Dynamic Test Data Research Articles

A Dynamic Constitutive Model and Simulation of Braided CFRP under High-Speed Tensile Loading.

In this study, a dynamic constitutive model for woven-carbon-fiber-reinforced plastics (CFRP) is formulated by combining dynamic tensile test data and fitting curves and incorporating variation rules established for the modulus of elasticity, strength, and fracture strain with respect to the strain rate. The dynamic constitutive model is then implemented with finite element software. The accuracy and applicability of the dynamic constitutive model are evaluated by comparing the numerically predicted load–displacement curves and strain distributions with the test data. The stress distribution, failure factor, modulus, and strength of the material under dynamic tension are also explored. The results show that the response simulated with the dynamic constitutive model is in good agreement with the experimental results. The strain is uniformly distributed during the elastic phase compared with the DIC strain field. Subsequently, it becomes nonuniform when stress exceeds 600 MPa. Then, the brittle fracture occurs. With the increase in the strain rate, the input modulus decreased, and the tensile strength increased. When the displacement was 0.13 mm, the simulation model was damaged at a low strain rate, and the stress value was 837.8 MPa. When it reached the high strain rate of 800 s−1, no failure occurred, and the maximum stress value was 432.5 MPa. For the same specimen, the strain rate was the smallest on both clamped ends, and the modulus and strength were large at the ends and small in the middle. The fitting curve derived from the test data was completely input into the dynamic constitutive model to better capture the dynamic change in the material properties.

A method of automatically obtaining master surfaces of resin matrix composites by time–temperature superposition

AbstractThe time–temperature superposition (TTS) is a data processing method of viscoelastic mechanics, which is realized by translating and superposing the responses at different temperatures to get master curves beyond the test time or frequency. In this study, an automatic shift method is developed to obtain master surfaces of the carbon fiber reinforced plastics and epoxy resin. First step, an interpolation is used to process the dynamic mechanical analysis test data measured by frequency sweep/temperature step or continuous heating‐up method. Second step, the Prony series of the generalized Maxwell model are used to fit the storage and loss modulus at each temperature, which makes the fitting curves have physical meaning and causality. Third step, the automatic shift is achieved by minimizing the sum of squares of the vertical distances between two fitting curves. Last step, master surfaces are created by Prony series fitting and interpolation, and the storage modulus, loss modulus, loss factors, and relaxation modulus at any temperature, frequency or time can be found on the master surfaces. Both storage modulus and loss modulus are considered at same time according to the weight. The effects of different weights are studied.

SOC Estimation Based on Hysteresis Characteristics of Lithium Iron Phosphate Battery

In order to improve the estimation accuracy of the state of charge (SOC) of lithium iron phosphate power batteries for vehicles, this paper studies the prominent hysteresis phenomenon in the relationship between the state of charge and the open circuit voltage (OCV) curve of the lithium iron phosphate battery. Through the hysteresis characteristic test of the battery, the corresponding SOC-OCV data when the battery is charged or discharged from different SOC states are analyzed. According to the approximation trend of the hysteresis main loop curve by the data points, a differential equation model for approximately solving the charge or discharge hysteresis small loop curve under any SOC state is established, and the adjustment parameters of the model are analyzed and debugged in sections. Then, based on the second-order Thevenin equivalent circuit model, the forgetting factor recursive least squares method is used to identify the model parameters online. When deriving the relationship between the OCV and SOC, according to the state of charge and discharge and the current SOC value, the approximate model of the real hysteresis small loop curve in the current state is solved in real time, and the extended Kalman recursion algorithm is substituted to correct the corresponding relationship between the OCV and SOC. Finally, the integrated forgetting factor recursive least squares online parameter identification and extended Kalman filter to correct the SOC-OCV hysteresis relationship in real time considering the hysteresis characteristics are used to complete the real-time estimation of the SOC of the lithium iron phosphate battery. The synthesis algorithm proposed in this paper and the Kalman filter algorithm without considering the hysteresis characteristics are compared and verified under the Dynamic Stress Test (DST) data. Based on the method proposed in this paper, the maximum error of terminal voltage is 0.86%, the average error of terminal voltage is 0.021%, the root mean square error (RMSE) of terminal voltage is 0.042%, the maximum error of SOC estimation is 1.22%, the average error of SOC estimation is 0.41%, the average error of SOC estimation is 0.41%, and the RMSE of SOC estimation is 0.57%. The results show that the comprehensive algorithm proposed in this paper has higher accuracy in both terminal voltage following and SOC estimation.

