Hydrostatic Loading Research Articles

Development and Application of STORMTOOLS Design Load (SDL) Maps

Under the STORMTOOLS initiative, maps of the impact of sea level rise (SLR) (0 to 12 ft), nuisance flooding (1–10 yr), 25, 50, and 100 yr storms, and hindcasts of the four top ranked tropical storms have been developed for the coastal waters of Rhode Island (RI). Estimates of the design elevations, expressed in terms of the Base Flood Elevation (BFE) and thus incorporating surge and associated wave conditions, have also been developed, including the effects of SLR to facilitate structural design. Finally, Coastal Environmental Risk Index (CERI) maps have been developed to estimate the risk to individual structures and infrastructure. CERI employs the BFE maps in concert with damage curves for residential and commercial structures to make estimates of damage to individual structures. All maps are available via an ArcGIS Hub. The objective of this senior design capstone project was to develop STORMTOOLS Design Load maps (SDL) with a goal of estimating the hydrostatic, hydrodynamic, wave, and debris loading, based on ASCE/SEI 7–16 Minimum Design Standards methods, on residential structures in the RI coastal floodplain. The resulting maps display the unitized loads and thus can be scaled for any structure of interest. The goal of the maps is to provide environmental loads that support the design of structures, and reduce the time and cost required in performing the design and the permitting process, while also improving the accuracy and consistency of the designs. SDL maps were generated for all loads, including the effects of SLR for a test case: the Watch Hill/Misquamicut Beach, Westerly, along the southern RI coast. The Autodesk Professional Robot Structural Analysis software, along with SDL loading, was used to evaluate the designs for selected on-grade and pile-elevated residential structures. Damage curves were generated for each and shown to be consistent with the US Army Corps of Engineers empirical damage curves currently used in CERI.

On the design of multimaterial structural topologies using Integer Programming

This paper presents a framework for the discrete design of optimal multimaterial structural topologies using integer design variables and mathematical programming. The structural optimization problems: compliance minimization subject to mass constraint, and mass minimization subject to compliance constraint are used to design the multimaterial topologies in this work. The extended SIMP interpolation is used to interpolate the different materials available for structural design, and the material phases in each element are represented using binary design variables, one variable per available material. The Topology Optimization of Binary Structure (TOBS) method (Sivapuram and Picelli, 2018) is employed, wherein the nonlinear objective/constraint functions of optimization are sequentially approximated (herein, linearized) to obtain a sequence of Integer Linear Programs (ILPs). A novel truncation error-regulating constraint in terms of the Young’s moduli of the elements is introduced to maintain the sequential approximations valid, by restricting large changes in successive structural topologies. A commercial branch-and-bound solver is used to solve the integer subproblems yielding perfectly binary solutions which guarantee discrete structural topologies with clear material interfaces at each iteration. Adjoint sensitivities are computed to generate the integer subproblems, and the sensitivities are filtered using a conventional mesh-independent sensitivity filter. Few examples show the design of multimaterial structures in the presence of design-dependent loads: hydrostatic pressure loads and self-weight loads. This work also demonstrates through few examples, convergence of optimal multimaterial topologies at inactive constraint values when different type of loadings simultaneously act on the structure.

Hydrostatic Pressure Modulates Intervertebral Disc Cell Survival and Extracellular Matrix Homeostasis via Regulating Hippo-YAP/TAZ Pathway.

