Showing papers by "Jiandong Li published in 2020"

Energy-Efficient Multiuser Partial Computation Offloading With Collaboration of Terminals, Radio Access Network, and Edge Server

Abstract: Mobile-Edge Computing (MEC) could relieve computing pressure and save energy of resource-constrained Smart Mobile Devices (SMDs) via computation offloading. Nevertheless, offloading strategy design for multiuser MEC systems is challenging. Specifically, offloading operations (i.e., terminal execution strategy, access rate, and cloud execution strategy) are not only inner-coupled for each SMD due to parallel local and cloud execution, but also inter-coupled among SMDs due to competition for radio and computation resources. Worse still, the inner- and inter-coupling interplay each other. However, existing works generally weaken this inner-inter-coupling, resulting in an inability to adapt to network differences, terminal capacity differences, and application requirements differences. Hence, only suboptimal performance could be achieved. As motivated, we jointly optimizes terminal execution strategy, radio resource allocation, and MEC computation resource allocation to minimize weighted sum of terminal energy consumption. Additionally, via dynamically matching individual offloading behavior and group’s competitive resources allocation, our proposed algorithm could not only reflect mechanism of interaction between inner- and inter-coupling relationship, but also well adopt to diversities of network conditions, terminal capacity, and application requirements to further harvest MEC gain. Finally, simulation results demonstrate that our algorithm significantly outperforms existing schemes, more specifically up to 73.8% less energy consumption.

Multi-mode OAM Radio Waves: Generation, Angle of Arrival Estimation and Reception With UCAs

Abstract: Orbital angular momentum (OAM) at radio frequency (RF) provides a novel approach of multiplexing a set of orthogonal modes on the same frequency channel to achieve high spectrum efficiencies. However, there are still big challenges in the multi-mode OAM generation, OAM antenna alignment and OAM signal reception. To solve these problems, we propose an overall scheme of the line-of-sight multi-carrier and multi-mode OAM (LoS MCMM-OAM) communication based on uniform circular arrays (UCAs). First, we verify that UCA can generate multi-mode OAM radio beam with both the RF analog synthesis method and the baseband digital synthesis method. Then, for the considered UCA-based LoS MCMM-OAM communication system, a distance and AoA estimation method is proposed based on the two-dimensional ESPRIT (2-D ESPRIT) algorithm. A salient feature of the proposed LoS MCMM-OAM and LoS MCMM-OAM-MIMO systems is that the channel matrices are completely characterized by three parameters, namely, the azimuth angle, the elevation angle and the distance, independent of the numbers of subcarriers and antennas, which significantly reduces the burden by avoiding estimating large channel matrices, as traditional MIMO-OFDM systems. After that, we propose an OAM reception scheme including the beam steering with the estimated AoA and the amplitude detection with the estimated distance. At last, the proposed methods are extended to the LoS MCMM-OAM-MIMO system equipped with uniform concentric circular arrays (UCCAs). Both mathematical analysis and simulation results validate that the proposed OAM reception scheme can eliminate the effect of the misalignment error of a practical OAM channel and approaches the performance of an ideally aligned OAM channel.

A WiFi fingerprint based high-adaptability indoor localization via machine learning

Abstract: For received signal strength (RSS) fingerprint based indoor localization approaches, the localization accuracy is significantly influenced by the RSS variance, device heterogeneity and environment complexity. In this work, we present a high-adaptability indoor localization (HAIL) approach, which leverages the advantages of both relative RSS values and absolute RSS values to achieve robustness and accuracy. Particularly, a backpropagation neural network (BPNN) is devised in HAIL to measure the fingerprints similarities based on absolute RSS values. With this aid, the characteristics of the applied area could be specially learned such that HAIL could be adaptive to different environments. The experiments demonstrate that HAIL achieves high localization accuracy with the average localization error of 0.87m in the typical environments. Moreover, HAIL has the minimum amount of large errors and decreases the average localization error by about 30%∼50% compared with the existing approaches.