Objective comparison of numerical spin study with aircraft model free-flight spin tests

This paper reports on the results of a research project that investigated the spin and recovery characteristics of a multirole fighter aircraft. In the first phase, numerical/computational methods were used to predict full scale aircraft spin and recovery characteristics. The aerodynamic data used in the numerical study was obtained from rotary balance steady coning and oscillatory coning motion dynamic wind tunnel tests conducted on 1/13th scale aircraft dynamic model. All the possible steady spin modes were numerically computed, a complete set of dynamic modes of the spinning aircraft were evaluated and six degree of freedom simulations of predicted flat spins were performed to investigate their dynamic stability and recovery characteristics. In the second phase, free-flight spin trials were conducted using 1/5th scale dynamic model of the understudy aircraft to validate the results of the analytical spin studies. Dynamic characteristics of the analytically predicted flat spins were objectively compared with flat spins found in free-flight spin trials as a validation process. Our results reveal that the numerically predicted full scale aircraft spin and recovery dynamic characteristics correlate well with those estimated from model test flights. The present study is an important step toward objective comparison of numerical spin studies based on dynamic wind tunnel tests data with free-flight spin trials, yielding important guidelines and results for future aircraft spin studies.

Stress prediction of bridges using ANSYS soft and general regression neural network

Bridge managers are often eager to identify the carrying capacities and service performance characteristics of bridge structures. In view of the massive number of bridges managed and maintained in China, providing a quick evaluation of bridge performance bridges has become an urgent challenge for bridge engineering. Aiming at many adverse problems of bridge load tests, such as their high costs, long time consumption, low efficiency, impact on traffic, and damage to bridge structures, a new method for bridge static behavior prediction is proposed herein, based on dynamic load test data. The method adopts a generalized regression neural network algorithm with fast convergence and a nonlinear approximation, determines the sensitive parameters based on a full-bridge sensitivity analysis, forms training samples using a uniform design sampling method, and establishes intelligent agent model. The initial finite element analysis model of the bridge structure is updated using the proposed proxy model and dynamic load test data, and the static behavior of the existing bridge structure is accurately predicted based on the updated finite element model. To verify the correctness of the proposed method, a practical bridge is considered as the research object, and the static response of the bridge structure is predicted. The predicted results are consistent with the static load test results for the bridge, verifying the correctness of the proposed method. The results show that the maximum error between the theoretical calculation result and measured value is only 4.34% and the minimum error is only 3.52%. The strain prediction results are consistent with the measured results, and the modified theoretical analysis model provides high accuracy for strain prediction results under different working conditions. The application in practical engineering shows that the prediction results under different load conditions are adaptable and highly accurate.

Numerical study on dynamic properties of rubberised concrete with different rubber contents

As a green environmentally-friendly material, rubberised concrete (RuC), which has the characteristics of low elastic modulus, large deformation capacity, high damping, good energy dissipation and good crack resistance, has attracted extensive attention and research in the civil engineering discipline. However, most of existing studies are based on experimental tests on RuC material properties, and there has been no numerical study based on meso-scale modelling of RuC yet. To more comprehensively investigate the RuC dynamic material properties without conducting intensive experimental tests, this study developed a high-fidelity meso-scale model considering coarse and fine aggregates and rubber crumbs to numerically investigate the mechanical properties of rubberised concrete under different strain rates. The meso-scale model was verified against both quasi-static compressive testing data and Split Hopkinson Pressure Bar (SHPB) dynamic testing data. Using the verified numerical model, the dynamic properties of rubberised concrete with various rubber content (0%–30%) under different strain rates were studied. The numerical results show that the developed meso-scale model can use to predict the static and dynamic properties of rubberised concrete with high accuracy. The dynamic compressive strength of the rubberised concrete increases with the increment of the strain rate, and the strain rate sensitivity increases with the rubber content ranging from 0 to 30%. Based on intensive numerical simulation data, empirical DIFs is used as a function of strain rate and rubber content to predict the dynamic strength of rubberised concrete.

