A rate-dependent constitutive model for saturated frozen soil considering local breakage mechanism

A rate-dependent constitutive model for saturated frozen soil is vital in frozen soil mechanics,especially when simultaneously describing the nonlinearity,dilatancy and strain-softening characteristics.The distribution of the non-uniform strain rate of saturated frozen soil at the meso-scale due to the local icecementation breakage is described by a newly binary-medium-based homogenization equation.Based on the field-equation-based approach of the meso-mechanics theory,the interaction expression of the strain rate at macro-and meso-scale is derived,which can give the strain rate concentration tensor at different crushed degrees.With the thermodynamics and empirical assumption,a breakage ratio in the rate-dependent form is determined.This overcomes the limitations of the existing binary-medium-based models that are difficult to simulate rate-dependent mechanical response.Based on these assumptions,a newly binary-medium-based rate-dependent model is proposed considering both the ice bond breakage and material composition characteristics of saturated frozen soil.The proposed constitutive model has been validated by the test results on frozen soils with different temperatures and strain rates.

Implementation of OpenMP Parallelization of Rate-Dependent Ceramic Peridynamic Model

A rate-dependent peridynamic ceramic model,considering the brittle tensile response,compressive plastic softening and strain-rate dependence,can accurately represent the dynamic response and crack propagation of ceramic materials.However,it also considers the strain-rate dependence and damage accumulation caused by compressive plastic softening during the compression stage,requiring more computational resources for the bond force evaluation and damage evolution.Herein,the OpenMP parallel optimization of the rate-dependent peridynamic ceramicmodel is investigated.Also,themodules that compute the interactions betweenmaterial points and update damage index are vectorized and parallelized.Moreover,the numerical examples are carried out to simulate the dynamic response and fracture of the ceramic plate under normal impact.Furthermore,the speed-up ratio and computational efficiency by multi-threads are evaluated and discussed to demonstrate the reliability of parallelized programs.The results reveal that the totalwall clock time has been significantly reduced after optimization,showing the promise of parallelization process in terms of accuracy and stability.

CRITERION FOR JUDGING SATISFACTION OF CONSISTENCY CONDITIONS IN RATE-DEPENDENT CONSTITUTIVE RELATIONS

Based on irreversible thermodynamics, the criterion for judging the satisfaction of consistency conditions in rate-dependent constitutive relationship is deduced by introducing four basic hypotheses. Formulas for solving internal variables are given. It makes the rate-dependent model applicable no matter whether the consistency conditions can be satisfied or not.

A Rate-Dependent Peridynamic Model for the Dynamic Behavior of Ceramic Materials

In this study,a new bond-based peridynamic model is proposed to describe the dynamic properties of ceramics under impact loading.Ceramic materials show pseudo-plastic behavior under certain compressive loadings with high strain-rate,while the characteristic brittleness of the material dominates when it is subjected to tensile loading.In this model,brittle response under tension,softening plasticity under compression and strain-rate effect of ceramics are considered,which makes it possible to accurately capture the overall dynamic process of ceramics.This enables the investigation of the fracture mechanism for ceramic materials,during ballistic impact,in more detail.Furthermore,a bond-force updating algorithm is introduced to perform the numerical simulation and solve the derived equations.The proposed model is then used to analyze the dynamic response of ceramics tiles under impact loading to assess its validity.The results of damage development in ceramic materials are calculated and compared with the experimental results.The simulation results are consistent with the experiments,which indicates that the proposed rate-dependent peridynamic model has the capability to describe damage propagation in ceramics with good accuracy.Finally,based on a comparison between simulation and experimental results,it can be concluded that the damage results are in better agreement with experimental results than non-ordinary state-based peridynamic method.

AN ENDOCHRONIC CONSTITUTIVE MODEL FOR RATE-DEPENDENT AND NONPROPORTIONAL CYCLIC PLASTICITY

The total stress response of material is decomposed into a sum of an equilibrium stress response and a non-equilibrium overstress response. Correspondingly, the rate-independent intrinsic time and the rate-dependent intrinsic time are defined respectively. Additional hardening functions for describing the isotropic and anisotropic nonproportional effects are assumed to be related to the accumulation of plastic strain component along the normal of equilibrium stress trajectory, in which the effects of geometry of the loading path are included. An endochronic constitutive model for rate-dependent, nonproportional cyclic plasticity is formulated and applied to simulate the stress responses of stainless steel XCrNil8. 9 for some typical loading programs at different loading rates. A comparison between predicted results and experimental ones by Haupt and Lion shows that the former are in agreement with the latter.

