Hydrostatic Loading Conditions Research Articles

Modelling, optimization, and testing of novel cuboidal spherical plate lattice structures

ABSTRACT This study investigates the mechanical behavior of a novel set of Cuboidal Spherical Plate Lattice (CSPL) materials. The procedure of constrained-domain topology optimization is implemented with the aim of enhancing stiffness. The micromechanical finite element homogenization approach is used to evaluate the effective elastic-plastic properties of the CSPLs and their topologically optimized counterparts, TOCSPLs (Topologically Optimized Cuboidal Spherical Plate Lattices). The TOCSPLs demonstrate higher uniaxial, shear, and bulk moduli compared to the CSPLs, with an increase of 31%, 14%, and 36% respectively. Moreover, there is an increase in the yield strengths under uniaxial, shear, and hydrostatic loading conditions, with enhancements of 103%, 55%, and 62%, respectively. The topologies are additively manufactured through Fused Deposition Modeling (FDM) out of ABS thermoplastic material. The quasi-static compression experiments demonstrate the superiority of TOCSPL 111+100 over the other topologies in terms of uniaxial modulus. The suffix 111+100 denotes the crystallographic planar orientations in which the solid plate-like disks were formed within a cubic system. The topologies proposed herein outperform certain types of Triply Periodic Minimal Surface, honeycomb, truss-, and plate-based lattice materials. The proposed topologies offer a compelling justification for their utilization in applications that require load-bearing and impact absorption capabilities.

Out of-plane failure analysis of masonry walls subjected to hydrostatic and hydrodynamic loads induced by flash floods

Damage surveys from past flash flood events show that the combined hydrodynamic impulsive loading and the subsequent hydrostatic loading due to rising water levels caused the failure of masonry walls/buildings. However, limited studies have been conducted to understand the responses of masonry walls to these loading states. To bridge this knowledge gap, an explicit 3D shell element based finite element modelling method that incorporates a homogenised anisotropic masonry material model was developed and applied to analyse the out-of-plane collapse behaviour of masonry walls under flash flooding conditions. The developed modelling method was validated with an available experimental study of masonry wall subjected to hydrostatic loading conditions. It was then extended to comprehend the behaviour of masonry walls under hydrodynamic impulsive water pressures. Results reveal that the effect of hydrodynamic impulsive loading generated by the first hit of the flash flood water is significant in reducing the stiffness of the masonry. This reduction in stiffness can result in an early collapse of the wall, even with a gradual rise of hydrostatic water level. This study has also evaluated the behaviour and damage patterns of masonry walls with two different slenderness ratios (single brick/24.5 and double brick/11.7) under flash flooding and prescribed the maximum percentage of surface area of inundation that the walls can resist. The importance of considering hydrodynamic impulsive loading in designing masonry buildings vulnerable to flash flooding and the capability of the modelling technique developed in this research for evaluating their vulnerability under these flooding scenarios are highlighted.

Stress sensitivity of multiscale elastic properties under hydrostatic loading conditions of organic shales at different thermal maturity stages

Shales serve essential functions as seals for conventional hydrocarbon reservoirs, waste storage repositories and unconventional plays. Exploration and evaluation of shales rely on the characterization of their multiscale elastic properties. However, there are limited studies on the geologic controls of elastic stress sensitivity in organic shales. This study investigated dry Lokpanta, Bakken, and Niobrara shales of different thermal maturity stages. First, we used a pulse-transmission ultrasonic setup to conduct multidirectional (0o, 45o and 90o) hydrostatic-stress sensitivity (0–27.58 MPa) tests to measure elastic waves and derive other elastic properties. Furthermore, we inverted microscopic parameters from the elastic measurements based on effective medium theories such as damage parameters (αij and βijkl), crack density (ρ), normal to tangential microcrack compliance (B), specific tangential crack compliance (snBT) and microcracks orientation anisotropy (η). Finally, we studied the effects of organic matter maturity and clay diagenesis on the multi-scaled elastic stress sensitivity. Under applied hydrostatic stress, the non-linear elastic response in the shales is consistent with the closure of aligned microcracks. Microcrack closure decreased the elastic anisotropy at lower stress (<10 MPa), while aligned clays and organic matter control the stress-insensitive anisotropy at higher stress. As organic matter matures and smectite transforms to illite, orthogonal velocity stress sensitivity increases and extrinsic contribution to elastic anisotropy increases. There is also a corresponding increase in orthogonal damage second-rank tensor (α33) and a decrease in orthogonal damage fourth-rank tensor (β3333) with organic matter-clay thermal maturity. These relationships are due to the thermally-induced development of new and/or extensional roughly-textured microcracks parallel to the laminated microfabric, which is of higher compliance in the shear than compression. Microcrack closure also decreases ρ under applied pressure. Most of the samples had B < 0.5, suggesting the presence of non-idealized roughly textured microcracks. Generally, snBT broadly decreases and η increases with clay diagenesis and organic matter maturity also because of the generation and/or enhancement of aligned microcracks resulting in higher tangential stiffness.