Established studies proved that hydrostatic pressure had multiple effects on the biological behavior of the intervertebral disc (IVD). However, the conclusions of the previous studies were inconsistent, due to the difference in hydrostatic loading devices and observing methods used in these studies. The current study is aimed at investigating the role of dynamic hydrostatic pressure in regulating biological behavior of the notochordal nucleus pulposus (NP) and fibrocartilaginous inner annulus fibrosus (AF) and its possible mechanism using our novel self-developed hydrostatic pressure bioreactor. The differences in the biological behavior of the rabbit IVD tissues under different degree of hydrostatic pressure were evaluated via histological analysis. Results revealed that low-loading dynamic hydrostatic pressure was beneficial for cell survival and extracellular matrix (ECM) homeostasis in notochordal NP and fibrocartilaginous inner AF via upregulating N-cadherin (N-CDH) and integrin β1. In comparison, high-magnitude dynamic hydrostatic pressure aggravated the breakdown of ECM homeostasis in NP and inner AF via enhancing the Hippo-YAP/TAZ pathway-mediated cell apoptosis. Moreover, inner AF exhibited greater tolerance to physiological medium-loading degree of hydrostatic pressure than notochordal NP. The potential mechanism was related to the differential expression of mechanosensing factors in notochordal NP and fibrocartilaginous inner AF, which affects the fate of the cells under hydrostatic pressure. Our findings may provide a better understanding of the regulatory role of hydrostatic pressure on the cellular fate commitment and matrix metabolism of the IVD and more substantial evidence for using hydrostatic pressure bioreactor in exploring the IVD degeneration mechanism as well as regeneration strategies.

A plastic-damage model for rock-like materials focused on damage mechanisms under high pressure

The purpose of this study is to present a plastic-damage model that can well capture the mechanical behaviors of rock-like materials. To this end, a three-invariant yield function combined with a cap function is employed to concurrently consider the physical mechanisms due to the presence of microcracks and pores as well as their combinations. The major contribution falls into the establishment of three damage mechanisms with clear physical backgrounds, including hydrostatic damage due to pore collapse, shear damage due to shear-induced microcracking, and tensile damage due to tensile microcracking. Particularly, the hydrostatic damage that can accumulate under even purely hydrostatic loading is proposed to account for the material properties degradations due to pore collapse. Results show that pore collapse under high pressure will cause a great loss of material properties. Without consideration of this will cause overestimation of the residual strength and modulus of materials. The validation examples demonstrated that the proposed hydrostatic damage can well accommodate the degradations of material strength and modulus due to pore collapse, which, however, has not been considered in most of the existing material models.

Empirical rock physics relationships on carbonate dry-frame elastic properties

Laboratory tests were conducted to analyze the ultrasonic velocity response to the pressure change in dry carbonate rocks from the Weyburn oilfield, Canada. Twenty-four samples are from seven wells with helium porosities ranging from 1% to 29%. Thin-section images, SEM and mercury intrusion porosimetry were performed to show their inner structures and pore throat size distributions. P- and S-wave velocities (Vp and Vs) measurements were first done under hydrostatic loading and then while unloading, with confining pressures varying between 3 and 35 MPa. The results indicate that Vp and Vs in these samples follow a linear relation independent of the pressure change. The ratio Vp/Vs is more responsive to pressure change irrespective of the pore volume. One-third of the carbonate samples show abnormal Vp/Vs reduction with the increase in the effective pressure. The pressure dependence of velocities (PDV) of Weyburn carbonate rocks varies widely even for samples from the same formation with similar sedimentary history. Samples with loosely packed crystals and/or relatively large dominant pore diameter have higher PDV. The exponential empirical model V = A-Ctext{e}^{DP_{text{e}}} was tested; therein, V is the elastic wave velocity, Pe is the effective confining pressure, and A, C and D are the best fitting coefficients determined by curve fitting. The model gives good fits for most of the Weyburn carbonate samples. From a statistical point of view, there is no difference between the Vp- and Vs-derived exponential coefficient D.

Illustrating Membrane-Dominated Regimes in Pressurized Thin Shells

Pressurized thin-wall structures cover a broad range of applications, including storage tanks, pressurized rubber flood barriers, and large span enclosures. To accurately model such structures, the analyst must select the appropriate mechanical formulation (e.g.membrane vs shell). Membranes are assumed to have negligible bending stiffness and respond to compression by wrinkling; shells resist axial compression (before buckling) and bending efficiently. While theoretical research on these differences is vast, this study aims to explicitly clarify the consequences of this choice and permit a comparison of error between membrane and shell formulations. Therefore, this paper presents a parametric study of canonical pressurized thin-wall structural geometries (i.e.semi-cylinder, hemisphere) to illustrate the transitions between membrane and bending dominant behavior. The mathematical models of a pneumatic 5-parameter shell and membrane are presented and employed to quantify the effects of variables such as thickness and geometry on the amount of membrane, bending, and shear energy. The effects of inflation pressure, self-weight, and hydrostatic loads are also considered. The graphical results, presented in terms of dimensionless quantities in the design space, are general and should be of interest to the theorist and practitioner alike.

