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.

Effect of Elastic Constitutive Laws on the Deformation of Two-dimensional Red Blood Cell

Deformation of two-dimensional red blood cell in linear shear flow is simulated using the immersed boundary method,in which the cell is modeled as a force source instead of a real body.The effect of three constitutive laws,i.e.Hookean,Neo-Hookean and Skalak elasticity,on the deformation is studied by simulating the cell movement in two linear shear flows.The results show that the effect of the constitutive laws gets more obvious as the shear rate increases.Both the aspect ratio and the inclination of the steady shapes get bigger, and the differences between the periods of the cell tank-treading motion become larger.For the same shear flow, the period with Hookean elasticity is less than the period with Neo-Hookean elasticity and bigger than the period with Skalak elasticity.

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.

Data-driven modeling on anisotropic mechanical behavior of brain tissue with internal pressure

Brain tissue is one of the softest parts of the human body,composed of white matter and grey matter.The mechanical behavior of the brain tissue plays an essential role in regulating brain morphology and brain function.Besides,traumatic brain injury(TBI)and various brain diseases are also greatly influenced by the brain's mechanical properties.Whether white matter or grey matter,brain tissue contains multiscale structures composed of neurons,glial cells,fibers,blood vessels,etc.,each with different mechanical properties.As such,brain tissue exhibits complex mechanical behavior,usually with strong nonlinearity,heterogeneity,and directional dependence.Building a constitutive law for multiscale brain tissue using traditional function-based approaches can be very challenging.Instead,this paper proposes a data-driven approach to establish the desired mechanical model of brain tissue.We focus on blood vessels with internal pressure embedded in a white or grey matter matrix material to demonstrate our approach.The matrix is described by an isotropic or anisotropic nonlinear elastic model.A representative unit cell(RUC)with blood vessels is built,which is used to generate the stress-strain data under different internal blood pressure and various proportional displacement loading paths.The generated stress-strain data is then used to train a mechanical law using artificial neural networks to predict the macroscopic mechanical response of brain tissue under different internal pressures.Finally,the trained material model is implemented into finite element software to predict the mechanical behavior of a whole brain under intracranial pressure and distributed body forces.Compared with a direct numerical simulation that employs a reference material model,our proposed approach greatly reduces the computational cost and improves modeling efficiency.The predictions made by our trained model demonstrate sufficient accuracy.Specifically,we find that the level of internal blood pressure can greatly influence stress distribution and determine the possible related damage behaviors.

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.

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.

Finite element verification on constitutive law of AZ31 magnesium alloy at 400℃

A constitutive law is offered for an AZ31B-H24 Mg alloy within a strain rate range of 10-5-10-2 s-1 at a temperature of 400 ℃ The constitutive law, which is developed by curve fitting the tensile tests data, is expressed as a flow stress function of strain and strain rate. Furthermore, the constitutive law is embedded into a proper FE model to simulate the tensile experiments for the purpose of verifying reliability, where the incremental stress-strain relationships are calculated by an elastic-plastic theory in the finite element analysis （FEA）. The results show that the stress-strain characteristics and the final deformed shapes in the FEA agree well with the experiments. In addition, the predicting analysis of constant-velocity stretch conditions and the verification of a free bulge forming experiment show that the proposed FE model is practicable for mechanical analysis on superplastic forming problems. A selective numerical method is offered for advanced superplastic analysis on AZ31 Mg alloys.

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.

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.

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.

NONLINEAR VIBRATION ANALYSIS OF VISCOELASTIC CABLE WITH SMALL SAG

Both the inplane and out-of-plane transverse vibrations of aviscoelastic cable subjected to an initial stress distributinguniform on the cross section are studied. The constitution of thecable material is as- sumed to be of the hereditary integral type.The partial differential -integral equations of motion are derivedfirst. Then by applying Galerkin's method, the governing equationsare reduced to a set of second-order non- linear differential-integral equations which are solved by finite difference numericalintegration procedures. Finally, the effects of the viscosityparameter and the elastic parameter on the transient amplitudes ofthe first Mode are investigated by numerical simulation.

