Constitutive Relationship Model Research Articles

Study of Constitutive Relationship Model of Material Structure Based on Full State Function

The structural problem is the key and difficult point for the study of material composed of granules. In this paper, theory of full state function for material structure is put forward by examining the structural morphology of the material. The full state function of material structure reflects the structural properties of material. Thus it can also reflect the variations in of mechanical and geometric properties of material under external force, i.e. the constitutive relationship of material. The constitutive relationship established based on full state function is abbreviated as "full constitutive relationship”, which considers the structural properties of material. The constitutive relationship not only can derive constitutive relationship which considers material structure, but also the constitutive relationship with the identical form as that in classical theory when material degenerates into typical ideal elastic-plastic material. The theoretical method proposed in this paper transforms dynamic analysis of structural evolution into state analysis. By associating granular scale with macroscopic scale, a foundation is laid for solving of the structural problems of material macroscopically.

Research of Bond-Slip Constitutive Relation Model between Fiber Gypsum Board and Concrete Materials

How to establish the bond-slip constitutive relation model of concrete and gypsum board will be of great academic significance. Through the pull-out experiment of CFFP, the load-slip curves is obtained. The characteristics and research situation of bond-slip performance at the inter face of concrete and other materials are introduced, and the bond-slip constitutive relation models are summarized at the same time. By using the fitting operation, the proposed constitutive relation is put forward , which is feasible and can be applied to further research on CFFP.

A numerical study on the damage of projectile impact on concrete targets

This paper presents the numerical simulation of the rigid 12.6 mm diameter kinetic energy ogive-nosed projectile impact on plain and fiber reinforced concrete (FRC) targets with compressive strengths from 45 to 235 MPa, using a three-dimensional finite element code LS-DYNA. A combined dynamic constitutive model, describing the compressive and tensile damage of concrete, is implemented. A modified Johnson_Holmquist_Cook (MJHC) constitutive relationship and damage model are incorporated to simulate the concrete behavior under compression. A tensile damage model is added to the MJHC model to analyze the dynamic fracture behavior of concrete in tension, due to blast loading. As a consequence, the impact damage in targets made of plain and fiber reinforced concrete with same matrix material under same impact velocities (650 m/s) are obtained. Moreover, the damage distribution of concrete after penetration is procured to compare with the experimental results. Numerical simulations provide a reasonable prediction on concrete damage in both compression and tension.

Exact solutions for rotational flow of a fractional Maxwell fluid in a circular cylinder

This paper deals with the rotational flow of a fractional Maxwell fluid in an infinite circular cylinder, due to the torsional variable time-dependent shear stress that is prescribed on the boundary of the cylinder. The fractional calculus approach in the constitutive relationship model of a Maxwell fluid is introduced. The velocity field and the resulting shear stress are determined by means of the Laplace and finite Hankel transforms to satisfy all imposed initial and boundary conditions. The solutions corresponding to ordinary Maxwell fluids as well as those for Newtonian fluids, performing the same motion, are obtained as limiting cases of our general solutions. Finally, the influence of the relaxation time and the fractional parameter on the velocity of the fluid is analyzed by graphical illustrations.

The Constitutive Relationship of Self-Stress Concrete Filled Steel Tube

Based on the constitutive relationship model of general concrete filled steel tube, and combining with the results and theoretical analysis of several self-stress concrete filled steel tubular specimens, the constitutive relationship model of self-stress concrete filled steel tube was established by introducing an improvement coefficient of concrete strength related to self-stress level. The calculations of specimens’ bearing capacity with different sectional steel ratios, values of self-stress and concrete strengths were performed, which were in a good accordance with those of experimental values.

A Method for Initial Stress Analysis of Micro Vessel Wall

A blood vessel model of pseudo-elastic constitutive relation in an absolute (vacuum) zero-stress state is employed, and analytical equations of the vessel wall in the three-dimensional stress state are obtained in this paper. The stress distributions in circumferential and axial directions with different blood pressure levels and material parameters are discussed. The results show that the initial stresses of the vessel wall will increase with increment of the blood pressure, the material parameters also affect the distributions of initial stress, in particular, the increase of axial material parameters, will significantly increase axial stress. These methods are importance in the investigation of the vascular dynamic problem, and conclusions are of use in prevention of the related vascular diseases.