An explicit formulation of the macroscopic strength criterion for porous media with pressure and Lode angle dependent matrix under axisymmetric loading

This paper aims to propose an explicit formulation of the macroscopic strength criterion for porous media with spherical voids. The matrix is assumed rigid and perfectly plastic with yield surface described by the three-parameter strength criterion, which is Lode angle and pressure dependent and capable of accounting for distinct values of the uniaxial tensile strength, uniaxial compressive strength (UCS) and equal biaxial compressive strength (eBCS). An exact upper bound of the macroscopic strength is derived for porous media subjected to purely hydrostatic loading. Besides, an estimate of the macroscopic strength profile of porous media under axisymmetric loading is obtained in parametric form. Moreover, a heuristic strength criterion in explicit form is further developed by examining limit cases of the parametric strength criterion. The developed strength criteria are assessed by finite-element based numerical solutions. Compared with the parametric strength criterion which involves cumbersome functions, the heuristic one is convenient for practical applications. For specific values of the matrix's strength surface, the proposed heuristic strength criterion can recover the well-known Gurson criterion. The present work also addresses the effect of the ratio of matrix's eBCS to UCS on the macroscopic strength of porous media. For matrix with distinct values of eBCS and UCS, neglecting the difference between eBCS and UCS would result in an underestimation of the macroscopic strength, especially when the pressure is large.

Структурная модель деформирования и разрушения гетерогенных материалов типа сферопластика при действии гидростатического давления

Object and purpose of research. The paper investigates polymeric composite material of syntactic foams type being by nature a heterogeneous medium and consisting of polymeric matrix, filled with spherical inclusions: microspheres. The main purpose of this this paper is to develop a structural model of straining and failure for this type of materials under hydrostatic pressure and software and mathematical apparatus for model implementation. Materials and methods. The input data for this research were composition and structure of syntactic foam material as well as the performance of its components (polymeric matrix and glass microspheres). Structural model was developed on the basis of solutions to linear elasticity theory problems using Lubachevsky – Stillinger algorithm for the formation of structure, homonization methods, etc. A calculation algorithm implemented in code in the С++ language was developed on the basis of the designed mathematical apparatus. Verification of calculation results was carried out by comparison with failure test results of samples of one of the grades of syntactic foam under short-term hydrostatic pressure loading. Main results. Structural model of syntactic foam type material straining and failure under hydrostatic pressure was developed. A calculation algorithm implemented in program code written in the С++ language which is relatively highly efficient for analysis of real structures with a large number of microspheres of the order of 105. Correlation with experimental results showed compatibility of modelling results in terms of both quantitative and qualitative estimates. Conclusion. The developed structural model allows with a high degree of confidence to describe the processes of damage and failure accumulation in syntactic foam under hydrostatic pressure. For practical purposes the model can be used applied for prediction of syntactic foam performance (strength, bulk strain and buoyancy), based on the properties of the initial components – microspheres and polymeric matrix.

The Effect of Subgrade Coefficient on Static Work of a Pontoon Made as a Monolithic Closed Tank

