Compressive Loading Conditions Research Articles

Biomechanical testing of canine tibiae: Changes resulting from different tibial tuberosity advancement techniques - Pilot study.

The objective of the present pilot study was to determine the force required to break (a) intact canine tibiae, (b) tibiae following the osteotomy of the tibial tuberosity and (c) tibiae following Tibial Tuberosity Advancement- (TTA-) rapid surgery. Six pairs of tibiae of dogs between 15 and 35 kg body weight were used in a cadaver study. Three groups were created with four tibiae in each group; intact (Group 1), osteotomy of the tibial tuberosity and tibial crest (Group 2) and TTA-rapid (Group 3). The tibiae were put under static axial compressive load, applied until failure. The force required to break the tibiae was termed maximal force (F max). The mean of F max was 8193.25 ± 2082.84 N in Group 1, 6868.58 ± 1950.44 N in Group 2 and 7169.71 ± 4450.39 N in Group 3. The sample size was small for a statistical analysis but as a preliminary result, we have determined the force (F max) required to break canine tibiae. Furthermore, we hypothesise that osteotomies result in weakening of the tibial structure.

Mechanical testing and biomechanical CT analysis to assess vertebral flexion strength of Chinese cadavers.

Biomechanical CT (BCT), i.e., quantitative computed tomography-based finite element analysis (QCT-FEA), promises an improved technique over bone mineral density (BMD) in predicting bone strength and the risk of osteoporotic vertebral fractures. However, most of the BCT models only consider a uniform compressive loading condition and they have not been validated for Chinese subjects. This study examined the ability of BCT to predict wedge fracture-related vertebral flexion strength in a cohort of Chinese cadaveric vertebrae. Twelve human vertebrae were scanned with dual energy X-ray absorptiometry (DXA) and QCT to measure areal and volumetric BMD, respectively. To produce wedge fractures, the cadaveric vertebrae were experimentally loaded until failure under a 15^° flexion. Vertebral flexion stiffness and strength were measured from the force-displacement curve. Voxel-based heterogeneous FE models of the vertebrae were created and virtually tested in uniform compression and 15^° flexion to compute compressive and flexion strength (and stiffness), respectively. The predictions of vertebral flexion strength with BMD or BCT measures were evaluated with linear regression analyses. Results showed weak correlations between experimentally-measured flexion strength vs. DXA-aBMD (R²=0.26) or QCT-vBMD (R²=0.39). However, there were strong correlations between experimentally-measured flexion strength vs. BCT-computed vertebral strength under either flexion (R²=0.71) or compression (R²=0.70) loading conditions, although flexion reduced the BCT-computed vertebral strength by 9.2%. These results suggest that, regardless of whether a uniform compression or a flexion loading is simulated, BCT can predict in vitro vertebral flexion strength better than BMD.

Numerical Studies on Failure Mechanisms of All-Composite Sandwich Structure with Honeycomb Core under Compression and Impact Loading Conditions.

The all-composite sandwich structure with the honeycomb core is a lightweight and high-strength structure with broad application scenarios. The face sheet and honeycomb core of the proposed all-composite sandwich structure in this work are composed of carbon-fiber-reinforced polymer (CFRP) composites. The mechanical response and damage mechanism of the all-composite sandwich structure under out-of-plane quasi-static compression and out-of-plane impact are studied by numerical methods. The refined finite element models of the sandwich structures are built on the ABAQUS/Explicit platform. The micromechanics of failure (MMF) theory based on physical component failure is used to describe the intralaminar damage mechanism of the face sheet and honeycomb core, and the mixed-mode exponential cohesive zone model (ECZM) is utilized to simulate the initiation and evolution of interlayer damage. In addition, the cohesive contact approach is adopted to capture the debonding failure at the face-sheet/core. The numerical results show that the all-composite sandwich structure has the characteristics of large structural stiffness and strong energy absorption ability. The failure mechanism of the all-composite sandwich structure under compression is mainly matrix damage and delamination of the honeycomb core, with buckling and folding in appearance. Under out-of-plane impact, matrix damage and delamination arise on the upper sheet, little damage is observed on the lower sheet, and the delamination damage morphology tends to be circular with increasing impact energy. In addition, the interface failure of the upper-sheet/core is more than that of the lower-sheet/core. In addition, the matrix damage near the impact center of the honeycomb core tends to be consistent with the delamination contour, and a small amount of fiber failure is also observed, which manifests as a collapse morphology of the impact area. The research results enrich the understanding of the mechanical behavior of all-composite sandwich structures with honeycomb cores and provide theoretical support for their potential applications.

