Development and Application of a Power Law Constitutive Model for Eddy Current Dampers

Eddy current dampers (ECDs) have emerged as highly desirable solutions for vibration control due to theirexceptional damping performance and durability. However, the existing constitutive models present challenges tothe widespread implementation of ECD technology, and there is limited availability of finite element analysis (FEA)software capable of accurately modeling the behavior of ECDs. This study addresses these issues by developing anewconstitutivemodel that is both easily understandable and user-friendly for FEAsoftware. By utilizing numericalresults obtained from electromagnetic FEA, a novel power law constitutive model is proposed to capture thenonlinear behavior of ECDs. The effectiveness of the power law constitutive model is validated throughmechanicalproperty tests and numerical seismic analysis. Furthermore, a detailed description of the application process ofthe power law constitutive model in ANSYS FEA software is provided. To facilitate the preliminary design ofECDs, an analytical derivation of energy dissipation and parameter optimization for ECDs under harmonicmotionis performed. The results demonstrate that the power law constitutive model serves as a viable alternative forconducting dynamic analysis using FEA and optimizing parameters for ECDs.

Nonlinear constitutive models of rock structural plane and their applications

Structural planes play an important role in controlling the stability of rock engineering,and the influence of structural planes should be considered in the design and construction process of rock engineering.In this paper,mechanical properties,constitutive theory,and numerical application of structural plane are studied by a combination method of laboratory tests,theoretical derivation,and program development.The test results reveal the change laws of various mechanical parameters under different roughness and normal stress.At the pre-peak stage,a non-stationary model of shear stiffness is established,and threedimensional empirical prediction models for initial shear stiffness and residual stage roughness are proposed.The nonlinear constitutive models are established based on elasto-plastic mechanics,and the algorithms of the models are developed based on the return mapping algorithm.According to a large number of statistical analysis results,empirical prediction models are proposed for model parameters expressed by structural plane characteristic parameters.Finally,the discrete element method(DEM)is chosen to embed the constitutive models for practical application.The running programs of the constitutive models have been compiled into the discrete element model library.The comparison results between the proposed model and the Mohr-Coulomb slip model show that the proposed model can better describe nonlinear changes at different stages,and the predicted shear strength,peak strain and shear stiffness are closer to the test results.The research results of the paper are conducive to the accurate evaluation of structural plane in rock engineering.

An elasto-plastic constitutive model of moderate sandy clay based on BC-RBFNN

Application research of neural networks to geotechnical engineering has become a hotspot nowadays.General model may not reach the predicting precision in practical application due to different characteristics in different fields.In allusion to this,an elasto-plastic constitutive model based on clustering radial basis function neural network(BC-RBFNN) was proposed for moderate sandy clay according to its properties.Firstly,knowledge base was established on triaxial compression testing data;then the model was trained,learned and emulated using knowledge base;finally,predicting results of the BC-RBFNN model were compared and analyzed with those of other intelligent model.The results show that the BC-RBFNN model can alter the training and learning velocity and improve the predicting precision,which provides possibility for engineering practice on demanding high precision.

An elasto-plastic and viscoplastic damage constitutive model for dilatancy and fracturing behavior of soft rock squeezing deformation

Soft rock squeezing deformation mainly consists of pre-peak damage-dilatancy and post-peak fracture-bulking at the excavation unloading instant,and creep-dilatancy caused by time-dependent damage and fracturing.Based on the classic elastoplastic and Perzyna over-stress viscoplastic theories,as well as triaxial unloading confining pressure test and triaxial unloading creep test results,an elastoplastic and viscoplastic damage constitutive model is established for the short-and long-term dilatancy and fracturing behavior of soft rock squeezing deformation.Firstly,the criteria for each deformation and failure stage are expressed as a linear function of confining pressure.Secondly,the total damage evolution equation considering time-dependent damage is proposed,including the initial damage produced at the excavation instant,in which the damage variable increases exponentially with the lateral strain,and creep damage.Thirdly,a transient five-stages elasto-plastic constitutive equation for the short-term deformation after excavation that comprised of elasticity,pre-peak damage-dilatancy,post-peak brittle-drop,linear strain-softening,and residual perfectly-plastic regimes is developed based on incremental elasto-plastic theory and the nonassociated flow rule.Fourthly,regarding the timedependent properties of soft rock,based on the Perzyna viscoplastic over-stress theory,a viscoplastic damage model is set up to capture creep damage and dilatancy behavior.Viscoplastic strain is produced when the stress exceeds the initial static yield surface fs;the distance between the static yield surface fs and the dynamic yield surface fd determines the viscoplastic strain rate.Finally,the established constitutive model is numerically implemented and field applied to the-848 m belt conveyer haulage roadway of Huainan Panyidong Coal Mine.Laboratory test results and in-situ monitoring results validate the rationality of the established constitutive model.The presented model takes both the transient and time-dependent damage and fracturing into consideration.

