Stress Configuration Research Articles

Instability design analysis in tied-arch bridges

ABSTRACTA numerical investigation is proposed to identify instability strength of tied-arch bridges due to vertical loads, taking into account of a proper definition of the initial stress configuration and nonlinear geometrical effects involved in the bridge components. The main aim of the paper is to propose comparisons with data arising from existing codes by using a very detailed finite element model, emphasizing those scenarios in which current design methods overestimate the bridge instability capacity. Parametric analyses and new design methodologies are developed to identify instability strength and the influence of the bracing system on the bridge behavior.

On the Understanding of Cathode Related Trapping Effects in GaN-on-Si Schottky Diodes

Cathode related current collapse effect in GaN on Si Schottky barrier diodes is investigated in this paper. Capacitance and current relaxation measurements on diodes and gated-Van Der Pauw are associated with temperature dependent dynamic ${R_{\mathrm{ ON}}}$ transients analysis to identify the parasitic trapping locations in the devices. We show here that the main part of the current collapse at the cathode comes from a combination of electron trapping in the passivation layer and in a carbon related trap in the GaN buffer layers ( ${E_{A}} = \mathrm {E_{T}} - {E_{V}} \simeq 0.9 \,\mathrm {eV}$ ) that can be studied independently by using the appropriate stress configurations. These two parasitic effects can lead to long recovery time (>1 ks) after reverse bias stress.

The interaction of a mode II crack with an inhomogeneity undergoing a stress-free transformation strain

In this investigation, general approximate solutions for the stress intensity factor (SIF) and configuration force (CF) are derived, respectively, based on the Eshelby theory for the interaction between an inhomogeneous inclusion of arbitrary shape undergoing a stress-free transformation strain and plane stress mode II crack. For common inclusion shapes, some simplified approximate formulae are also developed. Then, the relationship between the normalized CF and SIF is discussed, as well as the effects of inclusion shape, location, and size on the CF and SIF of a plane stress mode II crack. To give deep insight into the complex three-dimensional interaction between an inclusion undergoing a stress-free transformation strain and a crack, two typical cases of the triaxial stress state are analyzed, and no significant difference occurs among most engineering materials.

Reaction-induced grain boundary cracking and anisotropic fluid flow during prograde devolatilization reactions within subduction zones

Devolatilization reactions during prograde metamorphism are a key control on the fluid distribution within subduction zones. Garnets in Mn-rich quartz schist within the Sanbagawa metamorphic belt of Japan are characterized by skeletal structures containing abundant quartz inclusions. Each quartz inclusion was angular-shaped, and showed random crystallographic orientations, suggesting that these quartz inclusions were trapped via grain boundary cracking during garnet growth. Such skeletal garnet within the quartz schist formed related to decarbonation reactions with a positive total volume change (∆V t > 0), whereas the euhedral garnet within the pelitic schists formed as a result of dehydration reaction with negative ∆V t values. Coupled hydrological–chemical–mechanical processes during metamorphic devolatilization reactions were investigated by a distinct element method (DEM) numerical simulation on a foliated rock that contained reactive minerals and non-reactive matrix minerals. Negative ∆V t reactions cause a decrease in fluid pressure and do not produce fractures within the matrix. In contrast, a fluid pressure increase by positive ∆V t reactions results in hydrofracturing of the matrix. This fracturing preferentially occurs along grain boundaries and causes episodic fluid pulses associated with the development of the fracture network. The precipitation of garnet within grain boundary fractures could explain the formation of the skeletal garnet. Our DEM model also suggests a strong influence of reaction-induced fracturing on anisotropic fluid flow, meaning that dominant fluid flow directions could easily change in response to changes in stress configuration and the magnitude of differential stress during prograde metamorphism within a subduction zone.

