysical observations can be accounted for by a small number of key first order boundary conditions.

The influence of anisotropic growth and geometry on the stress of solid tumors

Solid stresses can affect tumor patho-physiology in at least two ways: directly, by compressing cancer and stromal cells, and indirectly, by deforming blood and lymphatic vessels. In this work, we model the tumor mass as a growing hyperelastic material. We enforce a multiplicative decomposition of the deformation gradient to study the role of anisotropic tumor growth on the evolution and spatial distribution of stresses. Specifically, we exploit radial symmetry and analyze the response of circumferential and radial stresses to (a) degree of anisotropy, (b) geometry of the tumor mass (cylindrical versus spherical shape), and (c) different tumor types (in terms of mechanical properties). According to our results, both radial and circumferential stresses are compressive in the tumor inner regions, whereas circumferential stresses are tensile at the periphery. Furthermore, we show that the growth rate is inversely correlated with the stresses’ magnitudes. These qualitative trends are consistent with experimental results. Our findings therefore elucidate the role of anisotropic growth on the tumor stress state. The potential of stress-alleviation strategies working together with anticancer therapies can result in better treatments.

Bacterial biofilm under flow: First a physical struggle to stay, then a matter of breathing.

Bacterial communities attached to surfaces under fluid flow represent a widespread lifestyle of the microbial world. Through shear stress generation and molecular transport regulation, hydrodynamics conveys effects that are very different by nature but strongly coupled. To decipher the influence of these levers on bacterial biofilms immersed in moving fluids, we quantitatively and simultaneously investigated physicochemical and biological properties of the biofilm. We designed a millifluidic setup allowing to control hydrodynamic conditions and to monitor biofilm development in real time using microscope imaging. We also conducted a transcriptomic analysis to detect a potential physiological response to hydrodynamics. We discovered that a threshold value of shear stress determined biofilm settlement, with sub-piconewton forces sufficient to prevent biofilm initiation. As a consequence, distinct hydrodynamic conditions, which set spatial distribution of shear stress, promoted distinct colonization patterns with consequences on the growth mode. However, no direct impact of mechanical forces on biofilm growth rate was observed. Consistently, no mechanosensing gene emerged from our differential transcriptomic analysis comparing distinct hydrodynamic conditions. Instead, we found that hydrodynamic molecular transport crucially impacts biofilm growth by controlling oxygen availability. Our results shed light on biofilm response to hydrodynamics and open new avenues to achieve informed design of fluidic setups for investigating, engineering or fighting adherent communities.

Measurement of microscale residual stresses in multi-phase ceramic composites using Raman spectroscopy

A methodology is described for characterizing the spatial distribution of thermal mismatch stresses at grain level in B4C-SiC-Si ceramic composites using Raman spectroscopy. Unlike traditional methods to detect residual stresses (e.g., X-ray diffraction) which provide average values of stress over the entire specimen surface, Raman peak-shift analysis provides residual stress distributions within the microstructure at high spatial resolution. While classical formulation predicts uniform compressive stress within a Si-phase surrounded by the ceramic matrix, the Raman measurements revealed non-uniform residual stress distributions in Si when the particle size was larger than 5 microns. For large irregular shaped particles, the two methods coincide only along the interface between the particle and matrix, but vary drastically both in magnitude and nature in the interior of the particle where large tensile stresses have been measured. The presence of anomalous tensile stress in the interior of the minor Si-phase results in defect generation and structural disorder which has been confirmed by TEM analysis. Raman spectroscopic mapping was also used to compute an average macroscale residual stress value for a given material composition allowing links to be drawn between processing, microstructure and properties. The average residual stress within the microstructure was found to correlate well with the estimates based on volume fraction of the constituents and material properties.

STATISTICAL ANALYSIS FOR RUPTURE RISK PREDICTION OF ABDOMINAL AORTIC ANEURYSMS (AAA) BASED ON ITS MORPHOMETRY

The morphometry of the abdominal aortic aneurysms (AAA) has been recognized as one of the main factors that may predispose its rupture. The variation of the AAA morphometry, over time, induces modifications in hemodynamic behavior which, in turn, alters the spatial and temporal distribution of hemodynamic stress on the aneurismatic wall, establishing a bidirectional process that can influence the rupture phenomenon. In order to evaluate potential correlations between the main geometric parameters characterizing the AAA and hemodynamic stresses, 13 unrupture AAA patient-specific models were created. To AAA geometric characterization, 12 indices based on lumen center line were defined and determined. The computing of temporal and spatial distributions of hemodynamic stresses was conducted through Computational Fluid Dynamics. Statistical techniques were used to assess the relationships between the hemodynamic parameters and the different geometrical indices of the AAA. Regression analyses were conducted to obtain linear predictor models for hemodynamic stresses using the different indices defined in this paper as predictor variables. The statistical analysis confirmed that the length L, the asymmetry and the saccular index significantly influenced the hemodynamic stresses. The results obtained show the potential of the use of statistical techniques in predicting the rupture risk of patient-specific AAA.