ITERATIVE ALGORITHM FOR AXIALLY ACCELERATING STRINGS WITH INTEGRAL CONSTITUTIVE LAW

A numerical method is proposed to simulate the transverse vibrations of a viscoelastic moving string constituted by an integral law. In the numerical computation, the Galerkin method based on the Hermite functions is applied to discretize the state variables, and the Runge- Kutta method is applied to solve the resulting differential-integral equation system. A linear iterative process is designed to compute the integral terms at each time step, which makes the numerical method more efficient and accurate. As examples, nonlinear parametric vibrations of an axially moving viscoelastic string are analyzed.

A MODIFIED THERMAL VISCOPLASTIC CONSTITUTIVE LAW INVOLVING THE EFFECT OF TEMPERATURE RISE RATE

At high temperature rise rate, the mechanical properties of 10 # steel were determined experimentally in a very wide range of temperature and strain rates. A new constitutive relationship was put forward, which can fit with the experimental results and describe various phenomena observed in our experiments. Meanwhile, some interesting characteristics about the temperature rise rate, strain and strain rate hardening and thermal softening are also shown in this paper. Finally, the reliability of the constitutive law and the correctness of the constitutive parameters were verified by comparing the calculation results with the experimental data.

Constitutive Laws for Visco-plastic Porous Medium Shaped by Regularly Distributed Circular Particles

A numerical study is presented,using a homogenization technique to consider the plain strain problem of visco-plastic porous medium shaped by regularly distributed circular particles. Based on a rigid plastic material,the paper derives the macroscopic constitutive laws for homogenous equivalent medium. By changing the shape parameter of circular particles,the effect of pore shape on macroscopic constitutive laws is explored. Yield surfaces with different pore shapes are obtained. About voids,a two-scale conception is introduced,which regards main void as macroscopic scale and secondary cavities as microscopic scale. The macroscopic potential involving main and secondary voids is achieved. The proposed macroscopic constitutive law taking microscopic features as influence factors is helpful for exploring the macroscopic mechanical properties of porous medium when numerical simulation is required.

Predictive Elastoplastic Damage Constitutive Law: Establishment of Equivalence Relation between Intrinsic and Extrinsic Material Parameters

The purpose of the current work is the development and application of a new identification method of material parameters of elastoplastic damage constitutive model under large strains. A relationship relating the intrinsic and extrinsic parameters of a reference material is built and transformed in equivalence relation. Extrinsic parameters concern the shape of their experimental tensile force/elongation curve, however, intrinsic parameters deal with Swift hardening law coupled with an isotropic damage variable. The relationship is carried out from a statistical characterization of a material reference (standard-steel E24). It based on multiple linear regression of a data set obtained according to a full factor design of numerical simulations of mechanical tensile tests. All materials satisfying this equivalence relation belong to the same equivalence class. This is motivated by observing that gathered materials must behave somewhat like the reference material. The material parameters can be immediately identified by only one task by running the found relationship. The current method facilitates the identification procedure and offers a substantial savings in CPU time. However it just needs only one simulation for the identification of similar behavior instead of the few hundred required when using other methods.

A SIMPLE CONSTITUTIVE MODEL FOR FERROELECTRIC CERAMICS UNDER ELECTRICAL/MECHANICAL LOADING

A simple phenomenological model is developed for describing the macroscopic constitutive response of ferroelectric materials based on consideration of the fact that domain switching is a progressive evolution process with loading. The volume fraction of domain switching is taken as an internal variable, which is derived from the domain nucleation theory. The proposed theory can simulate the dielectric hysteresis, reversed butterfly hysteresis, nonlinear strain-stress hysteresis, as well as electric displacement-stress relation of ferroelectric materials. Its compaxison with experimental results and two other theoretical models reveals that the model presented can well predict the nonlinear hysteresis of ferroelectrics under electrical or mechanical loading.

A constitutive model for evaluation of mechanical behavior of fiber-reinforced cemented sand

The aim of this study is to present a constitutive model for prediction of the mechanical behavior of fiberreinforced cemented sand. For this purpose, a generalized plasticity constitutive model of sandy soil is selected and the parameters of the model are determined for three types of sandy soils using the results of triaxial tests. Next, the proposed model is developed using the existing models based on the physicomechanical characteristics of fiber-reinforced cemented sand. The elastic parameters, flow rule and hardening law of the base model are modified for fiber-reinforced cemented sand. To verify the proposed model, the predicted results are compared with those of triaxial tests performed on fiber-reinforced cemented sand. Finally, the efficiency of the proposed model is studied at different confining pressures, and cement and fiber contents.