Effects of temperature variations on nonlinear planar free and forced oscillations at primary resonances of suspended cables

This paper is concerned with the analysis of the free and forced nonlinear vibrations of the suspended cable with thermal effects. By introducing the new thermal stressed configuration, the effect of temperature variation on the nonlinear vibration equations of motion is reflected by a non-dimensional cable tension variation factor. The partial differential equations of the planar motion are discretized to the ordinary equations via the Galerkin method, and the single-mode discretization is investigated. The Lindstedt–Poincare method and multiple scales method are applied to obtain the higher-order approximate solutions of the nonlinear free vibrations and primary resonances, respectively. Parametric investigations of temperature effects on the linear and nonlinear vibration characteristics of the suspended cable with different sag-to-span ratios and excitation amplitudes are performed. The results of the perturbation analysis show that the nonlinear free and forced vibration characteristics would be changed by the temperature variations qualitatively and quantitatively, depending on the sag-to-span ratio and the excitation amplitude. The asymmetric phenomena between the effects of warming and cooling conditions on the vibration characteristics can be observed. The crossover points between next two mode frequencies are shifted under the temperature variation, and these would significantly influence the internal resonances of the suspended cable. Finally, temperature effects on the time-history diagram of the cable axial total tension force are investigated.

Analysis of the sensitivity to pressure and temperature of a membrane based SAW sensor

ABSTRACTThis paper presents a FEM analysis of a membrane-based Surface Acoustic Wave (SAW) sensor. The sensor is a 2.45GHz Reflective Delay Line (R-DL) based on Lithium Niobate (LiNbO3). As the wave propagation time is much smaller than the typical time constant of the phenomena to be monitored (deformation, temperature change etc.), the analysis can be performed in three successive steps. First, a static FEM study of the complete sensor (housing included) is carried out, to compute the temperature, stress and strain fields generated in the sensitive area by the measured parameters (pressure, temperature, etc.). Then, a dynamic electro-mechanical study of the R-DL is performed. The simulation takes the previously computed fields into account, which makes it possible to compute the sensor sensitivity to the measured parameters. The model takes advantage of the periodicity of the components of the R-DL to compute phenomenological parameters (Coupling-of-Mode parameters), which can later on be used to compute the electrical response of the sensor (step 3). In this paper, we focus on the first two steps. The COM parameters are extracted, under simultaneous thermal and mechanical stresses. Especially, the sensor sensitivity is obtained from the evolution of the velocity, under various stress configurations.

Far Back End of Line Aluminum Stress Reduction Methods for Two-Dimensional/2.5D Fine Pitch Assemblies

Fine pitch interconnects when used with two-dimensional (2D)/2.5D packaging technology offer enormous potential toward decreasing signal latency and by making it possible to package increased electrical functionality within a given area. However, fine pitch interconnects present their own set of challenges not seen in packages with coarse pitch interconnects. Increased level of stresses within the far back end of line (FBEOL) layers of the chip is the primary concern. Seven different types of 2D and 2.5D test vehicles with fine pitch and coarse pitch interconnects were built and tested for mechanical integrity by subjecting them to accelerated thermal cycling between −55 °C and 125 °C. Finite element based mechanical modeling was done to determine the stress level within the FBEOL layers of these test vehicles. For all the tested assemblies, experimental data and modeling results showed a strong correlation between reduced pitch and increased level of stresses and increased incidence of failures within the FBEOL region. These failures were observed exclusively at the passivation layer and aluminum pad interface. Experimental data in conjunction with mechanical modeling were used to determine a safe level of stress at the aluminum to passivation layer interface. Global and local design changes were explored to determine their effect on the stresses at this interface. Several guidelines have been provided to reduce these stresses for a 2D/2.5D package assembly with fine pitch interconnects. Finally, a reliable low stress configuration, which takes into account all the design changes, has been proposed, which is expected to be robust with very low risk of failure within the FBEOL region.

Oscillatory tendency of interevent direction in earthquake sequences

The epicenter motion direction carries important information about the seismogenic dynamics but, to our knowledge, lacks systematic study. In this work, we studied the earthquake process from this perspective. To grasp the feature in directional information, we proposed a new descriptor, i.e., the direction of motion change defined as the difference in azimuths between two consecutive earthquake events. For the aftershock sequences of the Landers and the Northridge Earthquakes, the regional earthquake catalogs of south China, southern California, and New Zealand, and the corresponding aftershock depleted catalogs, we studied the distribution and long-range correlation of the direction of motion change. Similar results are found for the aftershock and regional earthquake process even if aftershocks depleted from the catalogs: Both of them hold a tendency for successive events to migrate in opposite directions along fault zones and show no long-range correlation, rendering plausibly a fundamental characteristic governed by seismogenic dynamics. For aftershocks, the phenomenon is conjectured to be the alternate release of residual stress at both ends of the fissures. With regard to regional earthquakes, the underlying physics and mechanisms are not very clear. It should be something related to the seismodynamic process, such as stress configuration modified by earthquakes. The study from this new perspective of directional information is believed to benefit a better understanding of the earthquake process.