A fractional-order model of lithium-ion batteries and multi-domain parameter identification method

A multi-domain parameter identification method for a fractional-order model of lithium-ion batteries is presented. The fractional-order model is studied, and twenty-five identification parameters are determined. An intelligent optimization method named the genetic algorithm-particle swarm optimization algorithm is used to identify the parameters. Based on electrochemical impedance spectroscopy in the frequency domain and the terminal voltage of the dynamic stress test in the time domain, a multi-domain identification method is proposed. In synthetic experiment, the proposed genetic algorithm-particle swarm optimization algorithm has higher accuracy and faster convergence speed than the traditional optimization methods, and the proposed multi-domain identification method has more accurate parameter identification results than the frequency-domain identification and time-domain identification. In experiment on lithium-ion batteries, the model parameters are identified by electrochemical impedance spectroscopy and dynamic stress test data, and the parameter identification results are verified by verification test data. The results demonstrate that the genetic algorithm-particle swarm optimization algorithm and multi-domain identification method can be used as robust and reliable tools for parameter identification of lithium-ion batteries. A MATLAB application with the proposed method is also published on the community MATLAB website, providing researchers with a more convenient and effective tool.

Vertical field behavior of a deep large-diameter driven pipe pile in multilayered soils

Field testing was performed to examine vertical performances of a deep large-diameter driven pile used to support wind turbines in multilayered soils. The large-diameter pile was semiopen-ended and had an external diameter and length of 2.4 m and 113 m. The vertical load-displacement relationships were determined, and the shaft and base resistances were derived by analyzing segmented axial forces. The ultimate compressive capacity, determined using a modified Davisson's criterion, was 89.48 MN, which was nearly 20% and 100% larger than that estimated using the CABR JGG106-2014 (2014) criterion and dynamic load test data, respectively. The β values obtained using the modified Davisson's criterion were slightly larger than those obtained using the CABR JGG106-2014 (2014) criterion, and the MOT JTS167-2018 (2018) results were the most conservative. Although empirical methods incorporating parameters directly interpreted from standard penetration test results provided the most consistent estimates, they are limited to some geological conditions. Appropriate coefficients were suggested for empirical methods to calculate the base resistance. The shaft resistance contributed approximately 86% of the compressive axial force. In comparison, the ultimate tensile capacity was approximately 54.58 MN when using the CABR JGG106-2014 (2014) criterion, and the shaft resistance contributed approximately 93% of the tensile force.

Graded Control Technology of Oil Stability and Water Control in Fracture-Pore Carbonate Reservoirs

In view of the prominent problems of extremely strong heterogeneity, fracture development of different scales, and serious rapid water channelling in the process of water injection development in fracture-pore carbonate reservoirs, a comprehensive treatment method of oil stabilizing and water controlling is proposed, which includes fracture classification control, combination of adjustment and plugging, and wettability change. Based on the static and dynamic test data, the characteristics of reservoir fracture development and fracture scales are described in detail. By means of reservoir engineering and numerical simulation, the water flooding rule under different grade fracture reservoir conditions is studied, the influence of different levels of fractures on water injection development is evaluated, and the improvement effect of different control methods on water drive sweep is demonstrated. Research shows that a large amount of remaining oil trapped in pores is affected by fracture water channelling, which makes it difficult to use effectively. The water flooding sweep characteristics of reservoirs with different scales of fractures are quite different, and large-scale fractures are the main reason for ineffective water injection. The hierarchical control techniques of plugging large-scale fractures, intervening and adjusting small- and medium-scale fractures, and changing the wettability of microscale pore media can significantly extend the water flooding spread range and effectively improve oil well production. The research results have been applied in the field and achieved good results. This technology can provide theoretical guidance and a technical basis for the comprehensive treatment of oil stabilization and water control in fractured-porous carbonate oil and gas reservoirs.