CAS FGOALS-f3-L Model Datasets for CMIP6 GMMIP Tier-1 and Tier-3 Experiments

Abstract: The Chinese Academy of Sciences (CAS) Flexible Global Ocean–Atmosphere–Land System (FGOALS-f3-L) model datasets prepared for the sixth phase of the Coupled Model Intercomparison Project (CMIP6) Global Monsoons Model Intercomparison Project (GMMIP) Tier-1 and Tier-3 experiments are introduced in this paper, and the model descriptions, experimental design and model outputs are demonstrated. There are three simulations in Tier-1, with different initial states, and five simulations in Tier-3, with different topographies or surface thermal status. Specifically, Tier-3 contains four orographic perturbation experiments that remove the Tibetan–Iranian Plateau, East African and Arabian Peninsula highlands, Sierra Madre, and Andes, and one thermal perturbation experiment that removes the surface sensible heating over the Tibetan–Iranian Plateau and surrounding regions at altitudes above 500 m. These datasets will contribute to CMIP6’s value as a benchmark to evaluate the importance of long-term and short-term trends of the sea surface temperature in monsoon circulations and precipitation, and to a better understanding of the orographic impact on the global monsoon system over highlands.

Application of Time-Varying Graph Theory over the Space Information Networks

Abstract: SIN is constructed to support real-time data acquisition, massive data transmission and processing, and systematized information services. Different from static networks, both the network topologies and the available network resources are dynamic in SIN. However, the existing networking technologies treat SIN as segmented static networks, and ignore the relationship among different segmented subnetworks, which results in low resource utilization and poor transmission QoS. This article exploits the time-varying graph theory to characterize and allocate the dynamic resources of SIN. We first introduce the overall SIN architecture, and discuss its key technologies in terms of network slicing and dynamic routing. Then, we construct a novel STAG to precisely depict the multi-dimensional time-varying resources and reveal their connection relationships in SIN. With STAG, we propose the dynamic network slicing strategy to build the dedicated network slices for different services, and design the intra-slice routing scheme to guarantee the service transmission QoS. Simulation results demonstrate our methods can complete more space missions with higher resource utilization. Finally, we discuss the promising future of the time-varying graph theory.

Modeling and Performance Analysis for Satellite Data Relay Networks Using Two-Dimensional Markov-Modulated Process

Abstract: Satellite Data Relay Networks (SDRNs) play an important role in the data relay from User Satellites (USs) to ground stations by Tracking Data Relay Satellites (TDRSs). For better exploitation of SDRNs, the development of the systematic model and accurate system analysis is essential. To describe the end-to-end data transmission in SDRNs, we construct an MMOO/MMSP/1/K-G/G/1 tandem queuing model where the two parts depict the traffic arrival and transmission service of USs and TDRSs, respectively. Because the active and inactive periods of the data transmission are determined by the visibility between two satellites, classical buffer state based vacation policies become imprecise. Moreover, these two kinds of periods appear alternatively and their duration varies over time so that it is hard to model such intermittent transmission by existing service models. To overcome these difficulties, we propose a Markov Chain Monte Carlo based Markov Modulated Service Process (MMSP) which can tightly match the distributions of the active and inactive periods. In this process, we propose two algorithms to calculate the service state transition probability and the number of the sub-states in each service state, respectively, which guarantees the alternative transition between the active and inactive states as well as the sojourn time spent in each state. For the quality of service analysis, we find the different features of the queue variation under different arrival and service rate conditions. By separately calculating the related mean queue lengths and emergence probabilities, we first derive the expressions of the system loss probability, mean queue length, and mean delay. Finally, we conduct numerous simulations to verify the accuracy of our system model and performance evaluation, which provides the guidance to the buffer design and transmission resource allocation.

Assisting Intelligent Wireless Networks with Traffic Prediction: Exploring and Exploiting Predictive Causality in Wireless Traffic

Abstract: Predicting traffic by exploiting its regularity in spatio- temporal variation enables intelligent resource provisioning and management in wireless networks. Traditional prediction techniques are largely based on exploiting traffic spatio-temporal correlation, that is, the statistical relationship between the current traffic and the historical data in a single cell (temporal correlation) or neighboring cells (spatial correlation). Such an approach is effective in predicting the regular components in traffic. However, as traffic types are becoming increasingly diversified, the random components in traffic are becoming dominant. This results in decreasing accuracy in correlation-based prediction techniques. In view of the limitation of existing techniques, we propose a new approach of traffic prediction by exploiting the predictable causality in wireless traffic, which arises from the causal relationship between the occurrences of special events and the triggered traffic variations. Building on the approach, we propose a novel framework of correlation- and causality-based prediction (Coca-Predict) that integrates the two types of prediction to exploit their complementary strengths to maximize prediction accuracy. Specifically, traffic information in spatio-temporal and other dimensions are fed into the correlation and causality sub-predictors to predict the regular component and variation tendency of the traffic, respectively. Experimental results based on realistic traffic data at a specific airport demonstrate that Coca-Predict outperforms the state-of-the-art prediction techniques by exploiting traffic causality. Finally, open challenges and opportunities for wireless traffic prediction are highlighted to shed light on this important direction in designing intelligent wireless networks.