Spatial variations of the crustal stress field in the Philippine region from inversion of earthquake focal mechanisms and their tectonic implications

This paper presents the spatial variations in the crustal stress field for the Philippine region. Based on the stress configuration, we divided the stress regime in the area of the Philippines into four parts: (1) Trench-perpendicular compressive stress axes (σ1) with an intermediate plunge were observed along the eastern subduction systems of the Philippine Mobile Belt (PMB), which suggests that the subduction of the Philippine Sea Plate (PSP) is the primary factor controlling the stress distribution. (2) Characterized by systematically rotated σ1 with very shallow plunge, the central-western portion of the Philippines appears to be largely affected by the collision between the Palawan Block and the PMB. (3) The σ1 distribution in the northern part of Luzon Island (north of 14°N) is compatible with the plate motion of the PSP, whereas the extensional axes (σ3) has a fan-shaped stress signature with N-S direction at the south and a more spreading direction to the north, which implies its north escapement. (4) Bounded by the Scarborough Seamount, the northern and southern portions of the Manila Trench reveal a very distinct stress pattern with a trench-parallel σ3 to the north and a trench-perpendicular σ3 to the south. This observation may infer a potential effect caused by the presence of the oceanic bathymetric highs on the behavior of the subduction process. In addition to the identification of the four provinces with different stress regimes, we suggest that the Philippine Fault Zone may play an important role to alter the stress state in the region of the Philippines.

High Temperature Coupling of IR Inactive CC Mode in Complementary Metal Oxide Semiconductor Metamaterial Structure

High temperature (up to 400 °C) coupling of infrared (IR) inactive >CC< mode is reported in complementary metal oxide semiconductor (CMOS)‐compatible refractory metamaterial filter and absorber structure by leveraging the carbon defects in tetraethyl orthosilicate obtained plasma enhanced chemical vapor deposition SiO2 thin film. Here, the role of strain gradient induced dipole moment in high stress configuration on the activation of otherwise inactive >CC< vibration at IR is confirmed. The unusual suppression of the transition is also observed in the absorber structure when the cavity mode strongly overlaps with it. Finally, 14 times better modulation of resonance spectrum is reported by such coupling in absorber configuration that supports thin film interference. The numerical and analytical study of the effect is found to be qualitatively in agreement with the experimental results. The study can set new paths toward more efficient design of spectrally selective thermophotovoltaic energy emitter at mid‐IR and novel mechanism for high temperature sensing on the ubiquitous CMOS platform.

Some advancements in the ultrasonic evaluation of initial stress states by the analysis of the acoustoelastic effect

The acoustoelastic effect – that is the correlation between the acoustic properties and the stress state for a solid body – can be profitably employed for experimental measurements of applied and/or residual stress, for example starting from the results of ultrasonic tests. Usually, the interpretation of the results of acoustoelastic experiments is performed in the theoretical framework of the so-called third-order elasticity. In the recent past, more general theoretical models aimed at overcoming some limitations of the third-order elasticity for acoustoelastic stress measurements have been developed. In particular, here we refer to a model developed within the linearized finite elasticity theory and describing the propagation of small amplitude waves in prestressed elastic materials. In this model, no assumption on the origin of initial stress neither on the initial anisotropy of the material is made, but the only hypothesis is that ultrasonic waves superimposed on the stressed reference configuration behaves elastically; then, this theoretical approach is also applicable for the experimental stress analysis of plastically deformed bodies and of anisotropic materials. Moreover, this model leads to “universal relations” relating ultrasonic velocities to the stress in a prestressed configuration of a body. Ultrasonic acoustoelastic tests on specimens under known stress states allows us for showing that the application of the above mentioned theoretical model, together with the use of a suitable experimental setup developed at our laboratory, may lead to stress measurements with an high level of accuracy.