Integrated strategy for in vitro characterization of a bileaflet mechanical aortic valve

BackgroundHaemodynamic performance of heart valve prosthesis can be defined as its ability to fully open and completely close during the cardiac cycle, neither overloading heart work nor damaging blood particles when passing through the valve. In this perspective, global and local flow parameters, valve dynamics and blood damage safety of the prosthesis, as well as their mutual interactions, have all to be accounted for when assessing the device functionality. Even though all these issues have been and continue to be widely investigated, they are not usually studied through an integrated approach yet, i.e. by analyzing them simultaneously and highlighting their connections.ResultsAn in vitro test campaign of flow through a bileaflet mechanical heart valve (Sorin Slimline 25 mm) was performed in a suitably arranged pulsatile mock loop able to reproduce human systemic pressure and flow curves. The valve was placed in an elastic, transparent, and anatomically accurate model of healthy aorta, and tested under several pulsatile flow conditions. Global and local hydrodynamics measurements and leaflet dynamics were analysed focusing on correlations between flow characteristics and valve motion. The haemolysis index due to the valve was estimated according to a literature power law model and related to hydrodynamic conditions, and a correlation between the spatial distribution of experimental shear stress and pannus/thrombotic deposits on mechanical valves was suggested. As main and general result, this study validates the potential of the integrated strategy for performance assessment of any prosthetic valve thanks to its capability of highlighting the complex interaction between the different physical mechanisms that govern transvalvular haemodynamics.ConclusionsWe have defined an in vitro procedure for a comprehensive analysis of aortic valve prosthesis performance; the rationale for this study was the belief that a proper and overall characterization of the device should be based on the simultaneous measurement of all different quantities of interest for haemodynamic performance and the analysis of their mutual interactions.

Spatial Residual Stress Distribution in Multi-Phase Steel

Residual stress measurements were carried out on duplex steel samples using X-ray diffraction technique. Directional residual stress was investigated on the surface of the heat effected zone of joints. Spatial residual stress distribution were examined in the ferrite and austenite phases separately, using different radiation-ray source. The different mechanical properties of each phases were taken into account during the stress calculations. Noticeable stress gradient was observed between ferrite and austenite phases.

Spatial stress distribution analysis by thermoelastic stress measurement and evaluation of effect of stress concentration on durability of various orthopedic implant devices

Toward the development of highly durable devices, we investigated the effect of the thermoelastic constants of implantable raw metals and the surface stress distribution on the durability of various types of implant device by thermoelastic stress measurement and by evaluating the effect of the stress concentration. Surface stress was dynamically calculated from the bending moment, and the modulus of a section of a device was found to be consistent with the surface stress obtained by thermoelastic stress measurement. The durability limits of various types of bone plate and compression hip screw (CHS) calculated from maximum load vs number of cycles data (L–N data) were close to the notch fatigue strength of the raw material. The concentration factor of an artificial hip stem surface was estimated by comparing the L–N data of the stem and the S–N curve of the raw material. The dynamic analysis of durability by thermoelastic stress measurement is useful for selecting the worst case (a product deteriorating to the most severe state) in medical device design.

Dynamic Responses of Subway Tunnel in Clay Stratum to Moving Loads

An elaborate three-dimensional nonlinear numerical model of a rail-tunnel-foundation system in a clay stratum was developed. The model closely represented an actual subway tunnel and described the rail, sleeper, track slab, inverted arch, lining and foundation. Operation of a subway train with six wagons traveling at 100 km/h was simulated. Large-scale nonlinear dynamic finite element computation for the system was performed. The analysis showed that the system is in a state of loading and unloading repeatedly as the train passes through the tunnel. The spatial distributions of dynamic displacement, velocity, acceleration and stresses in different parts of the system all vary simultaneously with time and space. The characteristics of dynamic stresses in the clayey stratum are much different from those in the inverted arch and lining. The dynamic stresses in the tunnel lining and inverted arch have small values, but the rate effects of dynamic stress for ballastless track slab, inverted arch and tunnel lining are much higher than that of the foundation clay. The rotations of principal stress axes in the XY and YZ planes are predominant for ballastless track slab, inverted arch, tunnel lining and foundation soil just below the tunnel lining, while rotation in the YZ plane is predominant for deeper foundation soil elements. These results justify a conclusion that the thickness of inverted arch and backfill concrete can be optimized. Much attention should be paid during design to the long-term stability of a clayey foundation. The results can be referred in the dynamic design of subways.