Hydrostatic high strain rate loading response of closed-cell polymeric foams as a function of mass density

Closed cell polymeric foams are widely used in naval structures as sandwich core material owing to their lightweight and high energy absorption capabilities. There has been a great push towards understanding their material response under multiple loading scenarios, however, the loading scenarios have been limited to uniaxial or multiaxial in air loadings at different strain rates. Here, the hydrostatic elastic response and yield behavior of PVC foams with varying mass densities under a high strain rate hydrostatic loading state have been investigated. A novel underwater high strain rate loading facility is utilized to subject these foams to near blast strain rate hydrostatic loading. Using the 3-D Digital Image Correlation (DIC) technique in conjunction with ultra-high-speed photography, full-field volumetric deformation data is obtained. The dynamic loading data is obtained using a piezoelectric pressure sensor. This enables the measurement of material yield strength and bulk modulus for these materials under high strain rate hydrostatic loading conditions. The foams demonstrate increment in bulk modulus and yield strength under high strain rate loading. Further, the increment observed is highly sensitive to the material bulk mass density.

Optimization of Composite Cylindrical Shell Structures for Hydrostatic Pressure Loading

Abstract Deep-sea structures will collapse/implode under hydrostatic pressure when the structure dives below an instability threshold, leading to catastrophic failure. To better understand how the layup angle of composite cylindrical shells influences this instability threshold, this work explores how composite cylinders can achieve the highest (optimum) critical collapse pressure under hydrostatic loading conditions. To perform this analysis, a closed-form analytical cylinder buckling solution developed by previous work is used in conjunction with different cylindrical geometrical configurations and composite properties for glass, carbon, and intraply hybrid composite properties for woven and unidirectional structures. The results show that a composite structure's optimum layup configuration is unique to the structure's geometry and material system. However, general trends are observed for these different systems, such as how symmetric and asymmetric constructions place the axial-resistant layers near the neutral plane of the composite system. In addition, both constructions need an increase in shear-resistance layers as the L/D ratio decreases regardless of the material system. Lastly, the analytical approach presented in this work can be used to accurately determine the optimum layup angle for thin composite cylindrical structures that are subjected to external hydrostatic pressure.

Vertical velocity at hydrostatic and anisotropic stresses

Sonic and dipole wireline tools measure Vp and Vs along the vertical direction. The state of stress in the subsurface is predominantly anisotropic, while most laboratory experiments measuring the dynamic elastic properties are conducted under hydrostatic stress. The question we ask is whether such laboratory experiments provide the velocities that are close to those measured in the vertical wellbore where the stresses are anisotropic. To address this question, we conducted ultrasonic pulse transmission experiments on several room-dry rock samples. The comparison was made between the P- and S-wave velocities obtained at pure hydrostatic loading conditions and those at a smaller hydrostatic stress with added axial stress, so that the total stress along the axis of a cylindrical plug was the same as under pure hydrostatic loading. These differences were significant in the extreme case of only 1 MPa hydrostatic confining stress with the axial stress increasing up to 40 MPa. However, as the hydrostatic (confining) stress increased, the differences between the velocities along the axis of the sample became smaller and smaller. For example, at 1 MPa confining and 30 MPa axial stress, the relative difference in Vp was about 10%, while that in Vs was about 20%. However, at 10 MPa confining stress, these differences became about 3% and 6%, respectively, and further decreased as the confining stress increased. This means that even at strong in-situ contrasts between the vertical and horizontal stresses, the results of laboratory hydrostatic experiments can be used for in-situ velocity estimates. These results also appear to be consistent with a theoretical model that predicts the directional velocities at any triaxial stress conditions from those measured versus hydrostatic stress.