Dynamic conductivity of proppant-filled fractures

A common challenge in matching the production from hydraulically fractured wells is related to changes in conductivity of propped fractures due to changes in the stress configuration. In this paper, we investigate the dynamic nature of fracture conductivity, by evaluating the permeability and width of a propped fracture segment at variable differential stress conditions. We combine the Discrete Element Method (DEM) and the Lattice Boltzmann Model (LBM) to simulate the evolution of a fracture segment filled with proppant and to evaluate the related fracture conductivity at various stress states. An ensemble of spherical proppant particles is generated and compacted under a specified confining stress via DEM to generate an initial propped fracture segment. A representative elementary volume (REV) of the proppant pack is then extracted from the DEM representation and used for fluid flow simulations. LBM is used to calculate the detailed single-phase flow field, at the pore-scale, and allows for calculation of permeability. In-situ conditions are then simulated by applying confining and differential stress on the REV via DEM. The differential stress is gradually increased on the REV, to simulate a reduction in the pore pressure due to production, until the formation of shear band(s) is observed and fracture failure begins. Permeability of the proppant pack, from LBM simulations, combined with the fracture aperture, from DEM simulations at different differential stress levels, allow us to determine the dynamic conductivity of the propped fracture segment. From a range of proppant-size distributions, we demonstrate that a well-graded proppant pack outperforms a poorly graded pack in maintaining the fracture conductivity over a broader range of differential stress conditions. Furthermore, we demonstrate that a well-graded proppant pack keeps the fracture segment open over a larger range of differential stress states.

Stress Controls of Monogenetic Volcanism: A Review

The factors controlling the preparation of volcanic eruptions in monogenetic fields are still poorly understood. The fact that in monogenetic volcanism each eruption has a different vent suggests that volcanic susceptibility has a high degree of randomness, so that accurate forecasting is subjected to a very high uncertainty. Recent studies on monogenetic volcanism reveal how sensitive magma migration is to the existence of changes in the stress field caused by regional and/or local tectonics or rheological contrasts (stratigraphic discontinuities). These stress variations may induce changes in the pattern of further movements of magma, thus conditioning the location of future eruptions. This implies that a precise knowledge of the stress configuration and distribution of rheological and structural discontinuities at crustal level of such volcanic systems would aid in forecasting monogenetic volcanism. This contribution reviews several basic concepts relative to the stress controls in monogenetic volcanic fields, and uses this information to explain how magma migrates inside such volcanic systems and how it prepares to trigger a new eruption.

(Invited) UTBB FDSOI PMOSFETs Including Strained SiGe Channels at the 14nm Technology Node and Beyond

The 28 nm Ultra-Thin Body and Buried Oxide (UTBB) Fully Depleted Silicon-On-Insulator (FDSOI) technology is in production [4]. This technology addresses both high performance and low power / low voltage applications. Indeed, a 28 nm FDSOI Processor (CPU) has been demonstrated to run at 3 GHz for a 1.3 V supply voltage (Vdd), 1 GHz for 0.6 V, still 300 MHz at 0.5 V [1]. This latter result evidences the high potential of FDSOI for Low Voltage operation, required for the next handheld, mobile or Internet-of-Things markets. The 14nm FDSOI technology extends this offer to even more performance (+50% frequency at a given dissipated power), with a 100mV supply voltage reduction [5]. For the 14nm FDSOI, we have integrated SiGe channel, which enables to achieve high biaxial compressive stress due to the lattice mismatch between Silicon and Germanium. The compressive stress enhance the hole mobility, and in turn pMOSFETs performance. In such an approach, one of the main challenges is to conserve the strain during the CMOS integration. Especially, it is well known that the patterning of SiGe leads to partial relaxation close to the active edges. This relaxation affects especially the level of stress in the channel when the dimensions of the active are small. The stress configuration becomes thus strongly layout-dependent. We have physically and electrically characterized the strain-induced layout effects in SiGe pMOSFETs built on Ultra-Thin-Body and Buried-Oxide Fully-Depleted-Silicon-On-Insulator (UTBB FDSOI). This layout effect is reproduced by an accurate physics-based electrical model, which enable us to predict the device and design performance for various technological configurations: germanium concentration in the channel, isolation and channel process integration. In order to mitigate the impacts of the SiGe channel relaxation, we have studied two kinds of solutions. First, technological solutions are possible, leading to +21% effective current increase in short transistor at Lg=20nm gate length and in turn -15% delay reduction for ring-oscillator of 1-gate finger inverters. Secondly, we demonstrate the benefits induced by smart design layouts, enabled by process integration goodies and some layout constructs. Especially, a continuous-RX design, which consists in a long active line configuration, optimizes the stress management, maintaining longitudinal stress component while relaxing the transverse one. A 28% ring oscillator delay improvement is experimentally demonstrated at same leakage for 1-finger inverter at VDD=0.8V supply voltage [10]. This demonstrates the interest of process/design co-optimization of strain-induced layout effects. For next UTBB-FDSOI nodes below 14nm, both the electrostatics and the carrier mobility must be improved. For the hole mobility, one may think about changing the crystalline orientation of the channel and using (110)-oriented substrates. However, in terms of electronic transport, the long channel carrier mobility is no longer the most relevant electrical parameter. One should pay a great attention to i) the strain compatibility and ii) the evolution of the apparent mobility with the gate length and width. Taking them into account, for pMOSFETs, SiGe channel + SiGeB source/drain + compressive contact etch stop layers in the (100) <110> direction is the best combination. For nMOSFETs, different technological solutions have been assessed, especially based on strain memorization techniques [6-7]. Strain-SOI substrates (sSOI) is another option, which brings enough performance boost to ensure a one-node scaling (+20-30% performance increase for nMOSFETs due to tensile strain, even for narrow active regions) [8]. Finally, the gate-last integration on planar FDSOI could be another strain booster because it leverages not only a low thermal budget for EOT and a threshold voltage optimization, but also a strain improvement during the final gate formation [9].