The sub-crustal stress estimation in central Eurasia from gravity, terrain and crustal structure models

We investigate the horizontal stress field beneath crustal structures of central Eurasia. The numerical procedure applied for a simultaneous determination of the sub-crustal stress and the crustal thickness from the global gravity, terrain and crustal structure models is based on solving Navier-Stokes’ problem which incorporates the inverse solution to the Vening Meinesz- Moritz’s problem of isostasy. The numerical results reveal that a spatial distribution of the sub-crustal stress in this study area closely resembles the regional tectonic configuration comprising parts of the Eurasian, Indian and Arabian lithospheric plates. The maximum shear stress intensity is generated by a subduction of the Indian plate beneath the Tibetan block. The intra-plate tectonic configuration is marked by the stress anomalies distributed along major active strike-slip fault systems and sections of subduction which separate the Tibetan and Iranian blocks from the rest of the Eurasian plate. The most pronounced intra-plate stress anomalies are related with a subduction of the Eurasian plate beneath the Tibetan block. We also demonstrate that a prevailing convergent orientation of stress vectors agree with the compressional tectonism of orogenic formations (Himalaya and Tibet Plateau, Than Shan, Zargos and Iranian Plateau), while the extensional tectonism of continental basins (Tarim, Ganges-Brahmaputra, Sichuan) is manifested by a divergence of stress vectors.

Heat Stress in the Urban and Suburban Landscape and its Spatial Differentiation Through the Example of a Medium-Sized City

Članek obravnava prostorsko razporeditev toplotnega stresa v srednjeevropskem mestu in njegovi okolici. Preučevali smo čas, ko so bile na merskih postajah presežene mejne vrednosti indeksa Humidex in zračnih temperatur. Najdaljše obdobje neugodnih temperatur je bilo na stiku med srednje visokimi zgradbami in odprtim prostorom, najkrajše v sklenjeno pozidanih delih in blizu gozda. Ugotovili smo razlike v razporeditvi postaj z dolgimi obdobji visokih temperatur in postaj z dolgimi intervali visokih vrednosti indeksaHumidex. Pri vrednotenju toplotnega stresa z vidika mortalitete pa Humidex ni dal boljših rezultatov kot podatki o temperaturah zraka.

Heat Stress in the Urban and Suburban Landscape and its Spatial Differentiation Through the Example of a Medium-Sized City

The spatial distribution of heat stress in a Central European city and its surroundings was examined. We evaluated the length of time for which the threshold values of Humidex and air temperatures were exceeded at individual stations. The longest interval of temperature discomfort was detected at the border of open mid-rise development and open spaces. The shortest intervals were found in compact mid-rise development and near a forest. There are spatial differences between locations with long periods of high temperatures and locations with long intervals of high Humidex values. However, when the heat stress is being assessed in relation to the mortality rate, Humidex does not show better results than the air temperature.

Static analysis of doubly curved film-substrate shells with thickness-dependent material properties

Based on Reissner’s mixed variational theorem (RMVT), we develop a weak-form formulation of finite doubly curved layer (FDCL) methods for the static analysis of simply-supported, multilayered functionally graded material (FGM) doubly curved shells (DCSs) under mechanical loads. This formulation is used to examine the spatial distributions of interlaminar stress and displacement components induced in a pressure-loaded FGM film-substrate DCS, and these solutions are compared with those obtained by using the principle of virtual displacements. The material properties of the multilayered (or film-substrate) shell are thickness-dependent, and the effective material properties of the FGM layer are estimated using the rule of mixtures and Mori–Tanaka scheme. The trigonometric functions and Lagrange polynomials are used to interpolate the in-surface and thickness variations of the primary variables of each individual layer, respectively. The orders used to expand the primary variables through the thickness direction are taken to be the same as one another, which are linear, quadratic and cubic variations. The accuracy and convergence rate of these RMVT-based FDCL methods are validated by comparing their solutions with the exact three-dimensional and accurate two-dimensional solutions available in the literature.