Design optimisation of hollow box pultruded FRP profiles using mixed integer constrained Genetic algorithm

Hollow Pultruded Fibre-Reinforced Polymer (FRP) profiles are increasingly used as structural members in many infrastructure applications. However, there is still a lack of coherent design methodology considering local buckling. This research presents a fast-converging numerical approach combining the Finite Element Modelling (FEM) and the Genetic Algorithm (GA) to design the optimal configuration of the geometry and layup design parameters against local buckling under two separate loading conditions of axial compression and four-point bending. The FEM model was validated experimentally. The mixed-integer constrained optimisation GA code (MI-LXPM) was used to solve the problem. The optimisation objective was to minimise the manufacturing cost per metre of pultrusion while maintaining the same stiffness and strength properties of the control profile. The Kriging model was used to interpolate the design space based on the intermediate optimisation data output and produce a practical design chart linking the profile geometry to the ultimate load capacity. An experimental case study on the design of a hollow rectangular pultruded FRP girder demonstrated the proposed optimisation approach. The new design saved 10.6% of the material cost and enhanced the ultimate strength by 41%.

Tension-compression asymmetry of quadruple CuCoNiBe alloys processed by high-temperature multi-pass equal channel angular pressing (ECAP)

Abstract Among copper alloys, the precipitation (age) hardening quadruple CuCoNiBe alloys due to their superior mechanical properties in terms of the highest strength and elasticity achieved by peak aging have been used over the years in a wide range of industrial applications including aircrafts, coil systems, blast-proof materials, and molding dies. Combined thermomechanical treatment (i.e., equal channel angular pressing [ECAP] processing followed by post-ECAP aging) can result in a further enhancement of the strength of CuCoNiBe alloys due to the grain refinement and the formation of fine precipitates from α-Cu supersaturated solid solution. In this study, for the first time, the effect of severe plastic deformation by ECAP processing on the mechanical behavior of CuCoNiBe alloys is discussed thoroughly based on the material responses to tensile and compressive loading conditions. The results show that, besides a considerable strength enhancement, ECAP processing leads to a strong tension-compression asymmetry and significantly accelerated precipitation kinetics in CuCoNiBe alloys.

Mechanical Characterization of Anchor under Uniaxial Compression Loading Conditions

Bolt reinforcement technology plays an important role in supporting the construction of many engineering fields, and the uniaxial loading characteristics and behavior tests of anchors have great significance to the research and application of anchors. Therefore, four anchor specimens GA ∼ GD were fabricated and tested to explore the macro and microbehavior characteristics of anchors under uniaxial compression. The stress-strain curves for GA ∼ GC specimens under uniaxial compression were analyzed. The stress-strain curve, elastic strain and creep strain, the failure results, and electrochemical impedance spectroscopy of specimen GD under multistage loading were investigated. The results showed a series of behavior characteristics of anchor under uniaxial compression. Under uniaxial compression, the shapes of stress-strain curves of three specimens GA ∼ GC were similar, and they had experienced four different stages from stage I to stage IV, respectively. After calculating the uniaxial compressive strength of the three specimens, the average uniaxial compressive strength of these specimens was σ c ¯ = 8.31 MPa. The stress-strain curve of the specimen GD was obtained by a multi-stage loading test. The total strain of the specimen consisted of elastic strain and creep strain. In the whole process of loading, the proportion of elastic strain was greater than that of creep strain, and the proportion range of elastic strain was 51.90% ∼ 55.82%. Seven electrochemical impedance spectrum curves of the specimen GD under multi-stage compression load were obtained. The dispersion and concentration of Nyquist curves were affected by different loading levels; the higher the loading level, the more dispersed the Nyquist curve is. In the measured Bode diagram, compared with the previous six measurements, the variation laws of impedance value and phase angle measured at the seventh time in the failure stage of the specimen were quite different. The above research and conclusions can provide some reference for the test theory and engineering application of anchors.