(Invited) UTBB FDSOI PMOSFETs Including Strained SiGe Channels at the 14nm Technology Node and Beyond

We have physically and electrically characterized pMOSFETs of compressively strained SiGe channel built on Ultra-Thin-Body and Buried-Oxide Fully-Depleted-Silicon-On-Insulator (UTBB FDSOI). Such a channel greatly contributes to the FDSOI CMOS high-performance at the 14nm node. At the same time, it induces strong layout effects, which are reported and explained in this paper. They can be reproduced by an accurate physics-based electrical model, which enables us to predict the device and design performance for various technological configurations: germanium concentration in the channel, isolation and channel process integration. In order to mitigate the impacts of the SiGe channel relaxation, we have studied two kinds of solutions. First, technological solutions are possible, leading experimentally to a -15 percent delay reduction for a ring-oscillator of 1-gate finger inverters at 0.8V supply voltage. Secondly, we demonstrate the benefits induced by smart design layouts, enabled by process integration goodies and some layout constructs. Namely, a continuous-RX design, which consists in a long active line configuration, optimizes the stress configuration, maintaining a high level of longitudinal compressive stress, while relaxing the transverse one. A 28 percent ring oscillator delay improvement is experimentally demonstrated at a given leakage for 1-finger inverter at 0.8V supply voltage. This demonstrates the interest of process/design co-optimization of strain-induced layout effects. Finally, we discuss the technological knobs and especially the strain boosters that can furthers the scaling of FDSOI below the 14nm node: SiGe channel and source/drain of high-Ge content, influence of the surface orientation and channel direction, as well as the gate last integration.

Influence of Hydrogenation on Residual Stresses of Pipeline Steel Welded Joints

Hydrogen embrittlement is a phenomenon that affects the performance of steel used for oil and gas pipelines. This paper presents a study of the effect of hydrogenation on the residual stresses of an API 5L X65 steel pipe. Residual stresses were analyzed by X-ray diffraction technique using the sin2Ψ method. The hydrogenation of base metal and welded joint specimens was performed by electrochemical tests in a simulated soil solution NS4. Results show that the hydrogenation led to significant changes in residual stress configuration and in the mechanical properties of steel. The hydrogenation increased the magnitude of the longitudinal residual stress of base metal and fusion zone, without changing the tensile/compressive nature. On the other hand, the hydrogenation increased the intensity of the tangential stress of base metal, and changed from compressive to tensile the residual stress of the fusion zone. The microstructural characterization by optical and scanning electron microscopy was used to complement this study.

