Uniqueness of rate-dependency, creep and stress relaxation behaviors for soft clays

This work focuses on the uniqueness of rate-dependency, creep and stress relaxation behaviors for soft clays under one-dimensional condition. An elasto-viscoplastic model is briefly introduced based on the rate-dependency of preconsolidation pressure. By comparing the rate-dependency formulation with the creep based formulation, the relationship between rate-dependency and creep behaviors is firstly described. The rate-dependency based formulation is then extended to derive an analytical solution for the stress relaxation behavior with defining a stress relaxation coefficient. Based on this, the relationship between the rate-dependency coefficient and the stress relaxation coefficient is derived. Therefore, the uniqueness between behaviors of rate-dependency, creep and stress relaxation with their key parameters is obtained. The uniqueness is finally validated by comparing the simulated rate-dependency of preconsolidation pressure, the estimated values of secondary compression coefficient and simulations of stress relaxation tests with test results on both reconstituted Illite and Berthierville clay.

A Hybrid Compensation Scheme for the Input Rate-Dependent Hysteresis of the Piezoelectric Ceramic Actuators

A hybrid compensation scheme for piezoelectric ceramic actuators(PEAs)is proposed.In the hybrid compensation scheme,the input rate-dependent hysteresis characteristics of the PEAs are compensated.The feedforward controller is a novel input rate-dependent neural network hysteresis inverse model,while the feedback controller is a proportion integration differentiation(PID)controller.In the proposed inverse model,an input ratedependent auxiliary inverse operator(RAIO)and output of the hysteresis construct the expanded input space(EIS)of the inverse model which transforms the hysteresis inverse with multi-valued mapping into single-valued mapping,and the wiping-out,rate-dependent and continuous properties of the RAIO are analyzed in theories.Based on the EIS method,a hysteresis neural network inverse model,namely the dynamic back propagation neural network(DBPNN)model,is established.Moreover,a hybrid compensation scheme for the PEAs is designed to compensate for the hysteresis.Finally,the proposed method,the conventional PID controller and the hybrid controller with the modified input rate-dependent Prandtl-Ishlinskii(MRPI)model are all applied in the experimental platform.Experimental results show that the proposed method has obvious superiorities in the performance of the system.

Safety evaluation of Dagangshan arch dam resisting strong earthquakes with a rate-dependency anisotropic damage model

This paper presents a model to simulate the safe behavior of Dagangshan arch dam with a rate-dependency anisotropic damage model. This model considers the damage of asymmetry and anisotropy under cyclic loading of tension and compression, and it is used in the compiled finite element code. The material parameters used in the model can be identified from uniaxial static and dynamic experiments. Thereafter, it is used for analyzing damage and failure patterns of the dam subjected to water pressure and strong earthquakes. The numerical results show that it is necessary to consider both asymmetry between tension and compression and anisotropy of damage. Severe damage regions of the dam reveal brittle and risky positions clearly. Meanwhile damage patterns show the failure trend and safety behaviors of the dam. These results match well with that of the experiments carried out in DUT. The proposed model may be used to predict the damage patterns and potential failure modes of concrete structures like the dam. And the aseismic performance of the dam can be figured out.

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.

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.

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.

Dynamic evolution of shear rate-dependent behavior of rock discontinuity under shearing condition

Rock blocks sliding along discontinuities can cause serious disasters,such as landslides,earthquakes,or rock bursts.The shear rate-dependent behavior is a typical time-dependent behavior of a rock discontinuity,and it is closely related to the stability of a rock block.To further study the shear rate-dependent behavior of rock discontinuities,shear tests with alternating shear rates(SASRs)were conducted on rock discontinuities with various surface morphologies.The dynamic evolution of the shear rate dependency was studied in detail based on the shear test results,and three stages were identified with respect to the shear stress and shear deformation states.The test results revealed that dynamic changes in shear stiffness and the energy storage abilities of the rock discontinuities occurred in relation to the shear rate-dependent behavior of crack growth,which increased with an increase in normal stress and/or the joint roughness coefficient.The stage of decreasing shear stiffness corresponded to a stage of noticeable shear rate-dependency,and the shear rate was found to have no influence on the initial crack stress.