A reliability study of springback on the sheet metal forming process under probabilistic variation of prestrain and blank holder force

This work deals with a reliability assessment of springback problem during the sheet metal forming process. The effects of operative parameters and material properties, blank holder force and plastic prestrain, on springback are in- vestigated. A generic reliability approach was developed to control springback. Subsequently, the Monte Carlo simula- tion technique in conjunction with the Latin hypercube sam- pling method was adopted to study the probabilistic spring- back. Finite element method based on implicit/explicit al- gorithms was used to model the springback problem. The proposed constitutive law for sheet metal takes into account the adaptation of plastic parameters of the hardening law for each prestrain level considered. Rackwitz-Fiessler al- gorithm is used to find reliability properties from response surfaces of chosen springback geometrical parameters. The obtained results were analyzed using a multi-state limit reli- ability functions based on geometry compensations.

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.

NONLINEAR DYNAMIC BEHAVIOR OF VISCOELATIC TPANSMISSION BELT

The nonlinear dynamic responses of viscoelastic axially transmission beltsare investigated and the Kelvin viscoelastic differential constitutive model is employed tocharacterize the material property of belts. The generalized equation of motion is obtained for aviscoelatic axially transmission belts with geometric nonlinearity first, and then is reduced to bea set of second-order nonlinear ordinary differential equations by applying Galerkin's method.Finally, the effects of viscosity parameter and elastic parameter and the moving velocity of thebelts on the transient responses are investigated by the research of digital simulation.

The effects of relative density of metal foams on the stresses and deformation of beam under bending

The exact analytic solution of the pure bending beam of metallic foams is given. The effects of relative density of the material on stresses and deformation are revealed with the Triantafillou and Gibson constitutive law （TG model） taken as the analysis basis. Several examples for individual foams are discussed, showing the importance of compressibility of the cellular materials. One of the objects of this study is to generalize Hill＇s solution for incompressible plasticity to the case of compressible plasticity, and a kinematics parameter is brought into the analysis so that the velocity field can be determined.

Large deflections of non-prismatic nonlinearly elastic cantilever beams subjected to non-uniform continuous load and a concentrated load at the free end

This work studies large deflections of slen- der, non-prismatic cantilever beams subjected to a combined loading which consists of a non-uniformly distributed con- tinuous load and a concentrated load at the free end of the beam. The material of the cantilever is assumed to be non- linearly elastic. Different nonlinear relations between stress and strain in tensile and compressive domain are considered. The accuracy of numerical solutions is evaluated by com- paring them with results from previous studies and with a laboratory experiment.

Exact Solution of a Cylinder Tube Made of Metallic Foam Under Inner Pressure

Exact solution of the stress and velocity fields of a cylinder tube of metallic foams under inner pressure is given in which the Triantafillou and Gibson constitutive law （TG model） for the material is taken as a basis of the calculation. The nonlinear equation is turned linear equation by introducing a kinematics parameter. The differences between the full condensed materials and the effect of the relative density are also discussed.

Compressible closure models for turbulent multifluid mixing

This paper studies governing equations describing the turbulent fluid mixing behavior effectively. The goal is to propose a closure for compressible multiphase flow models with transport and surface tension, which satisfy the boundary conditions at the mixing zone edges, the conservation requirements, and an entropy inequality constraint. Implicitness of positivity for the entropy of averaging requires entropy inequality as op- posed to conservation of entropy for microphysically adiabatic processes.

THE EXISTENCE OF SOLUTIONS IN NONLINEAR ELASTODYNAMICS

Under the small deformation assumption this paper shows the existence of solution for the system of elastic dynamics with the general nonlinear constitutive laws, and the existence of classical solution can be found under weaker conditions.

THE PROBABILITY STABILITY OF VISCOELASTIC PLATES

The almost sure stability of homogeneous viscoelastic platessubjected to a random wide-band stationary in-plane load isinvestigated. The viscoelastic behavior of the plate is described interms of the Bo- ltzmann superposition principle, the relaxationkernels of which are represented by the sums of exponents. On theassumption that the in-plane load is random wide-band stationaryprocess, sufficient conditions for al- Most sure stability ofviscoelastic plates are obtained by the applications of Lyapunov'sdirect method.