Intelligent modeling and control for nonlinear systems with rate-dependent hysteresis

A new modeling approach for nonlinear systems with rate-dependent hysteresis is proposed. The approach is used for the modeling of the giant magnetostrictive actuator, which has the rate-dependent nonlinear property. The models built are simpler than the existed approaches. Compared with the experiment result, the model built can well describe the hysteresis nonlinear of the actuator for input signals with complex frequency. An adaptive direct inverse control approach is proposed based on the fuzzy tree model and inverse learning and special learning that are used in neural network broadly. In this approach, the inverse model of the plant is identified to be the initial controller firstly. Then, the inverse model is connected with the plant in series and the linear parameters of the controller are adjusted using the least mean square algorithm by on-line manner. The direct inverse control approach based on the fuzzy tree model is applied on the tracing control of the actuator by simulation. The simulation results show the correctness of the approach.

A rate-dependent Prandtl-lshlinskii model for piezoelectric actuators using the dynamic envelope function based play operator

In this paper, a novel rate-dependent Prandtl- Ishlinskii （P-I） model is proposed to characterize the rate- dependent hysteresis nonlinearity of piezoelectric actua- tors. The new model is based on a modified rate-dependent play operator, in which a dynamic envelope function is introduced to replace the input function of the classical play operator. Moreover, a dynamic density function is utilized in the proposed P-I model. The parameters of the proposed model are identified by a modified particle swarm optimization algorithm. Finally, experiments are conducted on a piezo-actuated nanopositioning stage to validate the proposed P-I model under the sinusoidal inputs. The experimental results show that the developed rate-dependent P-I model precisely characterize the rate- dependent hysteresis loops up to 1000 Hz.

Rate-dependent tipping-delay phenomenon in a thermoacoustic system with colored noise

Tipping is a phenomenon in multistable systems where small changes in inputs cause huge changes in outputs.When the parameter varies within a certain time scale,the rate will affect the tipping behaviors.These behaviors are undesirable in thermoacoustic systems,which are widely used in aviation,power generation and other industries.Thus,this paper aims at considering the tipping behaviors of the thermoacoustic system with the time-varying parameters and the combined excitations of additive and multiplicative colored noises.Transient dynamical behaviors for the proposed thermoacoustic model are implemented through the reduced Fokker-Planck-Kolmogorov equation derived by a standard stochastic averaging method.Then,the tipping problems of the rate-dependent thermoacoustic systems with random fluctuations are studied by virtue of the obtained probability density functions.Our results show that the rate delays the value of the tipping parameter compared to the one with the quasi-steady assumption,which is called as a rate-dependent tipping-delay phenomenon.Besides,the influences of the initial values,the rate,the changing time of the parameters,and the correlation time of the noises on the rate-dependent tipping-delay phenomenon are analyzed in detail.These results are of great significance for research in related fields such as aviation and land gas turbines.

Robust intelligent modeling for giant magnetostrictive actuators with rate-dependent hysteresis

Purpose–This paper proposes a robust modeling method of a giant magnetostrictive actuator which has a rate-dependent nonlinear property.Design/methodology/approach–It is known in statistics that the Least Wilcoxon learning method developed using Wilcoxon norm is robust against outliers.Thus,it is used in the paper to determine the consequence parameters of the fuzzy rules to reduce the sensitiveness to the outliers in the input-output data.The proposed method partitions the input space adaptively according to the distribution of samples and the partition is irrelative to the dimension of the input data set.Findings–The proposed modeling method can effectively construct a unique dynamic model that describes the rate-dependent hysteresis in a given frequency range with respect to different single-frequency and multi-frequency input signals no matter whether there exist outliers in the training set or not.Simulation results demonstrate that the proposed method is effective and insensitive against the outliers.Originality/value–The main contributions of this paper are:first,an intelligent modeling method is proposed to deal with the rate-dependent hysteresis presented in the giant magnetostrictive actuator and the modeling precision can fulfill the requirement of engineering,such as the online modeling issue in the active vibration control;and second,the proposed method can handle the outliers in the input-output data effectively.

Modeling and H_∞ Robust Control of a Smart Structure with Rate-dependent Hysteresis Nonlinearity

The performance of smart structures in trajectory tracking under sub-micron level is hindered by the rate-dependent hysteresis nonlinearity.In this paper,a Hammerstein-like model based on the support vector machines(SVM)is proposed to capture the rate-dependent hysteresis nonlinearity.We show that it is possible to construct a unique dynamic model in a given frequency range for a rate-dependent hysteresis system using the sinusoidal scanning signals as the training set of signals for the linear dynamic subsystem of the Hammerstein-like model.Subsequently,a two-degree-of-freedom(2DOF)H∞robust control scheme for the ratedependent hysteresis nonlinearity is implemented on a smart structure with a piezoelectric actuator(PEA)for real-time precision trajectory tracking.Simulations and experiments on the structure verify both the efectiveness and the practicality of the proposed modeling and control methods.