Rate-Dependent Hysteresis Modeling and Compensation of Piezo-Driven Flexure-Based Mechanism

Updating parameters according to the driving rate of input, the rate-dependent Prandtl-Ishlinskii （PI） model is widely used in hysteresis modeling and compensation. In order to improve the modeling accuracy, two PI models identified at low and high driving rates separately are incorporated through a combination law. For the piezo- driven flexure-based mechanism, the very low damping ratio makes it easy to excite the structural vibration. As a re- suit, the measured hysteresis loop is greatly distorted and the modeling accuracy of the identified P1 model is signifi- cantly affected. In this paper, a novel time-efficient parameter identification method which utilizes the superimposed sinusoidal signals as the control input is proposed. This method effectively avoids the excitation of the structural vibra- tion. In addition, as the driving rate of the superimposed sinusoidal signals covers a wide range, all the coefficients required for modeling the rate-dependence can be identified through only one set of experimental data. Hysteresis modeling and trajectory tracking experiments were performed on a 2-DOF piezo-driven flexure-based mechanism. The experimental results show that the combined hysteresis model maintains the modeling accuracy over the entire work- ing range of the flexure-based mechanism. The mechanism＇s hysteresis is significantly suppressed by the use of the inverse PI model as the feedforward controller; and better result is achieved when a feedback loop is also incorporated. The tracking performance of the flexure-based mechanism is greatly improved.

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.

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.

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.

Numerical simulation of dynamic fracture properties of rocks under different static stress conditions

When underground cavities are subjected to explosive stress waves,a uniquely damaged zone may appear due to the combined effect of dynamic loading and static pre-load stress.In this study,a rate-dependent two-dimensional rock dynamic constitutive model was established to investigate the dynamic fractures of rocks under different static stress conditions.The effects of the loading rate and peak amplitude of the blasting wave under different confining pressures and the vertical compressive coefficient(K_(0))were considered.The numerical simulated results reproduced the initiation and further propagation of primary radial crack fractures,which were in agreement with the experimental results.The dynamic loading rate,peak amplitude,static vertical compressive coefficient(K_(0))and confining pressure affected the evolution of fractures around the borehole.The heterogeneity parameter(m)plays an important role in the evolution of fractures around the borehole.The crack propagation path became more discontinuous and rougher in a smallerheterogeneity parameter case.

The rate dependence of the dielectric strength of dielectric elastomers

Elastomers are widely used in electronics and electrical devices,either as insulators or transducers.The insulation and actuation performance of elastomers are highly suscepti-ble to their dielectric strength.Among the factors that influ-encethedielectricstrength ofelastomers,material viscoelasticity is an important factor that needs further inves-tigation.Since the material viscoelasticity is often character-ized by rate-dependent behaviors,we present two different sample configurations to experimentally examine the electrical and mechanical rate dependence of the dielectric strength of VHB 4905 elastomers.At pre-stretch ratio of 4,the improve-ment of the dielectric strength is about 30%from voltage ramp of 50 V/s to 800 V/s.Particularly,with an in-house biaxial test platform,the effect of the stretching rate on the dielectric strength is examined for the first time.The improvement of the dielectric strength is about 35%from stretching rate of 0.1 mm/s to 5 mm/s.Moreover,a dielectric strength predictor based on configurational stress is adopted to describe the experimental data.According to the predictor,the loading rate affects the dielectric strength of the elastomer mainly by influencing the evolution of the inelastic deformation.

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 constitutive model of poly(ethylene terephthalate) for dynamic analysis

Uniaxial tensile testing at strain rates ranging from 10-3 to 10-1 s-1 was carried out to study the rate-dependent me-chanical behavior for poly(ethylene terephthalate) (PET) used in the packaging industry. The experimental results show that a rate-dependent plastic behavior exists for PET material. The value of the yield strength was found to increase with the increasing strain rate. A new constitutive model based on the improved Cowper-Symonds rate-dependent constitutive model is proposed to describe the mechanical behavior of PET material in the strain rate ranging from 10-3 to 10-1 s-1, providing more accurate material data for the subsequent simulation analysis of drop test and dynamic buckling. The predictions obtained using the proposed model are compared with experimental results of the improved Cowper-Symonds model. The simulating results of the proposed model agree well with the experimental data. For a low strain rate, the predictions of this model are more precise than those obtained using the improved Cowper-Symonds model. This confirms that the new constitutive model is suitable for describing the me-chanical behavior of PET material at a low strain rate and modeling impact problem.

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.