Accurate Indoor Localization Assisted With Optimizing Array Orientations and Receiver Positions

Abstract: Owing to the multiple antennas equipped at modern Wi-Fi infrastructures, the angle-of-arrival (AoA) based indoor localization systems have successfully achieved the accuracy of tens of centimeters. However, the high accuracy is acquired at the cost of employing the additional resources in the domains of frequency, space or time, which requires complex processing and hinders the practical application. In this paper, we present the design and implementation of RcLoc, which takes full advantages of the flexible array orientations and receiver positions, based on limited resources. Particularly, RcLoc devises a receiver configuration scheme for guiding the system deployment. Optimized array orientation could effectively improve the AoA estimation accuracy and well-designed receiver positions contribute to the Cramer-Rao lower bound of localization error. In the stage of system realization, we further devise an array calibration method to calibrate the actual array and develop an improved AoA estimation algorithm, which make RcLoc robust to the array arrangement. We prototype RcLoc on commodity Wi-Fi devices without manual intervention. Comprehensive experiments in a multipath-rich indoor environment show that RcLoc achieves a median localization accuracy of 0.4 m, which provides useful insights for receiver deployment.

Mission QoS and Satellite Service Lifetime Tradeoff in Remote Sensing Satellite Networks

Abstract: The large-scale charging and discharging processes can accelerate the attenuation of battery components to further decrease the satellite service lifetime (SSL). Consequently, how to effectively manage the energy consumption during mission acquisition and transmission is an urgent problem under the condition of the stochastically fluctuating solar infeed and limited on-board battery storage resource. On the other hand, the QoS requirements of on-board missions should be guaranteed. Therefore, this letter proposes an intelligent energy management strategy by designing an online mission acquisition, processing, and transmission integration scheduling (MAPTIS) scheme, so as to control the risk of battery depletion thereby further guaranteeing SSL while improving mission QoS requirements. Particularly, we formulate the online battery management based MAPTIS problem as a finite-horizon expected total service reward Markov decision process problem. Furthermore, a backward induction battery management (BIBM) algorithm is proposed to achieve the optimal solution. Simulation results show that the BIBM scheme can effectively reduce the dynamic range of energy consumption, while achieving a compromise in the mission QoS.

Virtual Network Functions Orchestration in Software Defined LEO Small Satellite Networks.

Abstract: Software defined network technique is a novel approach introduced to manage low earth orbit (LEO) small satellite networks. One important challenge is the allocation of the scarce virtualized satellite network resources in space environment. We devise a virtual network functions orchestration based model to implement the virtualized resources management for LEO satellite networks. This model is formulated as an integer linear programming (ILP) problem. Further, we propose a method combining Dantzig-Wolfe decomposition, column generation and branch-and-bound algorithm for the ILP problem to attain the optimal solution. Finally, simulation results demonstrate the effectiveness and efficiency of the proposed algorithm.

Study of single-cell massive MIMO systems with channel aging and prediction

Abstract: In this paper we consider a single-cell massive multiple-input-multiple-output scenario, where the number of base station (BS) antennas is larger than the number of single antenna user terminals (UTs). We study and investigate common impairment named as channel aging caused by the relative movement between BS antenna and UTs. To acquire channel state information we apply minimum-mean-square-error detector. After that we study some commonly used channel predictors. Then we apply Wiener predictor and ARMA predictor to mitigate the effects of channel aging. We provide signal-to-interference-plus-noise ratios for each channel predictor and demonstrate their overall performance. We apply matched filtering for precoding. We perform thorough analysis with both predictors and observe that Wiener predictor performs better than ARMA predictor in all aspects such as achievable rates, cumulative distribution function and with higher Doppler spreads. The calculated results are deterministic and simulations show that they are even more accurate for system dimensions practically.