An improved Prandtl-Ishlinskii model for compensating rate-dependent hysteresis in fast steering mirror system

To solve the rate-dependent hysteresis compensation problem in fast steering mirror(FSM) systems, an improved Prandtl-Ishlinskii(P-I) model is proposed in this paper. The proposed model is formulated by employing a linear density function into the STOP operator. By this way, the proposed model has a relatively simple mathematic format, which can be applied to compensate the rate-dependent hysteresis directly. Adaptive differential evolution algorithm is utilized to obtain the accurate parameters of the proposed model. A fast steering mirror control system is established to demonstrate the validity and feasibility of the improved P-I model. Comparative experiments with different input signals are performed and analyzed, and the results show that the proposed model not only suppresses the rate-dependent hysteresis effectively, but also obtains high tracking precision.

Boosting rate performance of layered lithium-rich cathode materials by oxygen vacancy induced surface multicomponent integration

The rapid development of electric vehicles and portable energy storage systems demands improvements in the energy density and cost-effectiveness of lithium-ion batteries,a domain in which Lithium-rich layered cathode(LLO)materials inherently excel.However,these materials face practical challenges,such as low initial Coulombic efficiency,inferior cycle/rate performance,and voltage decline during cycling,which limit practical application.Our study introduces a surface multi-component integration strategy that incorporates oxygen vacancies into the pristine LLO material Li1.2Mn_(0.6)Ni_(0.2)O_(2).This process involves a brief citric acid treatment followed by calcination,aiming to explore rate-dependent degradation behavior.The induced surface oxygen vacancies can reduce surface oxygen partial pressure and diminish the generation of O_(2)and other highly reactive oxygen species on the surface,thereby facilitating the activation of Li ions trapped in tetrahedral sites while overcoming transport barriers.Additionally,the formation of a spinel-like phase with 3D Li+diffusion channels significantly improves Li^(+)diffusion kinetics and stabilizes the surface structure.The optimally modified sample boasts a discharge capacity of 299.5 mA h g^(-1)at a 0.1 C and 251.6 mA h g^(-1)at a 1 C during the initial activation cycle,with an impressive capacity of 222.1 mA h g^(-1)at a 5 C.Most notably,it retained nearly 70%of its capacity after 300 cycles at this elevated rate.This straightforward,effective,and highly viable modification strategy provides a crucial resolution for overcoming challenges associated with LLO materials,making them more suitable for practical application.

Fractional-order visco-plastic constitutive model for uniaxial ratcheting behaviors

This paper proposes a novel unified visco-plastic constitutive model for uniaxial ratcheting behaviors. The cyclic deformation of the material presents remarkable time-dependence and history memory phenomena. The fractional(fractional-order)derivative is an efficient tool for modeling these phenomena. Therefore, we develop a cyclic fractional-order unified visco-plastic(FVP) constitutive model. Specifically, within the framework of the cyclic elasto-plastic theory, the fractional derivative is used to describe the accumulated plastic strain rate and nonlinear kinematic hardening rule based on the Ohno-Abdel-Karim model. Moreover, a new radial return method for the back stress is developed to describe the unclosed hysteresis loops of the stress-strain properly.The capacity of the FVP model used to predict the cyclic deformation of the SS304 stainless steel is verified through a comparison with the corresponding experimental data found in the literature(KANG, G. Z., KAN, Q. H., ZHANG, J., and SUN, Y. F. Timedependent ratcheting experiments of SS304 stainless steel. International Journal of Plasticity, 22(5), 858–894(2006)). The FVP model is shown to be successful in predicting the rate-dependent ratcheting behaviors of the SS304 stainless steel.

A Fully Coupled Thermomechanical Model of Friction Stir Welding(FSW) and Numerical Studies on Process Parameters of Lightweight Aluminum Alloy Joints

This paper presents a new thermomechanical model of friction stir welding which is capable of simulating the three major steps of friction stir welding （FSW） process, i.e., plunge, dwell, and travel stages. A rate-dependent Johnson- Cook constitutive model is chosen to capture elasto-plastic work deformations during FSW. Two different weld schedules （i.e., plunge rate, rotational speed, and weld speed） are validated by comparing simulated temperature profiles with experimental results. Based on this model, the influences of various welding parameters on temperatures and energy generation during the welding process are investigated. Numerical results show that maximum temperature in FSW process increases with the decrease in plunge rate, and the frictional energy increases almost linearly with respect to time for different rotational speeds. Furthermore, low rotational speeds cause inadequate temperature distribution due to low frictional and plastic dissipation energy which eventually results in weld defects. When both the weld speed and rotational speed are increased, the contribution of plastic dissipation energy increases significantly and improved weld quality can be expected.