Contact dynamics of elasto-plastic thin beams simulated via absolute nodal coordinate formulation

Under the frame of multibody dynamics, the contact dynamics of elasto-plastic spatial thin beams is numerically studied by using the spatial thin beam elements of absolute nodal coordinate formulation（ANCF）. The internal force of the elasto-plastic spatial thin beam element is derived under the assumption that the plastic strain of the beam element depends only on its longitudinal deformation.A new body-fixed local coordinate system is introduced into the spatial thin beam element of ANCF for efficient contact detection in the contact dynamics simulation. The linear isotropic hardening constitutive law is used to describe the elasto-plastic deformation of beam material, and the classical return mapping algorithm is adopted to evaluate the plastic strains. A multi-zone contact approach of thin beams previously proposed by the authors is also introduced to detect the multiple contact zones of beams accurately, and the penalty method is used to compute the normal contact force of thin beams in contact. Four numerical examples are given to demonstrate the applicability and effectiveness of the proposed elasto-plastic spatial thin beam element of ANCF for flexible multibody system dynamics.

Machine learning-based constitutive models for cement-grouted coal specimens under shearing

Cement-based grouting has been widely used in mining engineering;its constitutive law has not been comprehensively studied.In this study,a novel constitutive law of cement-grouted coal specimens(CGCS)was developed using hybrid machine learning(ML)algorithms.Shear tests were performed on CGCS for the analysis of stress-strain curves and the preparation of the dataset.To maintain the interpretation of the trained ML models,regression tree(RT)was used as the main technique.The effect of maximum RT depth(Maxdepth)on its performance was studied,and the hyperparameters of RT were tuned using the genetic algorithm(GA).The RT performance was also compared with ensemble learning techniques.The optimum correlation coefficient on the training set was determined as 0.835,0.946,0.981,and 0.985 for RT models with Maxdepth=3,5,7,and 9,respectively.The overall correlation coefficient was over 0.9 when the Maxdepth≥5,indicating that the constitutive law of CGCS can be well described.However,the failure type of CGCS could not be captured using the trained RT models.Random forest was found to be the optimum algorithm for the constitutive modeling of CGCS,while RT with the Maxdepth=3 performed the worst.

Fluid-Structure Interaction Modeling of the Living Artery: Based on the Zero-Pressure Status and the Anisotropic Hyperelastic Constitutive Model

Vascular diseases such as aneurysm,hemadostenosis,aortic dissection are the primary causes of people’s death around world.As a result,it is significant to improve our knowledge about them,which can help to treat the disease.Measuring the hemodynamic factor like the blood pressure,the wall shear stress(WSS)and the oscillatory shear index(OSI)is,however,still beyond the capabilities of in-vivo measurement techniques.So the use of mathematical models and numerical simulations for the studies of the blood flow in arteries and,in general,of the cardiovascular system,both in physiological and pathological conditions,has received an increasing attention in the biomedical community during the last two decades.Indeed,such studies aims at enhancing the current knowledge of the physiology of the cardiovascular system,as well as providing reliable tools for the medical doctors to predict the natural course of pathologies and,possibly,the occurrence of cardiovascular accidents.The computational vascular fluid-structure interaction(FSI)methodology is a numerical simulation method which is used to explain the hemodynamic factors.The WSS on the luminal wall and the mechanical stress in the vascular wall are directly related to the location of the lesion,and the blood flow strongly interacts with the vascular wall motion.The arterial wall continually adapts to the charge of its mechanical environment(due to,for example,growth,atrophy,remodelling,repair,ageing,and disease)and consequently undergoes several irreversible processes.Primary acute mechanisms of vascularFSI numerical simulation seem to be associated with(1)the arterial histology and the patient-specific complex geometry,(2)the typical mechanical properties of the layer,(3)properties of the blood is assumed as Newtonian fluid or non-Newtonian fluid based on the scale ofthe diameter of a vessel,(4)residual stress in the zero-pressure configuration.The arterial system naturally function under permanent physiological loading conditions.Fung defined the residual stress and measured the opening angle which varies greatly along the aortic tree.Consequently,most of these systems never experience a stress-free state in their’service life’,so a stress and strain fields are present in any in vivo obtained patientspecific cardiovascular geometry.The residual stress always be ignored in FSI simulation or be assumed to equal zero,and the vivo patient-specific artery geometry is assumed as zero-pressure configuration.To define the in vivo stress state of artery,an inverse problem needs to be solved:the undeformed shape of a body or its stress state in its deformed state needs to be determined given the deformed configuration and the loads causing this deformation.The modular inverse elastostatics method is used to resolve the pressure-induced stress state for in vivo imaging based on cardiovascular modeling proposed by Peirlinck.Here,we build a living vessel FSI model based on 4 key factors.In order to get the universal simulation results,we focus on idealized geometries of the vessel that represent healthy(physiological)conditions of the cerebral vasculature.Blood can be assumed as the Newtonian fluid at this scale.The anisotropic hyperelastic constitutive law(Gasser-Holzapfel-Ogden)is used in zero-pressure configuration.Afterwards,we propose the material parameters for the different constitutive models and the computational configurations.We demonstrate the importance of introducing the residual stress into vascular blood flow modeling by performing a comparing zero-pressure configuration and no-resistance configuration.We get the conclusion that the zero-pressure status model has smaller displacement and larger stress distribution compared with no-resistance stress model.Hence,the methodology presented here will be particularly useful to study the mechanobiological processes in the healthy and diseased vascular wall.