This article presents the effect of taking into account the subgrade coefficient on static work of a pontoon with an internal partition, made in one stage and treated computationally as a monolithic closed rectangular tank. An exemplary pontoon is a single, ready-made shipping element that can be used as a float for a building. By assembling several floats together, the structure can form a floating platform. Due to the increasingly violent weather phenomena and the necessity to ensure safe habitation for people in countries at risk of inundation or flooding, amphibious construction could provide new solutions. This article presents calculations for a real pontoon made in one stage for the purpose of conducting research. Since it is a closed structure without any joint or contact, it can be concluded that it is impossible for water to get inside. However, in order to exclude the possibility of the pontoon filling with water, its interior was filled with Styrofoam. For static calculations, the variational approach to the finite difference method was used, assuming the condition for the minimum energy of elastic deflection during bending, taking into account the cooperation of the tank walls with the Styrofoam filling treated as a Winkler elastic substrate and assuming that Poisson’s ratio ν = 0. Based on the results, charts were made illustrating the change in bending moments at the characteristic points of the analysed tank depending on acting loads. The calculations included hydrostatic loads on the upper plate and ice floe pressure as well as buoyancy, stability and metacentric height of the pontoon. The aim of the study is to show a finished product—a single-piece pontoon that can be a prefabricated element designed for use as a float for “houses on water”.

Mechanical Response of Castlegate Sandstone under Hydrostatic Cyclic Loading

The stress history of rocks in the subsurface affects their mechanical and petrophysical properties. Rocks can often experience repeated cycles of loading and unloading due to fluid pressure fluctuations, which will lead to different mechanical behavior from static conditions. This is of importance for several geophysical and industrial applications, for example, wastewater injection and reservoir storage wells, which generate repeated stress perturbations. Laboratory experiments were conducted with Castlegate sandstone to observe the effects of different cyclic pressure loading conditions on a common reservoir analogue. Each sample was hydrostatically loaded in a triaxial cell to a low effective confining pressure, and either pore pressure or confining pressure was cycled at different rates over the course of a few weeks. Fluid permeability was measured during initial loading and periodically between stress cycles. Samples that undergo cyclic loading experience significantly more inelastic (nonrecoverable) strain compared to samples tested without cyclic hydrostatic loading. Permeability decreases rapidly for all tests during the first few days of testing, but the decrease and variability of permeability after this depend upon the loading conditions of each test. Cycling conditions do affect the mechanical behavior; the elastic moduli decrease with the increasing loading rate and stress cycling. The degree of volumetric strain induced by stress cycles is the major control on permeability change in the sandstones, with less compaction leading to more variation from measurement to measurement. The data indicate that cyclic loading degrades permeability and porosity more than static conditions over a similar period, but the petrophysical properties are dictated more by the hydrostatic loading rate rather than the total length of time stress cycling is imposed.

Time-dependent compaction of deep-water reservoirs: A study on the viscous behavior of unconsolidated sandstone

There have been many studies on reservoir compaction where different mechanisms being suggested as the reasons behind the changes of porosity, permeability, and integrity of reservoirs during production. The theory of poroelasticity is often used to evaluate the likelihood of reservoir compaction, however, it has failed to explain the time dependent viscous behavior of unconsolidated formations. In this study, attempts are made to have a closer look into the compaction mechanism of deep-water sandstone reservoirs by bringing a case study from a gas field in Australia. The results obtained indicated that depending on the type of clays presented in the rock matrix, confining pressure and the loading rate, unconsolidated/poorly consolidated sandstone may exhibit an elasto-plastic or viscoplastic behavior during compaction. It was also found that the deformations initiated during compaction is a time-dependent process and can be a function of clay type in the sandstone matrix. It appears that kaolinite pushes the sandstone to exhibit an elastoplastic behavior while sandstones with a huge amount (more than 45%) of illite/smectite show a viscous (time dependent) response to hydrostatic loading. It was also revealed that the viscous behavior is induced once the confining pressure reaches a certain threshold (above 10 MPa). It seems that as the loading rate increases from 0.5 MPa/min to 1 MPa/min, a viscoplastic deformation dominates but an elasto-plastic response is revealed once the loading rate reduces to 0.25 MPa/min. It was concluded that the type of clays and their contribution in the rock matrix should be analysed very carefully to determine the geomechanical responses of deep-water reservoirs under different in-situ stress conditions.