MODELLING OF HORIZONTAL DRILL STRING MOTION BY THE LUMPED-PARAMETER METHOD

The motion of drill strings is modeled in the drilling of geotechnological wells in the mining industry by the Lumped-Parameter Method (LPM). This method is widely used in structural mechanics and is most justified in modeling dynamic systems with a variable structure. On the example of horizontal drilling of geotechnological wells, longitudinal vibrations of a drill string with a static compressive load at the left end are considered [1]. The contact interaction of the drill string with the borehole walls and the inertia force of the bit on the destructible rock at the right end of the string are taken into account. The analysis of the column splits number, which specifies the dimension of the system of discrete equations, is carried out by verifying the obtained results with the previously known data [1]. For verification, the developed C# software was used, allowed to determine the error of the column splits in comparison with the test data. The optimal number of the drill string splits in terms of "implementation time - calculation error" by the LPM was identified. The numerical implementation of the model is conducted by the fourth-order Runge-Kutta method. In connection with the increase in the implementation time of the program code due to the increase in the dimension of the system, the numerical algorithm is optimized using the parallel programming tools. The expediency of this optimization is analyzed.

Electromechanical behavior of self-sensing composite sandwich structures for next generation more electric aerostructures

The composite sandwich structures being a leading load-bearing aero-structure with embedded sensors for monitoring and diagnosing its own health is a huge step toward next-generation, more electric, well-connected aero-structures. This work presents a unique design of self-sensing sandwich structure comprising active graphene coated glass fabric piezoresistive facesheets bonded to a Nomex™ honeycomb core. The piezoresistive response of coated fabrics was recorded throughout the manufacturing process using the vacuum assisted resin transfer molding (VARTM) process. The manufactured sandwich structures were tested under three-point bending and compression loading conditions. The effects of coated fabric sensor position and specimen geometrical parameters (span length, core thickness, and beam width) on piezoresistive response of the beams were evaluated during testing. The piezoresistivity was found to be proportional to the span length and width whereas, an inverse relationship was observed with regards to core thickness. By comparing the effects of spatial position, the bottom sided facesheet showed higher sensitivity than the top facesheet. Finally, the Ramberg-Osgood phenomenological model and exponential growth models were proposed to represent experimental piezoresistivity in three-point bending and compression tests, respectively.

Study of strength related resources of hybrid fiber reinforced concrete (HFRC) and energy absorption capacity (EAC)

Cement Concrete is the most widely used building material for all civil engineering applications due to its well-known benefits. However, its limited tensile strength is a concern. It understands, clearly that fiber reinforcement is finest and adaptable way to improve the post cracking tensile strength and energy absorption capacity during under diagonal split tension and under axial compression. In the present investigation study steel and polyester fibers remained in various volume fractions. Control concrete mixture was made with Ordinary Portland Cement (OPC), fine and coarse aggregate along with flyash, silicafume and high range water reducing admixtures. With no change in the constituents of concrete steel fiber reinforced concrete specimens were made with hooked end steel fibers of aspect ratio 80 vol fraction being 1.0%, 1.25% and 1.5%. Similarly, polyester fiber reinforced concrete specimens were made with 12 mm synthetic polyester fibers at 3%, 4% and 5% volume fraction. All the specimens were cured for 28 days and the fresh concrete was tested to ensure the workability by conducting slump test. In comparison to the control concrete, all the fiber reinforced specimens containing single and hybrid combinations exhibited significant improvement in tensile and flexural strength properties. Uni axial compression loading condition was adopted for all the 100 mm × 200 mm cylindrical specimens. In both the loading conditions load distortion curves stood plotted and the areas under the curves were calculated as a measure of energy absorption capacity. Compressive strength as compared to control concrete was enhanced due to polyester fiber, steel fiber, in that order. Split tensile strength has been significantly improved due to polyester hybridisation with steel fibers. Hence the hybridisation has improved the necessary belongings of concrete like split tensile strength and toughness significantly.