Bond-Slip Numerical Simulation of Concrete and Gypsum Board

The characteristics and research situation of bond-slip performance at the inter face of concrete and other materials are introduced, and the bond-slip constitutive relation models are summarized at the same time. Through the load-slip curves obtained from the pull-out experiment of CFFP, the proposed bond-slip constitutive relation models are presenting, including the simple one. With the numerical simulation analysis of CFFP is carried out by the use of the proposed constitutive relation, while the numerical simulation results are in good agreement with the experimental results conducted before, which is feasible and can be applied to further research on CFFP.

A full analytical solution for the force-driven compressible Poiseuille gas flow based on a nonlinear coupled constitutive relation

The compressible Poiseuille gas flow driven by a uniform force is analytically investigated using a phenomenological nonlinear coupled constitutive relation model. A new fully analytical solution in compact tangent (or hyperbolic tangent in the case of diatomic gases) functional form explains the origin behind the central temperature minimum and a heat transfer from the cold region to the hot region. The solution is not only proven to satisfy the conservation laws exactly but also well-defined for all physical conditions (the Knudsen number and a force-related dimensionless parameter). It is also shown that the non-Fourier law associated with the coupling of force and viscous shear stress in the constitutive relation is responsible for the existence of the central temperature minimum, while a kinematic constraint on viscous shear and normal stresses identified in the velocity shear flow is the main source of the nonuniform pressure distribution. In addition, the convex pressure profile with a maximum at the center is theoretically predicted for diatomic gases. Finally, the existence of the Knudsen minimum in the mass flow rate is demonstrated by developing an exact analytical formula for the average temperature of the bulk flow.

Unsteady MHD Couette flow of a generalized Oldroyd-B fluid with fractional derivative

This paper presents an analytical study for the magnetohydrodynamic (MHD) flow of a generalized Oldroyd-B fluid. The fractional calculus approach is used to establish the constitutive relationship model of a viscoelastic fluid. Exact analytic solutions for the velocity field and shear stress in terms of Fox H -function are obtained by means of the Laplace transform. The influence of the relaxation and retardation times, the orders of the time fractional derivative and the magnetic body force on the velocity and shear stress are analyzed. It is shown that the ordinary Oldroyd-B fluid, generalized second grade fluid and Maxwell fluid are the limiting cases of the presented results.

Deduction and experimental investigation of constitutive relation of liquefaction of saturated sand

According to the existing problems of liquefaction models of saturated sand that were put forward under dynamic action, on the basis of Handin-Drnevich model, a new calculating model of the dynamic constitutive relation of saturated sand was put forward. The model was based on the basic hypothesis of instantaneous limit balance according to the basic principle that the stress estate is the destroyed condition was not overstepped. The calculated method of increment nonlinear was referenced and combined with the excellence of the model of distributed particles. The process of vibrating liquefaction of saturated sand was divided into some areas. And the phenomena of shearing dilatation and unloading shrink of saturated sand were considered. On above basic a new calculating constitutive relation model was proposed. There are a few parameters in the model. The physical means of the parameters are very evident and quantized. They could be obtained from the dynamic triaxial test in door. The model was contrasted and validated with the results of the dynamic triaxial test in door. The comparison of the results of the dynamic triaxial test in door and the calculating results of the model indicates that all sorts of phenomenon appearing in the process of liquefaction of saturated sand could be more perfectly reflected by the model. Especially at the initial stage of development of pore water pressure and strain of saturated sand, the results of the dynamic triaxial test in door are consistent with the calculated results of the model very much. But there is some difference between the results at the anaphase of development of pore water pressure and strain. On the path of stress, the calculating and experimenting ultimate state surfaces are almost identical.

Modeling constitutive relationship of Ti40 alloy using artificial neural network

Constitutive relationship equation reflects the highly non-linear relationship of flow stress as function of strain, strain rate and temperature. It is a necessary mathematical model that describes basic information of materials deformation and finite element simulation. In this paper, based on the experimental data obtained from Gleeble-1500 Thermal Simulator, the constitutive relationship model for Ti40 alloy has been developed using back propagation (BP) neural network. The predicted flow stress values were compared with the experimental values. It was found that the absolute relative error between predicted and experimental data is less than 8.0%, which shows that predicted flow stress by artificial neural network (ANN) model is in good agreement with experimental results. Moreover, the ANN model could describe the whole deforming process better, indicating that the present model can provide a convenient and effective way to establish the constitutive relationship for Ti40 alloy.