Time Dependent Mechanical Crack Closure as a Potential Rapid Source of Post‐Seismic Wave Speed Recovery: Insights From Experiments in Carrara Marble

AbstractSeismological observations indicate strong variations in wave velocities around faults both co‐seismically during earthquakes, and post‐seismically. Recovery is commonly associated with a reduction in crack damage. Here, we explore the recovery associated with time‐dependent mechanical closure of cracks. We report results from laboratory experiments conducted on dry cores of Carrara marble at room temperature. We deformed cylindrical samples in the semi‐brittle regime to induce crack damage before subjecting them to hydrostatic and triaxial stress conditions for extended periods of time while recording dilatancy and wave speeds repeatedly. We report wave speed increases of up to 40% of the damage‐induced wave speed drop in samples subject to hydrostatic loading. Moreover, we report the occurrence of significant wave speed increases contemporaneously with time‐dependent creep in triaxially loaded samples. Wave speed recovery during creep is only observed below a threshold creep strain rate, a result we interpret as a transition from brittle to plastic creep with decreasing strain rate. We interpret the wave speed increase in terms of reduced crack density and increased contact area within the crack array, and show that around 40% of the total crack surface has to be closed to justify the observed wave speed recoveries. We propose that mechanical crack closure is driven by the viscous relaxation of the bulk rock under the influence of locked‐in stresses at low confining pressure, and of the external stresses at higher confining pressure. Our study shows that mechanical crack closure is a significant source of time‐dependent wave speed recovery.

EXPERIMENTAL VERIFICATION OF CONSTRUCTIVE SOLUTION OF A NEW TYPE FRAMEWORK

Experimental verification is an integral part of the study for both new designs and new materials and technologies. To assess the features of deformation of the lightweight frame, a series of tests using the method of hydrostatic loading, developed at the Department of Building Structures O.M. Beketov national university of urban economy in Kharkiv. A fragment of a monolithic reinforced concrete frame with a floor slab with a span of 6.0 m and a thickness of 500 mm (thickness of both claddings 100 mm, liner thickness 300 mm) was selected as the object of study. The purpose of the study is to assess the deformability of lightweight frame structures. The tests were implemented under the action of short-term and long-term evenly distributed loads, and were carried out in accordance with the method of hydraulic tests of plates and shells on the basis of the requirements of DSTU B B.2.6-7: 95. For research the research method based on hydrostatic loading of object when loading is set by weight of water is used, and its size is regulated by height of a water column. To carry out the described test procedure on the mezzanine floor of the seventh floor was assembled inventory pool of formwork panels with dimensions in terms of 5.2x2.8 m and a board height of 1.15 m. To register the measured displacements, sensors are supplied to the object under study, which allow to establish the characteristics of the stress-strain state of the object of study. Use of this method, in comparison with other existing, allows to define durability and deformability of various full-scale designs at short-term and long loading without their destruction and a stop of production process. The obtained results of field testing of a fragment of a lightweight frame indicate that the nature of the deformation of the floor under load correlates with the results of similar studies that have been repeatedly conducted for the frames of buildings with load-bearing elements with a continuous cross section.

Response of an underwater cylindrical composite shell to a proximal implosion

An experimental investigation is conducted to study the dynamic underwater response of a cylindrical composite shell under near critical hydrostatic pressure, to the implosion of another shell in proximity. A primary cylindrical composite shell is imploded in proximity to a secondary shell which is similar in all respects except for the secondary shell having a smaller length. Length differences of 10% and 20% are chosen to simulate variations in collapse pressures occurring in shells from real life manufacturing defects and/or degradation during operational use. The response of the secondary shell is investigated to understand if and how its collapse occurs in addition to studying the Fluid-Structure Interaction (FSI) phenomenon. The pair of shells are subjected to underwater hydrostatic loading using a large pressure vessel suitable for high-speed photography in conjunction with 3D Digital Image Correlation (DIC). 3D-DIC is employed to obtain full-field displacement measurements of both the shells, and local dynamic pressure histories are also simultaneously recorded. The primary shell always imploded first, causing a dynamic loading on the secondary shell. In cases of implosion of the secondary shell, although the transient radial deformations occurred in mode 2, the failure itself occurred with a localized failure of the shell walls. It is observed that there exists an inner critical stand-off distance for the secondary shell to fail catastrophically upon the implosion of the primary shell, and an outer critical stand-off distance beyond which the secondary shell does not implode. A critical stand-off distance is found to exist only in the case of the 10% smaller secondary shell length. If the secondary shell stand-off distance is more than the outer critical distance or when length of the secondary shell is 20% smaller, the secondary shell responds with bending and breathing modes and no visible damage is recorded. When the stand-off distance is in between the inner and the outer critical distances, the relative orientation of the incipient modal shapes of the two shells is the factor governing the collapse of the secondary shell. A method is also developed to decouple full-field 3D-DIC measurements into bending and breathing deformation measurements.