Prediction of Rubble-Stone Masonry Walls Response under Axial Compression Using 2D Particle Modelling

To predict the structural behaviour of ancient stone masonry walls is still a challenging task due to their strong heterogeneity. A rubble-stone masonry modeling methodology using a 2D particle model (2D-PM), based on the discrete element method is proposed given its ability to predict crack propagation by taking directly into account the material structure at the grain scale. Rubble-stone (ancient) masonry walls tested experimentally under uniaxial compression loading conditions are numerically evaluated. The stone masonry numerical models are generated from a close mapping process of the stone units and of the mortar surfaces. A calibration procedure for the stone-stone and mortar-mortar contacts based on experimental data is presented. The numerical studies show that the 2D-PM wall models can predict the formation and propagation of cracks, the initial stiffness and the maximum load obtained experimentally in traditional stone masonry walls. To reduce the simulation times, it is shown that the wall lateral numerical model adopting a coarser mortar discretization is a viable option for these walls. The mortar behaviour under compression with lateral confinement is identified as an important micro-parameter, that influences the peak strength and the ductility of rubble-masonry walls under uniaxial loading.

A five-parameter hydrodynamic-plastic model for crushable sand

Sand tends to dilate when sheared under small confining stresses, and compact under high stresses. This has been attributed to grain crushing, and associated with the development of a non-unique critical state in a stress-density space. This paper tackles a wide scope of crushable granular material phenomena that arise due to this interplay between crushing and dilation, by extending the recently proposed hydrodynamic-plastic formulation. The thermodynamic evolution of the state variables are defined by combining the mathematical frameworks of breakage mechanics, hypoplasticity and bounding surface plasticity. Accordingly, the model is distinguished from previous breakage models in that its stress–strain response is incrementally nonlinear, with possible plastic strain developing at any stress level. The model relies on only five mechanical constants which can be determined from typical geotechnical experiments. The predictions of the model are qualitatively compared against experimental tests under monotonic and cyclic compression and shear loading conditions, where it captures a broad range of sand phenomena.

On the Use of Digital Image Correlation to Assess the Damage Behavior of Composite Coupons Under Compression

AbstractA strong increase in the use of composite materials has been observed in all the industrial fields, related to manufacturing of lightweight load‐bearing components. However, despite the excellent mechanical properties that characterize such innovative materials, uncertainties still exist on their complex failure mechanisms. Hence, the use of non‐destructive techniques and experimental tests is needed to increase the understanding of composite materials damage evolution. This paper deals with the use of the Digital Image Correlation (DIC) technique to investigate the failure mechanisms of delaminated composite panels under compressive loading conditions, accounting for the complex phenomena related to unstable delamination growth due to buckling snap‐through. The panels have been produced by tuning manufacturing parameters to test their influence on toughening mechanisms such as fiber bridging. The main aim is to understand how to improve laminate out‐of‐plane performance and delay the delamination growth phenomenon. The obtained data in terms of strain and displacements distributions has been used to assess the phenomenon of delamination propagation related to local delamination and global panels’ instabilities.

The Validity and Inter-Rater Reliability of a Video-Based Posture-Matching Tool to Estimate Cumulative Loads on the Lower Back.

Background: Low back pain (LBP) is known as one of the most common work-related musculoskeletal disorders. Spinal cumulative loads (CLs) during manual material handling (MMH) tasks are the main risk factors for LBP. However, there is no valid and reliable quantitative lifting analysis tool available for quantifying CLs among Iranian workers performing MMH tasks.Objective: This study aimed to investigate the validity and inter-rater reliability of a posture-matching load assessment tool (PLAT) for estimating the L5-S1 static cumulative compression (CC) and shear (CS) loads based on predictive regression equations.Material and Methods: This experimental study was conducted among six participants performing four lifting tasks, each comprised of five trials during which their posture was recorded via a motion capture (Vicon) and simultaneously a three-camera system located at three different angles (0°, 45°, and 90°) to the sagittal plane.Results: There were no significant differences between the two CLs estimated by PLAT from the three-camera system and the gold-standard Vicon. In addition, ten raters estimated CLs of the tasks using PLAT in three sessions. The calculated intra-class correlation coefficients for the estimated CLs within each task revealed excellent inter-rater reliability (> 0.75), except for CS in the first and third tasks, which were good (0.6 to 0.75). Conclusion: The proposed posture-matching approach provides a valid and reliable ergonomic assessment tool suitable for assessing spinal CLs during various lifting activities.