Regional Characteristics of Cloud Radiative Effects before and after the South China Sea Summer Monsoon Onset

Abstract: The South China Sea summer monsoon (SCSSM) onset is characterized by rapid thermodynamical changes in the atmosphere that are critical to regional weather and climate processes. So far, few studies have focused on the changes in the associated cloud and radiative features. This study investigates spatiotemporal characteristics of top-of-atmosphere (TOA) cloud radiative effects (CREs) before and after the SCSSM onset over the South China Sea (SCS) and South China (SC), based on the 2001–2016 Clouds and the Earth’s Radiant Energy System (CERES) Energy Balanced and Filled (EBAF) satellite data and ERA-Interim reanalysis data. Before the SCSSM onset, strong net CRE (NCRE) dominated by its cooling shortwave component occurs over SC, while descending motion and weak NCRE prevail over the SCS. In the SCSSM onset pentad, convection, high clouds, and longwave and shortwave CREs (LWCRE and SWCRE) abruptly increase over the southern and central SCS, and their high-value centers subsequently move northeastward and are strongly affected by the western Pacific subtropical high. The strong offset between LWCRE and SWCRE enables the NCRE intensity (TOA radiation budget) to be quite small (large) between the SCS and the western North Pacific after the SCSSM onset. In contrast, low–middle-level clouds and strong cooling SWCRE remain over SC after the SCSSM onset, but the increasing high clouds and LWCRE weaken (intensify) the regional NCRE (TOA radiation budget) intensity. These marked latitudinal differences in CREs between the SCS and SC primarily arise from their respective dominant cloud types and circulation conditions, which manifest the differences between the tropical SCSSM and subtropical East Asian monsoon processes. The results indicate that regional cloud fractions and CREs before and after the SCSSM onset are strongly modulated by quickly changed large-scale circulation over the East Asian monsoon regions, and the spatiotemporal variation of CREs is a response to the monsoonal circulation adjustment to a large extent.

Access Points in the Air: Modeling and Optimization of Fixed-Wing UAV Network

Abstract: Fixed-wing unmanned aerial vehicles (UAVs) are of great potential to serve as aerial access points (APs) owing to better aerodynamic performance and longer flight endurance. However, the inherent hovering feature of fixed-wing UAVs may result in discontinuity of connections and frequent handover of ground users (GUs). In this work, we model and evaluate the performance of a fixed-wing UAV network, where UAV APs provide coverage to GUs with millimeter wave backhaul. Firstly, it reveals that network spatial throughput (ST) is independent of the hover radius under real-time closest-UAV association, while linearly decreases with the hover radius if GUs are associated with the UAVs, whose hover center is the closest. Secondly, network ST is shown to be greatly degraded with the over-deployment of UAV APs due to the growing air-to-ground interference under excessive overlap of UAV cells. Finally, aiming to alleviate the interference, a projection area equivalence (PAE) rule is designed to tune the UAV beamwidth. Especially, network ST can be sustainably increased with growing UAV density and independent of UAV flight altitude if UAV beamwidth inversely grows with the square of UAV density under PAE.

Access Points in the Air: Modeling and Optimization of Fixed-Wing UAV Network

Abstract: Fixed-wing unmanned aerial vehicles (UAVs) are of great potential to serve as aerial access points (APs) owing to better aerodynamic performance and longer flight endurance. However, the inherent hovering feature of fixed-wing UAVs may result in discontinuity of connections and frequent handover of ground users (GUs). In this work, we model and evaluate the performance of a fixed-wing UAV network, where UAV APs provide coverage to GUs with millimeter wave backhaul. Firstly, it reveals that network spatial throughput (ST) is independent of the hover radius under real-time closest-UAV association, while linearly decreases with the hover radius if GUs are associated with the UAVs, whose hover center is the closest. Secondly, network ST is shown to be greatly degraded with the over-deployment of UAV APs due to the growing air-to-ground interference under excessive overlap of UAV cells. Finally, aiming to alleviate the interference, a projection area equivalence (PAE) rule is designed to tune the UAV beamwidth. Especially, network ST can be sustainably increased with growing UAV density and independent of UAV flight altitude if UAV beamwidth inversely grows with the square of UAV density under PAE.

Towards Effective Tradeoff Between Content Caching and Retrieving in Dense Small Cell Network.