DEVELOPMENT OF EXPERIMENTAL METHODS FOR IMPACT TESTING BY COMBINING HOPKINSON PRESSURE BAR WITH OTHER TECHNIQUES

The split Hopkinson pressure bar（SHPB） technique and the wave propagation inverse analysis（WPIA） technique are both extensively used to experimentally investigate the impact behavior of materials, although neither of them alone provides a fully satisfactory analysis. In the present paper, attention is given to new experimental techniques by incorporating a damagemodified constitutive model into the SHPB technique and combining the Hopkinson pressure bar（HPB） technique with WPIA. First, to distinguish the response due to dynamic constitutive behavior and the response due to dynamic damage evolution, the SHPB method incorporating a damage-modified constitutive model is developed, including an explicit damage-modified Zhu–Wang–Tang model and an implicit damage-modified constitutive model. Second, when the SHPB results become invalid, a method of combining new Lagrange inverse analyses with the HPB technique is developed, including cases of the HPB arranged in front of a long specimen and behind the specimen. As examples of these new methods, typical results are given for nonlinear viscoelastic polymers and concretes considering damage evolution, a super-elastic Ti–Ni alloy with phase transformation and an aluminum foam with shock waves propagating within it.

THE USE OF VISCO-ELASTOPLASTIC DAMAGE CONSTITUTIVE MODEL TO SIMULATE NONLINEAR BEHAVIOR OF CONCRETE

A visco-elastoplastic damage constitutive model is proposed for simulating non-linear behavior of concrete. Based on traditional plastic theory, the irreversible deformation is simulated in effective stress space. In order to reflect different stiffness degradation mechanism of concrete under tensile and compressive loading conditions, both tensile and compressive damage variables are introduced, and then on the basis of energy release rate, the model is firmly derived within the concept of irreversible thermodynamics. The rate-dependent model is considered by introducing viscous regularization into the inelastic strain and damage variable, and combined with an additional elastic condition. Fully implicit backward-Euler algorithm is used to perform constitutive integration. Results of numerical examples using the proposed model agree well with test results for specimens under uniaxial tension and compression, biaxial loading and triaxial loading. Failure processes of single-edge-notched （SEN） beam and double-edge-notched （DEN） specimen are also simulated to further validate the proposed model.

CHARACTERISTIC DIMENSIONLESS NUMBERS IN MULTI—SCALE AND RATE—DEPENDENT PROCESSES

Multi-scale modeling of materials properties and chemical processes has drawn great attention from sci-ence and engineering. For these multi-scale and rate-dependent processes, how to characterize their trans-scale for-mulation is a key point. Three questions should be addressed:How do multi-sizes affect the problems?How are length scales coupled with time scales?How to identify emergence of new structure in process and its effect?For this sake, the macroscopic equations of mechanics and the kinetic equations of the microstructural transforma-tions should form a unified set that be solved simultaneously.As a case study of coupling length and time scales, the trans-scale formulation of wave-induced damage evolution due to mesoscopic nucleation and growth is discussed. In this problem, the trans-scaling could be reduced to two inde-pendent dimensionless numbers: the imposed Deborah number De=(ac)/(LV) and the intrinsic Deborah num-ber D = (nNc5)/V* ,where a. L, c, V and nN are wave speed, sample size, microcrack size, the rate of micro-crack grovvth and the rate of microcrack nucleation density, respectively. Clearly, the dimensionless number De=(ac)l(LV) includes length and time scales on both meso- and macro- Ievels and governs the progressive process. Whereas, the intrinsic Deborah number D' indicates the characteristic transition of microdamage to macroscopic rup-ture since D is related to the criterion of damage localization, which is a precursor of macroscopic rupture. This case study may highlight the scaling in multi-scale and rate-dependent problems.Then, more generally, we compare some historical examples to see how trans-scale formulations were achieved and what are stili open now. The comparison of various mechanisms governing the enhancement of meso-size effects re-minds us of the importance of analyzing multi-scale and rate-dependent processes case by case.For multi-scale and rate-dependent processes with chemical reactions and diffusions, there seems to be a need of trans-scale formulation of coupling effect of multi-scales and corresponding rates. Perhaps, two trans-scale effects may need special attention. One is to clarify what dimensionless group is a proper trans-scale formulation in coupled multi-scale and rate-dependent processes with reactions and diffusion. The second is the effect of emergent structures and its length scale effect.