Analytical assessment of nonlinear forced vibration of functionally graded porous higher order hinged beams

This study focuses on the nonlinear free and forced vibration behavior of functionally graded porous beams considering high-order bidirectional porosity distributions. It is assumed that the closed-cell voids are distributed non-uniformly along the thickness and length of the beam. A nonlinear formulation is derived based on the Reddy beam theory, von Karman geometrical nonlinearity using the Hamilton principle. Subsequently, Galerkin technique is implemented to reduce the partial differential equations to a set of nonlinear ordinary differential equations in time. The primary resonance of the system is inspected when the beam is under a combination of a harmonic transverse load and a static compressive axial load. Hence, the harmonic balance method and method of multiple scales are used to develop closed form approximate solutions. It is shown, the method of multiple scales underestimates the amplitude of vibration when either amplitude of vibration or axial load, or both are high. Effects of beam’s aspect ratio, porosity distributions, beam’s shear deformation and porosity volume fraction are studied. Results revealed, the proposed porosity distributions are more effective than the conventional porosity distributions. Furthermore, comparing beams with the same mass reveals that beams with more voids at the center have lowest amplitude of vibration.

Mechanical Behaviour of Magnesium Alloy Based - Fiber Metal Laminates after Fabrication Using Different Metal Surface Treatments

This paper presents an experimental investigation of the mechanical response and failure mode of magnesium alloy-based Fibre Metal Laminates (FMLs) having different surface pretreatments under axial compression loading conditions. To improve the interfacial bonding strength between the metal and composite layers, three categories of samples were fabricated by hot pressing using sandblasted, annealed and both sandblasted and annealed AZ31B magnesium alloy sheets. To evaluate the bonding strength along the shear and normal directions, single lap shear tests and T-peel tests were conducted. It was found that the combination of sandblasting and annealing can greatly enhance the shear and normal interfacial bonding strength compared with only sandblasting and annealing, separately. To assess the effect of the interfacial bonding strength on the FML compressive performance, quasi-static buckling tests were performed at varying surface treatments of the magnesium alloy sheets. The analysis of the load-stroke curves and failure modes indicates that delamination can significantly reduce the buckling capability and structural stability, and that the improvement of interfacial bonding strength can dramatically strengthen the FML compressive capability.

Analysis of Drill-String Nonlinear Dynamics Using the Lumped-Parameter Method

This work aims at studying the nonlinear dynamics of drill strings using the lumped-parameter method (LPM). The study is based on the good consistency of the results of the test problem where the model of the longitudinal vibrations of a horizontal drill string with a static compressive load at the left end is considered. In this paper, this method is applied to discretize linear and nonlinear models of the lateral vibrations of a vertical drill string under the effect of a supersonic gas flow. The obtained results are verified with the previously published data. The optimal number of the drill-string partitions is determined using the developed application, which allows us to estimate the accuracy of the loaded data. The numerical solution of the model is obtained using the fourth-order Runge–Kutta method. The optimization of the numerical algorithm using parallel-programming tools is carried out, and the efficiency of the method is analyzed.

The Influence of Ferrule on the Marginal Gap and Fracture Resistance of Zirconia Endocrowns.

To investigate the precementation mean marginal gap, fracture resistance, and mode of failure of monolithic zirconia endocrowns cemented to endodontically treated molar teeth with butt joint porcelain margins and added ferrule preparation designs. A total of 20 mandibular molars were endodontically treated and prepared to receive endocrown restorations. The teeth were randomly divided into two groups: Group B had a butt joint porcelain margin, while Group F received additional axial reduction with a shoulder finish line that added ferrule. Monolithic zirconia endocrowns were milled, and the marginal gaps were measured at four locations prior to cementation with resin cement. All samples were subjected to thermocycling, followed by compressive static loading. The maximum load causing fracture and mode of failure were recorded. The mean load to failure for Group B (5,616 ± 1,503 N) was not significantly different compared to Group F (5,762 ± 1,618 N) (P = .84). Both groups recorded high rates of irreparable fractures (P = .2699, df = 2). The mean marginal gap in Group B (48.20 ± 12.37 μm) was not statistically significantly different compared to Group F (45.14 ± 8.45 μm) (P = .527). The addition of ferrule to the preparation design had no significant effect on the precementation mean marginal gap, fracture resistance, or mode of failure of monolithic zirconia endocrowns cemented to endodontically treated molar teeth. Monolithic zirconia endocrowns failed predominantly in an irreparable manner, but these failures were at high failure loads. The precementation mean marginal gap for both groups was small in comparison to other materials.