Effects of multiaxial pre-stress on Lamb and shear horizontal guided waves

A theoretical model is derived to extend existing work on the theory of acoustoelasticity in isotropic materials subjected to uniaxial or hydrostatic loadings, up to the case of arbitrary triaxial loading. The model is applied to study guided wave propagation in a plate. The semi-analytical finite element method is adapted to deal with the present theory. Effects of triaxial loading on velocities of Lamb and shear horizontal (SH) modes are studied. They are non-linearly dependent on stress, and this nonlinearity is both frequency-dependent and anisotropic. Velocity changes induced by the effect of stress on the plate thickness are shown to be non-negligible. When a stress is applied, both Lamb and SH modes lose their simple polarization characteristics when they propagate in directions different from the principal directions of stress. The assumption that effects induced by a multiaxial stress equal the sum of effects induced by each of its components independently is tested. Its validity is shown to depend on frequency and propagation direction. Finally, the model is validated by comparing its predictions to theoretical and experimental results of the literature. Its predictions agree very well with measurements and are significantly more accurate than those of existing theories.

Cold deformation of non-circular drill pipes

In this paper, the pipe billet dimensions are determined according to the required kelly configuration. A finite element model of the deformation center at drawing junctions is created. Based on the stress-strain calculations, the following invariants are determined: hydrostatic pressure, load, and degree of shear strain. The metal damage extent is determined and proved to be reducible by performing the two-pass drawing. It is shown that the ‘pendulum’ heat treatment provides for complete healing of the metal defects caused by plastic deformation. As a result, a technology of producing high quality kellies is proposed.

Diamond-like structures under hydrostatic loading: Atomistic simulation

In the present work, the mechanical behavior of diamond-like phases under hydrostatic tension and compression is addressed. Three types of stable diamond-like phases composed from the carbon polymorphs (fullerene, carbon nanotube, and graphene) as structural units are considered by atomistic simulation. Elastic constants of the phases under consideration are calculated and analyzed. The Young modulus exhibits mechanical anisotropy and, for some carbon phases, obtained values are close to that of the diamond. The atomistic simulation indicates that these new carbon allotropes can sustain quite high applied compression similarly to diamond. The calculated critical values of applied tensile strain confirmed that diamond-like phases are high-strength structures with a promising application prospect. The deformation mechanisms of diamond-like phases under hydrostatic tension and compression are presented: for all the considered phases, deformation occurs due to changes in the lengths of valence bonds and valence angles, however, the peculiarities of the process depends on the phase morphology.