Ex Vivo Hydrostatic Pressure Loading of Atrial Tissues Activates Profibrotic Transcription via TGF-β Signal Pathway.

Excessive mechanical stress causes fibrosis-related atrial arrhythmia. Herein, we tried to investigate the mechanism of atrial fibrogenesis in response to mechanical stress by ex vivo approach. We collected atrial tissues from mice and then cultured them as "explants" under atmospheric pressure (AP group) or 50 mmHg hydrostatic pressure loading (HP group) conditions. Pathway-specific PCR array analysis on the expression of fibrosis-related genes indicated that the loading of atrial tissues to 50 mmHg for 24 hours extensively upregulated a series of profibrotic genes. qRT-PCR data also showed that loading atrial tissues to 50 mmHg enhanced Rhoa, Rock2, and Thbs1 expression at different time points. Interestingly, the enhanced expression of Thbs1 at 1 hour declined at 6-24 hours and then increased again at 72 hours. In contrast, an enhanced expression of Tgfb1 was observed at 72 hours. In contrast, daily loading to 50 mmHg for 3 hours significantly accelerated the outgrowth of mesenchymal stem-like stromal cells from atrial tissues; however, we did not observe significant phenotypic changes in these outgrowing cells. Our ex vivo experimental data clearly show the induction of profibrotic transcription of atrial tissues by HP loading, which confirms the common pathological feature of atrial fibrosis following pressure overload.

Evolution of shape and size of voids under shear dominated loading conditions in ductile materials

The micromechanism of ductile fracture involves processes of void nucleation, growth, and coalescence. The change of void volume fraction with loading in porous metals affects their stress carrying capability. These changes depend upon the stress triaxiality. Though the voids grow under hydrostatic loading conditions, they tend to distort in shear dominant loading conditions leading sometimes to change in porosity. In addition, the voids change their shape and orientation during the loading process which needs to be captured accurately in a material constitutive model in order to predict the deformation behavior. Many of the existing models in literature do not adequately represent the changes in void volume fraction and their shape for a wide range of values of stress triaxilities. In this work, a scheme has been proposed to evaluate the change of average shape of the ellipsoidal and cylindrical voids consistent with their change in volume fraction with loading for different types of loading conditions including those of shear dominated conditions. The results of the proposed method have been validated with 2D and 3D cell model finite element analysis under pure shear, combined tension-shear, and compression-shear loading conditions.

Viscoelastic properties of architected foams based on the Schoen IWP triply periodic minimal surface

In this article, we studied the viscoelastic properties of an architected foam based on the mathematically-known Schoen IWP triply periodic minimal surface (TPMS) under both time and frequency domains. IWP-based architectures possess unique multifunctional attributes when used as a three-dimensional (3D) reinforcement in composites. The 3 D representative volume elements (RVEs) of different relative densities (i.e., the ratio of the foam’s density to the density of its solid counterpart) were generated and studied using the finite element method in order to predict the effective uniaxial, shear, and bulk viscoelastic responses of IWP-foams as a function of relative density and/or frequency. The principle of time-temperature superposition principle was used to create the master curve of the observed relative-density dependent mechanical responses (loss tangent, storage and loss moduli) in frequency domains. Reduced uniaxial, bulk, and shear stiffness-loss map results suggested that the IWP-foam possesses strongest uniaxial viscoelastic response while highest damping can be achieved under shear responses. Relaxation behavior of IWP-foam was compared with other six different types of open-cell periodic foams. It was found that IWP-foam uniaxial response is similar to simple cubic foam, bulk relaxation response is similar to primitive-foam while shear response follows the behavior of body centered cubic foam. Among these foams, we found that IWP-foam is the best candidate to use as a damper under uniaxial and hydrostatic loading conditions.