Exploring the Effect of Dispersed Phase on the High Strain Rate Mechanical Response of Nanosilica Dispersions

Shear Thickening Fluids (STFs) constitute a special class of materials which exhibit phase transition from low to high viscosity state when exposed to shearing forces, particularly, when the applied shear rate exceeds a critical value. The last decade has witnessed a mutual symbiotic relationship between STF and high-performance fabrics such as Kevlar®, Dyneema®, Ultra High Molecular Weight Polyethylene (UHMWPE) etc., to produce new light weight and flexible protective materials systems with enhanced knife, stab and ballistic resistant properties than the existing ones. In this study, we explore the effect of particle shape and size on the high strain rate dynamic response of nanosilica dispersions. Shear thickening fluid (STF) was synthesized using fumed silica and spherical nanosilica particles, comprising the dispersed phase, whereas PPG400 (Polypropylene Glycol) was used as the dispersion medium. Ultrasonic homogenization technique was used for the synthesis of STF. The low strain rate rheological characterization was conducted on MCR302 rheometer at 25°C, whereas the high strain rate characterization was performed on inhouse designed and developed SHPB (Split Hopkinson Pressure Bar) apparatus. Fumed silica (FS) particles possess high specific surface area owing to their fractal structure. Therefore, their low molecular weight dispersions exhibit shear thickening behavior thus making them potential candidates for liquid body armour applications. On the other hand, spherical silica dispersions exhibit shear thickening behavior in high phase volume concentrations. Experimental studies showed that spherical silica based STF dispersions exhibited enhanced shear thickening in the low strain rate domain, as well as better mechanical response in terms of higher peak stress under high strain rate compressive loading conditions, during SHPB testing, in comparison to their fumed silica counterpart. Thus, it can be inferred that the mechanical response of nano-silica dispersions is influenced by the shape of the particles constituting the dispersed phase.

Experimental investigation of timber samples under triaxial compression conditions

Timber is re-emerging as a prominent structural material in construction due to its sustainability and aesthetic features. Timber is increasingly used in composite elements made along with steel and concrete. In the composite elements, timber is subjected to a triaxial confined stress state. However, the characteristics of timber under triaxial stress state are not well understood. An experimental campaign was carried out to characterise the triaxial confined behaviour of timber samples. Two types of timbers (soft and hardwood) were used in the experimental campaign. The selected timber samples were subjected to confined and unconfined axial compression loading conditions. In total, 50 samples were tested with five different lateral confining pressures (unconfined, 3, 5, 8 and 12 MPa). The experimental results are presented in terms of compressive strengths and axial compression stress-strain curves. The experimental data obtained was used to define the critical parameters of confined timber, such as confined strength, strain at peak stress and stress-strain behaviour. Test results demonstrate that the confinement pressure improves the strength and ductility, and the conventional Mohr-Coulomb criterion can be used to represent the confined timber strength and strain evolution. Finally, based on the data gathered, a suitable constitutive model to characterise the stress-strain behaviour of timber under the triaxial confined stress-state is proposed. This model is similar to the constitutive models typically used for concrete, mortar and rock under confined stress state. However, differences are highlighted in timber in terms of strength gain and ductility.

Impact resistance of engineered geopolymer composite (EGC) in cold temperatures

This paper was intended to investigate the impact resistance of engineered geopolymer composite (EGC) in cold temperatures. The ambient cured EGC based on local PVA fibers, which has favorable environmental and economic benefits, was first developed and tested under uniaxial compressive and tensile loading conditions. The drooping hammer test machine retrofitted with a liquid nitrogen canister was applied to conduct the impact tests of EGC specimens under different cold temperatures, i.e., −10 ℃, −20 ℃ and −50 ℃. The conventional engineered cementitious composite (ECC) specimens and the corresponding cement mortar were also tested as the control groups. The influences of alkali concentrations on the compressive, tensile and impact behaviors of EGC were investigated. According to the experimental results, it was found that the developed EGC could have comparable compressive strength and tensile behaviors with ECC. For both EGC, ECC and their corresponding matrixes, the impact load increased while the ultimate displacement decreased when the temperature dropped from −10 ℃ to −50 ℃. It was also found that the energy dissipation coefficient of EGC specimens increased with the decrease of temperature, indicating that EGC materials have preferable impact resistance under low or ultra-low temperature environments.