Numerical and experimental study of flow over stages of an offset merger dune interaction

Results of a coordinated research effort on unidirectional turbulent flows over canonical barchan dunes at high Reynolds number are presented. Large-eddy simulations (LES) and experiments are conducted under inertial-dominated flow conditions, thus capturing dynamics essential to fully understanding processes responsible for observed patterns of asymmetric erosion and migration. A series of dune field topographies have been considered wherein a small “impactor” dune is positioned at a series of positions upflow of a large “parent” dune, from a spanwise-offset position; this interaction constitutes a so-called “offset interaction” Kocurek and Ewing [14]. The small dune is geometrically similar, but one-eighth the volume of the large dune. Since migration rate is inversely proportional to volume, the prescribed volumetric ratio ensures that the synthetic topographies replicate instantaneous configurations exhibited during actual dune interactions in a laboratory or natural setting. In this sense, the static dune configurations provide a means to understand flow processes responsible for patterns of erosion and deposition that induce interactions. Experimental measurement and LES are both used to study these configurations, with strong agreement reported between resultant datasets. We report that flow channeling in the interdune space between the upflow and downflow dune induces a mean flow heterogeneity – termed “wake veering” – in which the location of maximum momentum deficit in the dune wake is spanwise displaced. We also report elevated turbulent stresses in the channeling region. These results are used to explain the mechanisms responsible for simultaneous merging and ejection between the small and large dunes. Finally, spatial distributions of surface stress from LES have been used to identify locations of elevated erosion and, therefore, to predict bedform migration patterns. Results show that locations of minimal erosion – whether associated with upflow sheltering or with vanishing spatial gradients of dune height – constitute spatial “junctions” of coalescing, proximal dunes. In the absence of upwind sheltering, or in locations with the least upwind sheltering, turbulent mixing facilitates downward fluxes of high momentum fluid. This augments downwind dune erosion, cumulatively accelerating the migration of downwind dunes.

Sensitivity of flow patterns in aneurysms on the anterior communicating artery to anatomic variations of the cerebral arterial network

Recent studies raised increasing concern about the reliability of computer models in reproducing in vivo hemodynamics in cerebral aneurysms. Boundary condition problem is among the most frequently addressed issues since three-dimensional (3-D) modeling is usually restricted to local arterial segments. The present study focused on aneurysms on the anterior communicating artery (ACoA) which represent a large subgroup of detected cerebral aneurysms and, in particular, have a relatively high risk of rupture compared to aneurysms located in other regions. The sensitivity of blood flows in three ACoA aneurysms to boundary conditions was investigated using 3-D hemodynamic models. The boundary conditions of the 3-D models were predicted by a one-dimensional (1-D) model of the cerebral arterial network. The parameters of the 1-D model were assigned based respectively on population-averaged data and patient-specific data derived from medical images, yielding a population-generic model and a patient-specific model. In addition, particle image velocimetry (PIV) experiments were performed to validate the code used to simulate intra-aneurysmal blood flows. Obtained results showed that switching the boundary conditions of the aneurysm models from population-generic ones to patient-specific ones led to pronounced changes in simulated intra-aneurysmal flow patterns in terms of vortex structure, impingement region and the magnitude and spatial distribution of wall shear stress and oscillatory shear index. In particular, the way and the degree in which hemodynamic quantities are influenced by boundary conditions exhibited pronounced inter-patient variability. In summary, our study underlines the importance of patient-specific treatment of boundary conditions in model studies focusing on ACoA aneurysms.

Comparison of solid and fluid constitutive models of bone marrow during trabecular bone compression

The mechanical environment and mechanobiology of bone marrow may play essential roles in bone adaptation, cancer metastasis, and immune cell regulation. However, the location of marrow within the trabecular pore space complicates experimental measurement of marrow mechanics. Computational models provide a means to assess the shear stress and pressure in the marrow during physiological loading, but they rely on accurate inputs for the marrow and the physics assumed for the interaction of bone and marrow. Elastic, viscoelastic, and fluid constitutive properties have all been reported from experimental measurements of marrow properties. It is unclear whether this ambiguity reflects the various length-scales, loading rates, and boundary conditions of the experiments, or if the material models are sufficiently similar as to be interchangeable. To address this question, we analyzed both the mean shear stress and its spatial distribution induced in marrow during compression of trabecular bone cubes when using linear elastic, neo-Hookean, viscoelastic, and power-law fluid constitutive models. Experimentally reported parameters were initially applied for all four constitutive models, resulting in poor agreement. The parameters of the soft solid models were calibrated by linear interpolation so that the volume averaged shear stress agreed with the fluid model for each, but this could only be accomplished on a specimen-by-specimen basis. Following calibration, the root-mean-squared (RMS) difference between the solid and fluid constitutive models was still greater than 26% even when the overall mean shear stress was in close agreement, indicating that the spatial distribution of stress is also sensitive to the constitutive model. As such, the choice of constitutive model should be backed by a strong rationale, and results should be interpreted with care.