Investigation of ultra-high performance concrete slabs under contact explosions with a calibrated K&C model

Karagozian and Case (K&C) concrete model is extensively adopted in the numerical simulations of ultra-high performance concrete (UHPC) structural members subjected to impulsive loads such as impact and blast. In this study, a calibration of the K&C concrete model was conducted for UHPC in terms of three strength surfaces, equation of state, shear dilatancy, damage evolution and strain rate effect to offer simple and general guidelines on the determination of key model parameters for this new class of concrete. With the calibrated concrete model, a single element method was adopted to verify its accuracy through a comparison to the results from the static tests of the uniaxial compression, direct tension and triaxial compression. Furthermore, the numerical simulations of contact explosion tests on the UHPC slabs with the incorporation of the strain rate effect were performed and the numerical results exhibited good predictions regarding the failure mode, crater and scabbing damage as compared to the test results. More importantly, this proposed numerical model and simulation methodology are reasonable to be generally used for structural members constructed of UHPC materials under contact explosions when lacking sufficient static and dynamic test data. Using the calibrated and validated K&C concrete model, parametric studies were conducted to derive a new empirical equation for predicting the local damage mode of UHPC slabs under contact explosions.

Discussion on the suitability of dynamic constitutive models for prediction of geopolymer concrete structural responses under blast and impact loading

Compared to ordinary Portland cement-based concrete (OPC), geopolymer concrete (GPC) is an environmental-friendly construction material because it is mixed by replacing Portland cement with industry wastes such as fly ash. Despite intensive researches in the last two decades, application of geopolymer concrete in construction is still rather limited. One of the reasons is the quasi-static and dynamic material properties of geopolymer concrete, which are different from those of ordinary Portland-cement concrete, are not well defined yet, and the available design guides for geopolymer concrete structures are very limited. The existing design guides and dynamic constitutive models for OPC cannot be directly employed in design analysis and numerical modelling of GPC structures subjected to blast and impact loads. This paper first summaries the available dynamic material testing data on GPC, compares them with the widely used dynamic constitutive models for OPC, and discusses the suitability of those models for modelling GPC structures. Then, based on the available GPC material testing data, new material constants for strength model, equation of state and dynamic increase factors are derived for GPC. Finally numerical modellings are carried out using these material models with modifications for GPC material to examine their accuracies in simulating the dynamic responses and damages of structural components made of GPC subjected to blast and impact loads.

Transient behaviour and optimal start-up procedure of closed Brayton cycle with high thermal inertia

• Precise dynamic simulation of a closed Brayton cycle with high thermal inertia is achieved based on test data and optimization algorithm. • Thermal inertia of the regenerator is critical to fast and stable full-load operation. • Initial pressure ratio takes great effect on the start-up time and start-up power consumption. • The rotor speed should be accelerated when the compressor inlet pressure arrives at 60%-65% design value. The closed Brayton cycle is promising as a power generation system owing to its output flexibility and compactness. In this study, a small closed Brayton cycle device was developed and its transient characteristics were studied experimentally and numerically. The start-up procedure for a closed Brayton cycle with considerable thermal inertia and heat dissipation was investigated. First, a modelling method based on both test data and an optimisation algorithm was developed to improve the accuracy of the dynamic simulation of the closed Brayton cycle. The optimal values of model parameters describing the thermal inertia and heat dissipation of the components were obtained by matching a group of dynamic test data using a genetic algorithm. The precision of the model was validated against additional experimental data. Then, the Pareto front of the start-up procedure, which was characterised by the time parameters concerning acceleration and injection, pressure coefficient, androtor speed, was acquired using a double-objective genetic algorithm with the goal of obtaining the smallest values for the start-up time and start-up power. Further studies showed that adjusting the sequence of acceleration and injection could help overcoming the thermal inertia of the regenerator, which was critical for fast and stable full-load operation. Firstly, selecting the appropriate initial pressure coefficient, then accelerating and then injecting was a favourable start-up procedure.

Experimental p-y curves for liquefied soils from centrifuge tests

The present study aims to obtain p-y curves (Winkler spring properties for lateral pile-soil interaction) for liquefied soil from 12 comprehensive centrifuge test cases where pile groups were embedded in liquefiable soil. The p-y curve for fully liquefied soil is back-calculated from the dynamic centrifuge test data using a numerical procedure from the recorded soil response and strain records from the instrumented pile. The p-y curves were obtained for two ground conditions: (a) lateral spreading of liquefied soil, and (b) liquefied soil in level ground. These ground conditions are simulated in the model by having collapsing and non-collapsing intermittent boundaries, which are modelled as quay walls. The p-y curves back-calculated from the centrifuge tests are compared with representative reduced API p-y curves for liquefied soils (known as p-multiplier). The response of p-y curves at full liquefaction is presented and critical observations of lateral pile-soil interaction are discussed. Based on the results of these model tests, guidance for the construction of p-y curves for use in engineering practice is also provided.