Abstract: Although the joint design of content caching and retrieving has the potential of relieving the backhaul pressure, either caching or retrieving would significantly influence the distribution of interference in caching-enabled small cell network (CSCN). The complicated interference, if not properly managed, would inversely deteriorate the network performance. In this work, we further investigate the tradeoff of content caching and retrieving in term of network spatial throughput (ST). Specifically, the analysis manifests that, compared to the condition of caching less content, ST is more likely to be reduced with increasing amount of retrieving content when more content is pre-cached by small cell base station (SBS). To maximize the ST, we formulate an optimization problem, which is solved by the joint design of content caching and retrieving. Moreover, a critical SBS density is derived from the optimization result, beyond which less content should be retrieving if more content is pre-cached by SBS. Therefore, the tradeoff between content caching and retrieving could be captured. More importantly, it is shown that a backhaul-free region exists, where the maximization of ST under joint optimization is identical to that under caching optimization. This indicates that the backhaul pressure can be significantly relieved through caching optimization in dense CSCN.

Balancing Coverage and Response Time in Area Target Scheduling for Satellite Networks

Abstract: We study the area target scheduling problem in satellite networks, aiming at maximizing coverage ratio whilst minimizing response time. To balance these two conflicting objectives, we consider their weighted sum and formulate an integer programming problem. By leveraging this problem's underlying structure, we equivalently decompose it into two nested subproblems. We then propose an approximation algorithm that is shown to have 1-e -1 performance bound. Finally, our simulation results show that the maximum performance loss is within 8% over a wide range of weights between the coverage ratio and the response time.

Delay-throughput tradeoff in satellite data relay networks with prioritized user satellites

Abstract: The efficient antenna scheduling strategy for data relay satellites (DRSs) is essential to optimize the throughput or delay of the satellite data relay network. However, these two objectives conflict with each other since the user satellites (USs) with higher priorities take up more transmission time of DRSs' antennas for greater throughput but the USs storing more packets cause a severer waiting delay to the whole network. To balance the conflicting metrics for meeting the delay-throughput integrated requirements, we formulate the antenna scheduling as a stochastic non-convex fractional programming, which is challenging to be solved. For the tractability, we equivalently transform the fractional programming to a parametric problem and implement the Lyapunov drift to guarantee the constraint of mean rate stability. By proposing a delay and throughput tradeoff based antenna scheduling algorithm, we further transform the parametric problem to a solvable weight matching problem. Simulation results reveal the feasible region of the preference control parameter for integrated QoS cases and its variation relationship with network delay and throughput.

Traffic-Aware Multiple Association in Ultradense Networks: A State-Based Potential Game

Abstract: In the fifth-generation (5G) mobile communication system, base stations become denser, and user equipment becomes more powerful. Multiple-association technique promises diversity gains for 5G. However, existing multiple-association schemes are centralized, which have high signal overhead and depend on the reference signal receiving power, and cannot adapt to the fluctuating traffic of users. Therefore, it calls for a new distributed multiple-association scheme. We model the multiple-association problem as a state-based potential game (SPG). With the aid of SPG, the association policy that we designed could drive the ultradense networks to evolve toward the global optimization in the flow level performance. Finally, the performance of our proposed traffic-aware multiple association (TAMA) algorithm is investigated through a practical and discrete simulation method.

Hybrid RSS/CSI Fingerprint Aided Indoor Localization: A Deep Learning based Approach

Abstract: In this work, we investigate the location error of a fingerprint-based indoor system with the application of hybrid received signal strength (RSS) and channel state information (CSI) fingerprints. It manifests that exploiting correlation between RSS and CSI could effectively reduce location error. On this basis, we propose a hybrid RSS/CSI localization algorithm (HRCL), which is designed based on the deep learning. The HRCL fully exploits quick construction of fingerprint database with the coarse-grained RSS and rich multipath information of the fine-grained CSI. The RSS and CSI with high correlation are selected to construct fingerprint database, aiming to improve localization accuracy. Moreover, the deep neural network is trained for location estimation. Especially, experimental results validate that the location error of HRCL can be reduced by 64.4%, compared with the existing localization method. Moreover, the location error of HRCL can be reduced by 29.1 %, compared with HRCL without RSS/CSI selection by correlation coefficient.