Central-force decomposition of spline-based modified embedded atom method potential

Central-force decompositions are fundamental to the calculation of stress fields in atomic systems by means of Hardy stress. We derive expressions for a central-force decomposition of the spline-based modified embedded atom method (s-MEAM) potential. The expressions are subsequently simplified to a form that can be readily used in molecular-dynamics simulations, enabling the calculation of the spatial distribution of stress in systems treated with this novel class of empirical potentials. We briefly discuss the properties of the obtained decomposition and highlight further computational techniques that can be expected to benefit from the results of this work. To demonstrate the practicability of the derived expressions, we apply them to calculate stress fields due to an edge dislocation in bcc Mo, comparing their predictions to those of linear elasticity theory.

Bayesian Inference of Forces Causing Cytoplasmic Streaming in Caenorhabditis elegans Embryos and Mouse Oocytes.

Cellular structures are hydrodynamically interconnected, such that force generation in one location can move distal structures. One example of this phenomenon is cytoplasmic streaming, whereby active forces at the cell cortex induce streaming of the entire cytoplasm. However, it is not known how the spatial distribution and magnitude of these forces move distant objects within the cell. To address this issue, we developed a computational method that used cytoplasm hydrodynamics to infer the spatial distribution of shear stress at the cell cortex induced by active force generators from experimentally obtained flow field of cytoplasmic streaming. By applying this method, we determined the shear-stress distribution that quantitatively reproduces in vivo flow fields in Caenorhabditis elegans embryos and mouse oocytes during meiosis II. Shear stress in mouse oocytes were predicted to localize to a narrower cortical region than that with a high cortical flow velocity and corresponded with the localization of the cortical actin cap. The predicted patterns of pressure gradient in both species were consistent with species-specific cytoplasmic streaming functions. The shear-stress distribution inferred by our method can contribute to the characterization of active force generation driving biological streaming.

Viscous stress distribution over a wavy gas–liquid interface

Viscous stress contributes to momentum transfer between two phases, which plays an important role in both industrial applications and environmental processes. Near a wavy interface, the flow is modulated and produces a spatially non-uniform normal and tangential viscous stress. This study presents measurements of these stresses at a liquid–gas interface populated with two-dimensional millimeter scale waves performed with multiphase particle image velocimetry. Large datasets enable conditional phase-averaging of the data based on wave steepness, which increases the precision of the results and allows statistical analysis. For the first time at this scale, the spatial distribution of normal and tangential viscous stress is obtained for a large range of wave steepness (ak = 0–1, with a the amplitude and k the wavenumber). As the steepness increases, the mean shear stress over a wavelength decreases in magnitude, while the normal viscous stress increases. These trends are linear for ak < 0.6, and correlations are proposed. At ak > 0.7, flow separation is observed in the gas phase near the troughs and drastically alters the viscous stress distribution.

Technical and functional analysis of Spanish windmills: 3D modeling, computational-fluid-dynamics simulation and finite-element analysis

A detailed study has been made of the two typologies of windmills in Spain, specifically the rectangular-bladed type, represented by the windmill ‘Sardinero’, located near the town of Campo de Criptana (Ciudad Real province, Spain) and the type with triangular sails (lateens), represented by the windmill ‘San Francisco’, in the town of Vejer de la Frontera (Cádiz province, Spain). For this, an ad hoc research methodology has been applied on the basis of three aspects: three-dimensional geometric modeling, analysis by computational-fluid dynamics (CFD), and finite-element analysis (FEA).The results found with the CFD technique show the correct functioning of the two windmills in relation to the spatial distribution of the wind velocities and pressures to which each is normally exposed (4–7m/s in the case of ‘Sardinero’, and 5–11 for ‘San Francisco’), thereby validating the operative functionality of both types. In addition, as a result of the FEA, the spatial distribution of stresses on the rotor has revealed that the greatest concentrations of these occurs in the teeth of the head wheel in ‘Sardinero’, reaching a value of 12MPa, and at the base of the masts in the case of the ‘San Francisco’, with a value of 24MPa. Also, this analysis evidences that simple, effective designs to reinforce the masts absorb a great concentration of stresses that would otherwise cause breakage. Furthermore, it was confirmed that the oak wood from which the rotors were made functioned properly, as the windmill never exceeded the maximum admissible working stress, demonstrating the effectiveness of the materials used in this period.