Damage effects of adhesives in modern glass façades: a micro-mechanically motivated volumetric damage model for poro-hyperelastic materials

This paper presents a micro-mechanically motivated volumetric damage model accounting for cavitation effects in modern glass connections, e.g. laminated glass connections. The volumetric part of an arbitrary Helmholtz free energy function is equipped with an isotropic damage formulation. To develop a micro-mechanical damage model, the porous micro-structure of a transparent structural silicone adhesive is analyzed numerically applying hydrostatic loading conditions. Based on the structural responses of different types of cubic representative volume elements incorporating an initial void fraction, three damage parameters are fitted utilizing the Levenberg–Marquard algorithm. The present volumetric damage model is implemented into ANSYS FE Code using a UserMat subroutine, where the algorithmic setting is described in detail in the present paper. To compare the structural responses of cubic equivalent homogeneous materials with representative volume elements, benchmark tests under hydrostatic loading are performed. The results indicate that the novel damage model accounts adequately for volumetric damage due to the cavitation effect. A special form of the pancake test is described briefly. The test allows for visualizing the cavitation effect during experimental testing. The experimental results of the pancake test are compared with numerical results, where the pancake test is simulated incorporating the micro-mechanical damage model. The micro-mechanically motivated scalar, internal damage variable is equipped with the obtained damage parameters from the structural response of the representative volume elements. The results show an adequate approximation of the experiment through the simulation. However, to optimize the results of the simulation, an optimization study on the damage parameters is conducted utilizing the Downhill-Simplex algorithm. Using the optimized damage parameters, the simulation of the pancake tests is further improved. Hence, it is shown that the novel micro-mechanically motivated volumetric damage model is excellently suited to represent the cavitation effect in poro-hyperelastic materials.

Transmissivity of aligned and displaced tensile fractures in granitic rocks during cyclic loading

The pressure dependent fracture permeability of four granitic rock samples was determined in a triaxial test cell under hydrostatic loading conditions at a temperature of 30°C. Tensile fractures were generated in cylindrical samples by Brazilian tests. Confining pressures were cycled twice between 2 and 50MPa. Permeability and strain responses were determined for two samples with aligned fracture surfaces and for two samples with a shear displacement of 1mm. Fracture apertures were also determined optically before and after testing and the fracture surfaces were scanned. Permeability of the intact granite matrix is below 1e−18m2 and sample permeabilities of fractured samples range between 1e−17m2 and 1e−12m2 depending on displacement and confining pressure. Fracture permeabilities of the aligned samples range from 1e−12m2 to 2e−10m2 and samples with displaced fracture surfaces have fracture permeabilities between 1e−11m2 and 2e−9m2. Without shear displacement, fracture permeability is reduced with time, even at low constant confining pressures of 2MPa, while fracture permeability is constant at the same conditions for the displaced samples. With increasing confining pressure, permeability reduction is significantly less for the displaced samples compared to the aligned samples. Fracture permeabilities of displaced fractures in granites are similar to fracture permeabilities in sedimentary rocks using proppants. The results indicate that self-propped displaced fractures in granites may allow sufficient fluid flow for reservoir engineering purposes such as enhanced geothermal system development, without the use of propping agents.

A model for elastic flexoelectric materials including strain gradient effects

A constitutive model for elastic flexoelectric materials under small deformation based on second gradient continuum theory is developed, using a Toupin-like variational formulation to simultaneously obtain constitutive relations, balance equations and boundary conditions. The model includes three different electromechanical “stresses”: a higher-order stress, an extended local electric force and a generalized Cauchy stress tensor. The constitutive equations of the model are obtained by postulating an internal energy density function which depends on both the strain and its gradient as well as the polarization. Finally, as an application of the model, we derive the explicit analytical expressions of the polarization and displacement vector fields for the problem of the polarization induced over a thin spherical shell subjected to hydrostatic loading conditions.