Field Evaluation of Wattle and Silt Fence Ditch Checks

Erosion and sediment control practices are implemented during construction activities to mitigate downstream effects, but limited field-performance data exists. Field assessments were conducted to evaluate ditch check installations during highway construction in Tama County, Iowa. Data collection included daily rainfall, topographical surveys of sediment deposition, pre- and post-rain event images, and visual observations. Variations to the standard Iowa Department of Transportation silt fence ditch check installation evaluated as part of this study include: (a) upgrading non-reinforced geotextile to a multi-belted, reinforced geotextile (i.e., SF-M1); (b) installing V-shape, as opposed to linear, while incorporating wire reinforcement to support hydrostatic loads placed on the geotextile, inclusion of a weir to facilitate controlled flow discharge, and offsetting the geotextile entrenchment location to improve ground securement (i.e., SF-M2); and (c) installing the dich check as described for SF-M2 substituting slicing for trenching (i.e., SF-M3). The modified wattle installation (i.e., W-M) incorporated a teepee staking configuration to facilitate ground contact, and an excelsior underlay, secured by sod staples, to minimize wattle undercutting. Results from field experiments indicated that sediment retention rates significantly improved for installations of SF-M2 and SF-M3 when compared with the standard installation and SF-M1 at the 85% confidence level, and served as viable control measures in concentrated flow applications. The W-M installation exhibited a statistically significant improvement in sediment retention over the W-S installation at the 95% confidence level. These findings suggest that ditch check performance is a function of specified practice and of installation methods described within regulatory agency specifications and design guidelines.

A closed-form yield criterion for porous materials with Mises–Schleicher–Burzyński matrix containing cylindrical voids

This work develops a closed-form yield criterion applicable to porous materials with pressure-dependent matrix presenting tension–compression asymmetry (Mises–Schleicher–Burzynski material) containing parallel cylindrical voids. To develop the strength criterion, the stress-based variational homogenization approach due to Cheng et al. (Int J Plast 55:133–151, 2014) is extended to the case of a hollow cylinder under generalized plane strain conditions subjected to axisymmetric loading. Adopting a strictly statically admissible trial stress field, the homogenization procedure results in an approximate yield locus depending on the current material porosity, tension–compression material asymmetry, the mean lateral stress, and an equivalent shear stress. The analytical criterion provides exact solutions for purely hydrostatic loading. Theoretical results are compared with finite element (FE) simulations considering cylindrical unit-cells with distinct porosity levels, different values of the tension–compression asymmetry, and a wide range of stress triaxialities. Based on comparisons, the theoretical results are found to be in good agreement with FE simulations for most of the loading conditions and material features considered in this study. More accurate theoretical predictions are provided when higher material porosities and/or lower tension–compression asymmetries are considered. Overall, the main outcome of this work is a closed-form yield function proving fairly accurate predictions to engineering applications, in which pressure-dependent and tension–compression asymmetric porous materials with cylindrical voids are dealt with. This can be the case of honeycomb structures or additively manufactured materials, in which metal matrix composites are employed.

Regulation of chondrocyte biosynthetic activity by dynamic hydrostatic pressure: the role of TRP channels

ABSTRACT Introduction: Chondrocytes perceive and respond to mechanical loading as signals that regulate their metabolism. Joint loading exposes chondrocytes to multiple modes of mechanical stress, including hydrostatic pressure; however, the mechanisms by which chondrocytes sense physiologically relevant levels of hydrostatic pressure are not well understood. We hypothesized that hydrostatic pressure is transduced to an intracellular signal through mechanosensitive membrane ion channels of chondrocytes. The goals of this study were to examine the effect of hydrostatic loading on the development of engineered cartilage tissue and the contribution of mechanosensitive ion channels on these hydrostatic loading effects. Methods: Using a 3D model of porcine chondrocytes in agarose, we applied specific chemical inhibitors to determine the role of transient receptor potential (TRP) ion channels TRPV1, TRPV4, TRPC3, and TRPC1 in transducing hydrostatic pressure. Results: Hydrostatic loading caused a frequency and magnitude-dependent decrease in sulfated glycosaminoglycans (S-GAG), without changes in DNA content. Inhibiting TRPC3 and TRPV4 decreased S-GAG content; however, only the inhibition of TRPV1 partially attenuated the hydrostatic loading-induced reduction in S-GAG content. Conclusions: Our findings indicate that TRPV1 may serve as a transducer of hydrostatic pressure in chondrocytes, and provide further support for the role of TRPV4 in regulating chondrocyte anabolism, as well as initial evidence implicating TRPC3 in chondrogenesis. These findings add to our further understanding of the chondrocyte “channelome” and suggest that a range of ion channels mediate the transduction of different biophysical stimuli such as hydrostatic pressure, membrane stretch, or osmotic stress.