CONSTITUTIVE RELATION OF UNSATURATED SOIL BY USE OF THE MIXTURE THEORY (Ⅱ)—LINEAR CONSTITUTIVE EQUATIONS AND FIELD EQUATIONS

The linear constitutive equations and field equations of unsaturated soils were obtained through linearizing the nonlinear equations given in the first part of this work. The linear equations were expressed in the forms similar to Biot's equations for saturated porous media. The Darcy's laws of unsaturated soil were proved. It is shown that Biot's equations of saturated porous media are the simplification of the theory. All these illustrate that constructing constitutive relation of unsaturated soil on the base of mixture theory is rational.

New constitutive model for the study of creeping solids

In this paper, a incremental form of constitutive laws for creeping studies are proposed. The equations are based on the concept of creep hardening surface. Damage effects were introduced to the new constitutive relations to study solids creeping effects with pre-existing damages. The present formula is easy to be adopted into other numerical procedures such as finite element methods.

The Protection of the Right to Dignity in the Connection and Interaction between the Constitution and Civil Law

In the report of 19;National Congress of the Communist Party of China,General Secretary Xi Jinping said that China seeks to"accelerate development of the crime prevention and control system,combat and punish in accordance with law all illegal and criminal activities such as pornography,gambling,drug abuse,gang violence,kidnapping,and fraud,and protect people’s personal rights,property rights,and right

The Concept of Human Rights in the Constitution and Its Functional Significance

To practice the constitutional provision that “The state respects and protects human rights”, we should clarify its connotation. The understanding of human rights is a natural requirement and the key. In domestic academia, human rights are considered natural rights and interpreted as “moral rights that everyone should enjoy as a human being”, hoping to provide theoretical support for the development of the system centered on the basic rights of citizens in China.Although it reveals the universal moral connotation of human rights, it does not cover the normative connotation of human rights as common international standards. Therefore, it is impossible to fully clarify the functional significance of the provision. It is conducive to scientifically clarifying the relationship between human rights and basic civil rights,better improving the institutional protection of human rights in China,and promoting the building of a community with a shared future for mankind to interpret human rights as common international standards that everyone should enjoy for human dignity based on the development of the international legal order under the Charter of the United Nations since the end of the World War Ⅱ.

“Fundamental Rights and Private Law” in China

The Qi Yuling case is a crucial juncture in the study of “fundamental rights and private law” in China, yet relevant research is underpinned on two clues. The first is that the increasing interest in the “constitutionalization of private law” worldwide provides knowledge resources and reference materials for scholars in China;the second is the understanding and exploration of the judicial application of the Constitution since the 1980s. Among them, such concepts as “the Constitution has direct legal effect” and “the Constitution needs to be implemented by the people” could have directly affected the Qi Yuling case. Focusing on such topics as the case of Qi Yuling, judicial enforcement of the Constitution, and the compilation of the Civil Code, scholars discussed the ways and scope for inclu ding fundamental rights in private law based on their experience abroad. They also looked into specific issues, covering how fundamental rights affect civil acts and the private law effects fundamental rights like personality rights, equali ty rights, freedom of speech, and protection of personal information. In the context of promoting the full implementation of the Constitution in the new era, “fundamental rights and private law” is still a field with great potential in both practice and theory.

论我国对法律的合宪性审查

长期以来,受观念、制度、程序等因素影响,对法律进行合宪性审查的制度推进较为缓慢。在党的二十大报告正式提出“健全保证宪法全面实施的制度体系”的背景下,落实对法律的合宪性审查,从学理上还是实践中对于完善我国的宪法监督制度都具有重大的意义。要依托法律草案合宪性说明制度,强化对法律草案的合宪性审查工作,还要根据我国宪法监督体制对法律实施阶段的合宪性审查设计科学、合理、可行的机制和程序,构建从事前到事后的全过程的合宪性审查环节,实现对法律是否合宪的有效监督。对法律的合宪性审查有利于保障宪法权威和法治统一,推进宪法全面实施,加快建设社会主义法治国家。