Quantifying uncertainty in Hoek–Brown intact strength envelopes

Uncertainty plays a critical role in geotechnical design projects. In addition to the natural variability of geomaterials, testing, transformation and modelling errors must also be considered to accurately characterize rockmass behaviour. By using statistical methods to quantify the intact rock strength and a measure of rockmass quality, a greater understanding of the variability in ground response and support performance can be achieved. This paper examines the issue of quantifying uncertainty in rockmass strength by using the generalized Hoek–Brown approach, which defines rockmass strength according to the intact strength envelope (based on test data) and the geological strength index (GSI). While uncertainty in GSI can be quantified through either a qualitative or quantitative approach, it is more difficult to assess the uncertainty in the intact strength envelope as it is defined by two correlated variables: the uniaxial compressive strength (UCS) and the Hoek–Brown material constant. A new set of linear and nonlinear regression approaches is proposed that can be used to accurately determine the mean intact strength envelope and quantify uncertainty from test data. A reliability-based design method is then presented that quantifies and utilizes uncertainty information at each stage of design to obtain a more complete understanding of rockmass behaviour. To demonstrate the usefulness of this approach, a reliability assessment is performed for a circular excavation under hydrostatic loading conditions.

Nonlinear Eulerian thermoelasticity for anisotropic crystals

A complete continuum thermoelastic theory for large deformation of crystals of arbitrary symmetry is developed. The theory incorporates as a fundamental state variable in the thermodynamic potentials what is termed an Eulerian strain tensor (in material coordinates) constructed from the inverse of the deformation gradient. Thermodynamic identities and relationships among Eulerian and the usual Lagrangian material coefficients are derived, significantly extending previous literature that focused on materials with cubic or hexagonal symmetry and hydrostatic loading conditions. Analytical solutions for homogeneous deformations of ideal cubic crystals are studied over a prescribed range of elastic coefficients; stress states and intrinsic stability measures are compared. For realistic coefficients, Eulerian theory is shown to predict more physically realistic behavior than Lagrangian theory under large compression and shear. Analytical solutions for shock compression of anisotropic single crystals are derived for internal energy functions quartic in Lagrangian or Eulerian strain and linear in entropy; results are analyzed for quartz, sapphire, and diamond. When elastic constants of up to order four are included, both Lagrangian and Eulerian theories are capable of matching Hugoniot data. When only the second-order elastic constant is known, an alternative theory incorporating a mixed Eulerian–Lagrangian strain tensor provides a reasonable approximation of experimental data.

Cavitation in elastomeric solids: I—A defect-growth theory

It is by now well established that loading conditions with sufficiently large triaxialities can induce the sudden appearance of internal cavities within elastomeric (and other soft) solids. The occurrence of such instabilities, commonly referred to as cavitation, can be attributed to the growth of pre-existing defects into finite sizes. This paper introduces a new theory to study the phenomenon of cavitation in soft solids that: (i) allows to consider general 3D loading conditions with arbitrary triaxiality, (ii) applies to large (including compressible and anisotropic) classes of nonlinear elastic solids, and (iii) incorporates direct information on the initial shape, spatial distribution, and mechanical properties of the underlying defects at which cavitation can initiate. The basic idea is to first cast cavitation in elastomeric solids as a homogenization problem of nonlinear elastic materials containing random distributions of zero-volume cavities, or defects. This problem is then addressed by means of a novel iterated homogenization procedure, which allows to construct solutions for a specific, yet fairly general, class of defects. These include solutions for the change in size of the defects as a function of the applied loading conditions, from which the onset of cavitation — corresponding to the event when the initially infinitesimal defects suddenly grown into finite sizes — can be readily determined. In spite of the generality of the proposed approach, the relevant calculations amount to solving tractable Hamilton–Jacobi equations, in which the initial size of the defects plays the role of “time” and the applied load plays the role of “space”. When specialized to the case of hydrostatic loading conditions, isotropic solids, and defects that are vacuous and isotropically distributed, the proposed theory recovers the classical result of Ball (1982) for radially symmetric cavitation. The nature and implications of this remarkable connection are discussed in detail.