Delineation of reservoir channels by different seismic attributes and geobody extractions for robust volumetric estimation, Saffron Field, offshore Nile Delta, Egypt

The Nile Delta Basin is a major gas province. Commercial gas discoveries there have been proven mainly in Pleistocene to Oligocene sediments, and most discoveries are within sandstone reservoirs. Three-dimensional seismic data acquired over the basin have helped greatly in imaging and visualization of stratigraphy and structure, leading to robust understanding of the subsurface. Channel fairways serve as potential reservoir units; hence, mapping channel surfaces and identifying and defining infill lithology is important. Predicting sand distribution and reservoir presence is one of the key tasks as well as one of the key uncertainties in exploration. Integrating state-of-the-art technologies, such as including 3D seismic reflection surveys, seismic attributes, and geobody extractions, can reduce this uncertainty through recognition and accurate mapping of channel features. In this study, seismic attribute analysis, frequency analysis through spectral decomposition (SD), geobodies, and seismic sections have been used to delineate shallow Plio-Pleistocene El Wastani Formation channel fairways within the Saffron Field, offshore Nile Delta, Egypt. This has led to providing more reliable inputs for calculation of volumetrics. Interpretation of the stacked-channels complex through different seismic attributes helped to discriminate between sand-filled and shale-filled channels and in understanding their geometries. Results include more confident delineation of four distinct low-sinuosity channelized features. Petrophysical evaluation conducted on five wells penetrating Saffron reservoirs included electric logs and modular dynamic test data interpretation. The calculated average reservoir properties were used in different volumetric calculation cases. Different approaches were applied to delineate channel geometries that were later used in performing different volumetric cases. These approaches included defining channels from root-mean-square amplitude extractions, SD color-blended frequencies, and geobodies, all calculated from prestack seismic data. The different volumetric cases performed were compared against the latest field volume estimates proven after several years of production in which an area-versus-depth input showed the closest calculated hydrocarbon volumes to the actual proven field volumes.

Non Shock Dynamic Compression of Tantalum

We start by simulating the response of tantalum to dynamic non-shock loading using a standard hydrocode, and the results we get are not consistent with test data. Standard hydrocodes use what we call the flowstress approach to describe the dynamic viscoplastic response of materials. We therefore transform our hydrocode to use what we call the overstress approach to dynamic viscoplastic response. It turns out that using the overstress approach makes the hydrocode more successful in reproducing non-shock dynamic compression test data.

An elasto-plastic constitutive model for frozen soil subjected to cyclic loading

Upon employing the theoretical frame of breakage mechanics for geological materials and homogenization, a new elasto-plastic constitutive model is proposed to investigate the dynamic mechanical behaviors and volumetric strain of frozen soil under cyclic loading. In this model, using a mesoscopic method to formulate the breakage of frozen soil by idealizing it as a binary medium, assuming respectively the unbroken state as bonded element and the damage state as frictional element. During the loading process, the evolution of the nonuniform deformation and ice cementation breakage is described by the local strain concentration coefficient and breakage ratio, respectively. The dynamic triaxial compression test data for different confining pressures, coarse particle contents, and dynamic deviatoric stress amplitudes are utilized to confirm the suitability of the new elasto-plastic constitutive model. In the results, the model presented the stress-strain curves and volumetric strain curves of frozen soil under cyclic loading which captured the basic dynamic characteristics, such as nonlinear variation, hysteresis behaviors, and plastic strain accumulation behaviors. Herein, the extensive experimental validation shows the applicability of the proposed model.

Empirical Models for the Viscoelastic Complex Modulus with an Application to Rubber Friction

Up-to-date predictive rubber friction models require viscoelastic modulus information; thus, the accurate representation of storage and loss modulus components is fundamental. This study presents two separate empirical formulations for the complex moduli of viscoelastic materials such as rubber. The majority of complex modulus models found in the literature are based on tabulated dynamic testing data. A wide range of experimentally obtained rubber moduli are used in this study, such as SBR (styrene-butadiene rubber), reinforced SBR with filler particles and typical passenger car tyre rubber. The proposed formulations offer significantly faster computation times compared to tabulated/interpolated data and an accurate reconstruction of the viscoelastic frequency response. They also link the model coefficients with critical sections of the data, such as the gradient of the slope in the storage modulus, or the peak values in loss tangent and loss modulus. One of the models is based on piecewise polynomial fitting and offers versatility by increasing the number of polynomial functions used to achieve better fitting, but with additional pre-processing time. The other model uses a pair of logistic-bell functions and provides a robust fitting capability and the fastest identification, as it requires a reduced number of parameters. Both models offer good correlations with measured data, and their computational efficiency was demonstrated via implementation in Persson’s friction model.