An analysis of key characteristics of the Frank-Read source process in FCC metals

A well-known intragranular dislocation source, the Frank-Read (FR) source plays an important role in size-dependent dislocation multiplication in crystalline materials. Despite a number of studies in this topic, a systematic investigation of multiple aspects of the FR source in different materials is lacking. In this paper, we employ large scale quasistatic concurrent atomistic-continuum (CAC) simulations to model an edge dislocation bowing out from an FR source in Cu, Ni, and Al. First, a number of quantities that are important for the FR source process are quantified in the coarse-grained domain. Then, two key characteristics of the FR source, including the critical shear stress and critical dislocation configuration, are investigated. In all crystalline materials, the critical stresses and the aspect ratio of the dislocation half-loop height to the FR source length scale well with respect to the FR source length. In Al, the critical stress calculated by CAC simulations for a given FR source length agrees reasonably well with a continuum model that explicitly includes the dislocation core energy. Nevertheless, the predictions of the isotropic elastic theory do not accurately capture the FR source responses in Cu and Ni, which have a relatively large stacking fault width and elastic anisotropy. Our results highlight the significance of directly simulating the FR source activities using fully 3D models and shed light on developing more accurate continuum models.

Peridynamic Modeling of Granular Fracture in Polycrystalline Materials

A new peridynamic (PD) formulation is developed for cubic polycrystalline materials. The new approach can be a good alternative to traditional techniques such as finite element method (FEM) and boundary element method (BEM). The formulation is validated by considering a polycrystal subjected to tension-loading condition and comparing the displacement field obtained from both PDs and FEM. Both static and dynamic loading conditions for initially damaged and undamaged structures are considered and the results of plane stress and plane strain configurations are compared. Finally, the effect of grain boundary strength, grain size, fracture toughness, and grain orientation on time-to-failure, crack speed, fracture behavior, and fracture morphology are investigated and the expected transgranular and intergranular failure modes are successfully captured. To the best of the authors' knowledge, this is the first time that a PD material model for cubic crystals is given in detail.

Exploring the influence of loading geometry on the plastic flow properties of geological materials: Results from combined torsion + axial compression tests on calcite rocks

For technical reasons, virtually all plastic deformation experiments on geological materials have been performed in either pure shear or simple shear. These special case loading geometries are rather restrictive for those seeking insight into how microstructure evolves under the more general loading geometries that occur during natural deformation. Moreover, they are insufficient to establish how plastic flow properties might vary with the 3rd invariant of the deviatoric stress tensor (J3) which describes the stress configuration, and so applications that use those flow properties (e.g. glaciological and geodynamical modelling) may be correspondingly compromised. We describe an inexpensive and relatively straightforward modification to the widely used Paterson rock deformation apparatus that allows torsion experiments to be performed under simultaneously applied axial loads. We illustrate the performance of this modification with the results of combined stress experiments performed on Carrara marble and Solnhofen limestone at 500°–600 °C and confining pressures of 300 MPa. The flow stresses are best described by the Drucker yield function which includes J3-dependence. However, that J3-dependence is small. Hence for these initially approximately isotropic calcite rocks, flow stresses are adequately described by the J3-independent von Mises yield criterion that is widely used in deformation modelling. Loading geometry does, however, have a profound influence on the type and rate of development of crystallographic preferred orientation, and hence of mechanical anisotropy. The apparatus modification extends the range of loading geometries that can be used to investigate microstructural evolution, as well as providing greater scope for determining the shape of the yield surface in plastically anisotropic materials.

First-order estimate of the Canary Islands plate-scale stress field: Implications for volcanic hazard assessment

In volcanic areas, the existing stress field is a key parameter controlling magma generation, location and geometry of the magmatic plumbing systems and the distribution of the resulting volcanism at surface. Therefore, knowing the stress configuration in the lithosphere at any scale (i.e. local, regional and plate-scale) is fundamental to understand the distribution of volcanism and, subsequently, to interpret volcanic unrest and potential tectonic controls of future eruptions. The objective of the present work is to provide a first-order estimate of the plate-scale tectonic stresses acting on the Canary Islands, one of the largest active intraplate volcanic regions of the World. In order to obtain the orientation of the minimum and maximum horizontal compressive stresses, we perform a series of 2D finite element models of plate scale kinematics assuming plane stress approximation. Results obtained are used to develop a regional model, which takes into account recognized archipelago-scale structural discontinuities. Maximum horizontal compressive stress directions obtained are compared with available stress, geological and geodynamic data. The methodology used may be easily applied to other active volcanic regions, where a first order approach of their plate/regional stresses can be essential information to be used as input data for volcanic hazard assessment models.