Improvement of energy efficiency of rock comminution through reduction of thermal losses

The principal objective of this work was to develop a thermal imaging technique to measure the radiant heat coming from rock particles during or immediately after crushing, with the purpose of minimising energy losses while maintaining the efficiency of rock crushing. The main goal of the work was energy optimization of crushing in High Pressure Grinding Rolls (HPGR). We were able to perform reproducible measurements of the temperature increase that occurs during transient events such as dynamic rock breakage and HPGR crushing. Results obtained show that with an increase of energy introduced, there is an increase in the maximum temperature along the fractured surface as well as increases in the overall amount of thermal energy. Results obtained during HPGR testing clearly indicate that there is an optimum intensity of pressure to which rock needs to be exposed. Any further increase in pressure, results in only a marginal increase in fragmentation and a significant increase in unproductive heating of rock. We were also concerned about the effect of the size of particles coming into the HPGR. The fraction of new fine material (fines) produced during HPGR crushing is much higher in the case of feed with a narrow size distribution, i.e. without pre-existing fines. Significantly, improved performance is achieved with a reduced amount of net comminution energy. Observed relative crushing inefficiency of feed with a wide fragment size distribution (containing fines and coarse particles), is due to a large amount of pre-exiting fines, which clog the pore space between coarser fragments. In the compressed zone of the HPGR this creates approximately hydrostatic compressive loading conditions, which require much higher pressure (i.e. energy) to cause breakage of coarser particles. Experimental results indicate that up to 40% of energy can be saved through optimization of the applied pressure and modification of feed fragments size distribution.

On the loading/shear strength coupling in the probabilistic formulation of the limit-state in shear for gravity dams

ABSTRACT This paper proposes a methodology to take into account of the dependence between hydraulic loading and shear strength in a probability-based procedure for assessing the gravity dam structural safety. This is a major point in a probability-based approach where extreme loadings are a determining factor of dam reliability. The proposed approach uses a parabolic formulation of concrete shear strength. It aims at providing a better representation of the intrinsic curve for normal stress lower levels that might develop in the dam upstream area under extreme hydrostatic loading conditions. Based on the FORM method and on Monte Carlo simulations, a case study shows how relevant the proposed method is and the impact thereof on the results of a reliability analysis completed for an existing gravity dam.

Application of rate‐and‐state friction laws to creep compaction of unconsolidated sand under hydrostatic loading conditions

Rate‐and‐state variable friction laws describe the time‐dependent fault‐normal compaction that occurs during holds in slide‐hold‐slide friction tests on unconsolidated materials. This time‐dependent deformation is qualitatively similar to that observed during volumetric creep strain tests on unconsolidated sands and shales under hydrostatic loading conditions. To test whether rate‐and‐state friction laws can be used to model volumetric creep processes in unconsolidated sands, the rate‐and‐state formulation is expanded to include deformation under hydrostatic stress boundary conditions. Results show that the hydrostatic stress form of the rate‐and‐state friction law successfully describes the creep strain of unconsolidated sand. More importantly, values obtained for rate‐and‐state friction parameters by fitting these data are in the same range as those obtained from more traditional tests by fitting the fault‐normal compaction of simulated gouge during a hold in a laboratory friction experiment.

Explicit formulas for effective piezoelectric coefficients of ferroelectric 0-3 composites

Explicit formulas have been found for the effective piezoelectric coefficients of a 0-3 composite of ferroelectric spherical particles in a ferroelectric matrix. Tensile loading and hydrostatic loading conditions were studied. Assuming that both phases are dielectrically and elastically isotropic, explicit expressions in simple closed form for the effective d33, d31 and dh coefficients were derived in terms of the constituents’ piezoelectric coefficients and the dielectric and elastic properties of the composite and constituents. Prediction of the piezoelectric coefficients for specific composite systems was compared with experimental values from published works, and good agreement with data was obtained. Goodness of fit is not limited to low volume fraction of inclusions.

Effective piezoelectric coefficients of ferroelectric 0–3 composites

We studied theoretically the effective piezoelectric strain coefficients of a 0–3 composite comprising spherical ferroelectric inclusions dispersed in a ferroelectric matrix. Tensile loading and hydrostatic loading conditions were considered. Explicit expressions for the effective d 31, d 33 and d h coefficients were derived for the case of low volume concentration of dispersed particles in terms of the electro-mechanical properties of the constituents. The theoretical predictions of the piezoelectric coefficients were compared with experimental data from previous works and good agreement was obtained.