A quantitative study of the scale and distribution of tight gas reservoirs in the Sulige gas field, Ordos Basin, northwest China

Gas and water distribution is discontinuous in tight gas reservoirs, and a quantitative understanding of the factors controlling the scale and distribution of effective reservoirs is important for natural gas exploration. We used geological and geophysical explanation results, dynamic and static well test data, interference well test and static pressure test to calculate the distribution and characteristics of tight gas reservoirs in the H8 Member of the Shihezi Formation, Sulige gas field, Ordos Basin, northwest China. Our evaluation system examines the scale, physical properties, gas-bearing properties, and other reservoir features, and results in classification of effective reservoirs into types I, II, and III that differ greatly in size, porosity, permeability, and saturation. The average thickness, length, and width of type I effective reservoirs are 2.89, 808, and 598 m, respectively, and the porosity is > 10.0%, permeability is > 10 × 10−3 µm2, and average gas saturation is > 60%. Compared with conventional gas reservoirs, tight gas effective reservoirs are small-scale and have low gas saturation. Our results show that the scale of the sedimentary system controls the size of the dominant microfacies in which tight gas effective reservoirs form. The presence of different types of interbeds hinders the connectivity of effective sand body reservoirs. The gas source conditions and pore characteristics of the reservoirs control sand body gas filling and reservoir formation. The physical properties and structural nature of the reservoirs control gas-water separation and the gas contents of effective reservoirs. The results are beneficial for the understanding of gas reservoir distribution in the whole Ordos Basin and other similar basins worldwide.

Experimental and mesoscopic study of dynamic tensile properties of concrete using direct-tension technique

Dynamic tensile properties of concrete play a very important role in the blast-resistant performance of concrete structure. Systematic tests on the tensile properties of normal concrete at high strain rates in the direct-tension way by using an improved Split Hopkinson Tension Bar (SHTB) technique were carried out. Quasi–static direct-tension test was also conducted for comparison. The obtained dynamic tensile stress–strain curves and tensile fracture energy of normal concrete were compared with the existing test data and formulae. Failure appearance of concrete rapidly loaded by direct stretching was also captured with the high-speed camera. A fine 3D mesoscopic concrete model, in which coarse aggregate with random shapes and sizes was randomly distributed in mortar matrix, was employed to conduct the parametric discussion. Experimental and numerical results reveal that the dynamic increase factor of tensile strength (DIF) obtained by the SHTB test is a little lower than that proposed by CEB that fits basically on the dynamic splitting test data. The tensile fracture energy and tensile strength both show significant strain–rate dependence. It acceleratingly increases with the strain rate exceeding a critical value of 2 s−1. The strength of aggregate has little effect on the tensile properties of concrete. The dynamic direct tensile properties of concrete increase with mortar strength and ITZ strength. Improved empirical formulae on DIF and DIFG that denotes the dynamic increase factor of tensile fracture energy of concrete were established that could be used in a very wide range of application.

Determination of creep compliance of asphalt mixtures at intermediate and high temperature using creep-recovery test

The linear viscoelastic (LVE) characterisation of asphalt mixtures in time domain is generally performed at temperature lower than 30°C to prevent the effect of permanent deformation. Although LVE properties in frequency and time domain can be mathematically interconverted, the determination of relaxation modulus and creep compliance through experiment is also necessary. This paper presents a method for determining the creep compliance of asphalt mixtures at intermediate and high temperature, at which permanent deformation takes place. Since the recovery of creep-recovery test is a pure LVE process, it was used to back-calculate the creep compliances (CCs) at various investigating temperatures. The results show that the CCs back-calculated from creep-recovery data achieve a good level of accuracy and repeatability. In addition, the obtained master curves of CCs agree well with those interconverted from dynamic modulus test data and the same shift factors are applicable for both creep compliance and dynamic modulus, phase angle.