Towards Efficient Retransmission in Dense Networks With Interference Correlation

Abstract: Exploiting the time-varying feature of wireless channels, retransmission could enable reliable data transmission. However, the growing deployment of small cell base stations (BSs) would induce significant temporal interference correlation. In consequence, once the current transmission fails, the subsequent ones are likely to fail as well. In this light, we investigate the retransmission performance in dense networks with temporally correlated interference in terms of network spatial throughput (ST). Our results reveal that the impact of temporal interference correlation on the retransmission performance critically depends on the BS density. Specifically, temporal interference correlation would cause a greater network ST attenuation when the BS density is closer to the critical density, under which network ST is maximized. Moreover, the impact of temporal interference correlation is shown to be cumulative as the number of retransmission attempts increases. Furthermore, towards efficient retransmission, we adopt and optimize a P-Activation strategy (PAS). It is shown that the optimized PAS is able to effectively mitigate the overwhelming strength and temporal correlation of interference. As a result, the retransmission performance in improving network ST is significantly enhanced in dense networks, while the variation of network ST with BS density exhibits sigmoid trend instead of the previous near-bell shape.

Indoor Communications with OAM Array

Abstract: It is reported by an online research that Wi-Fi is chosen as the top thing people would not be able to live without. Therefore, it is necessary to continuously develop Wi-Fi technology. On one hand, further increase of Wi-Fi throughput in a legacy spectrum needs new approaches rather than just widening the band or increasing the number of spatial streams. On the other hand, a great research effort has been focused on vortex electromagnetic waves carrying orbital angular momentum (OAM) as a new degree of freedom to enhance the throughput of wireless communication systems. In this paper, we investigate the feasibility and channel capacity performance of an OAM array-based MIMO system in an indoor multipath environment. Numerical results validate that OAM array-based MIMO is superior to conventional MIMO no matter with water-filling power allocation or equal power allocation at any SNR. This result provides a promising possibility to further improve the performance of Wi-Fi.

Regular Space TT&C Mission Planning Based on Hierarchical Progress in Space Information Networks

Abstract: With the development of space missions and the diversity of satellites, space information networks have become more complex. Space TT&C (Tracking Telemetry and Command) missions are faced with shortage of resources and complex demand characteristics. In view of these challenges, we propose a hierarchical progressive TT&C mission planning algorithm. Firstly, we model the TT&C mission planning problem as a mixed integer linear programming problem with aiming at maximizing the network reward, i.e., the weighted number of completed TT&C missions. Then, we decompose this problem into multiple levels of optimization sub-problems according to the types of constraints and use time buckets and binary conflict trees to reduce the complexity of the algorithm. Finally, we use the binary conflict tree to perform local disturbances Simulation results show that, compared with the existing planning algorithms, the proposed algorithm not only guarantees the efficiency of the algorithm, but also improves the total reward of TT&C mission planning.

Joint Sociality and Load Balance for Proactive Caching in Wireless Networks

Abstract: In cache-enabled wireless networks (CWN), the unbalanced traffic distribution due to the node's sociality may lead to local congestion, which significantly degrades system throughput. Especially, nodes prefer to share content with those that have social relationships with them, which may result in heavy traffic load in the nodes with great social relationships. Therefore, it is crucial to capture the interplay among sociality, content caching and traffic distribution. In this paper, we design a caching strategy through jointly considering sociality and load balance to maximize the throughput capacity. To this end, efficient betweenness (EB) is adopted to quantify the traffic distribution, where EB is the number of content delivery paths through a node. Aided by EB, the impacts of key system parameters including sociality and caching strategy on throughput capacity are elaborated. According to the critical condition of the steady state in CWN, we formulate an optimization problem aiming to maximize throughput capacity. Due to the non-convexity of the initial problem, we propose an effective heuristic algorithm to solve it, which can balance traffic load according to the node's sociality and transmission capacity. Simulation results show that the proposed algorithm can increase the throughput capacity by 35.7% against benchmark approaches.

Stabilized cyclic stress‐strain calculation for metals under multiaxial loading

Abstract: A simple plasticity model is proposed to model the stabilized cyclic stress‐strain by introducing the non‐proportionality factor and additional hardening coefficient. The two introduced factors take into account the effects of non‐proportional additional hardening. The proposed model is convenient for engineering application since only six material constants are necessary for modeling.