Development of constitutive relationship model of Ti600 alloy using artificial neural network

Constitutive equation which reflects the highly non-linear relationship of flow stress as function of strain, strain rate and temperature is a necessary mathematical model that describes basic information of materials deformation and finite element simulation. In this paper, based on the compression experiment data obtained from Gleeble-1500 thermal simulator, the prediction model for the constitutive relationship existed between flow stress and true strain, strain rate and deformation temperature for Ti600 alloy has been developed using back-propagation (BP) neural network method. A comparative evaluation of the traditional regression method and the trained network model was carried out. It was found that the established network model can not only predict flow stress better than the traditional hyperbolic sine constitutive relationship equation but also describe the whole deforming process for Ti600 alloy. Moreover, the ANN model provides a convenient and effective way to establish the constitutive relationship for Ti600 alloy.

Exact solutions for some oscillating motions of a fractional Burgers’ fluid

This article presents some starting solutions corresponding to the oscillating flows of a Burgers’ fluid with fractional derivatives. The fractional calculus approach in the constitutive relationship model is introduced and a fractional Burgers’ model is built. The exact solutions for the oscillating motions of a fractional Burgers’ fluid due to cosine and sine oscillations of an infinite flat plate as well as those corresponding to an oscillating pressure gradient are established with the help of integral transforms (Fourier sine and Laplace transforms). In order to avoid lengthy calculations of residues and contour integrals, the discrete Laplace transform method has been used. The expressions for the velocity field and the resulting shear stress that have been obtained, presented under integral and series form in terms of the generalized G functions, satisfy all imposed initial and boundary conditions. Similar solutions for generalized Oldroyd-B, Maxwell and second grade fluids as well as those for ordinary Oldroyd-B, Maxwell, second grade and Newtonian fluids are obtained as limiting cases of our general solutions. Finally, the obtained solutions are graphically analyzed for variations of interesting flow parameters.

Exact solution for the rotational flow of a generalized second grade fluid in a circular cylinder

This paper deals with the rotational flow of a generalized second grade fluid, within a circular cylinder, due to a torsional shear stress. The fractional calculus approach in the constitutive relationship model of a second grade fluid is introduced. The velocity field and the resulting shear stress are determined by means of the Laplace and finite Hankel transforms to satisfy all imposed initial and boundary conditions. The solutions corresponding to second grade fluids as well as those for Newtonian fluids are obtained as limiting cases of our general solutions. The influence of the fractional coefficient on the velocity of the fluid is also analyzed by graphical illustrations.

ANALYSIS OF DYNAMIC STRESS-STRAIN RELATIONSHIP OF LOESS

This paper aims to study dynamic properties of loess. This study is helpful to the subject on how to avoid or decrease the seismic disasters on loess ground. Dynamic triaxial tests are carried out with saturated remoulded soil samples taken form loess sites in Xi'an, China. Dynamic stress and strain relationship as well as the rule of the accumulated residual strain are obtained from the test results. Linear relationship between accumulated residual strain and vibration circle under constant amplitude circular loading is presented. A hypothesis about the accumulated residual strain is proposed. 1D dynamic constitutive relationship model which can well describe the real relationship between dynamic stress and strain under irregular dynamic loading is established. Numerical program with this model is developed and an example is tested. Numerical results of hysteresis loop, accumulated residual strain, amplitude of dynamic stress and damping ratio show good agreement with test results. It is indicated that the hypothesis of accumulated residual strain and the 1D dynamic constitutive relationship model can accurately simulate the dynamic triaxial tests of saturated remoulded loess.

Unsteady helical flows of a generalized Oldroyd-B fluid

Helical flows for Oldroyd-B fluid are studied in concentric cylinders and a circular cylinder. The fractional calculus approach in the constitutive relationship model Oldroyd-B fluid is introduced and a generalized Jeffreys model with the fractional calculus has been built. Exact solutions of some unsteady helical flows of Oldroyd-B fluid in an annular pipe are obtained by using Hankel transform and Laplace transform for fractional calculus. For α = β = 1 , λ 1 = 0 , λ 2 = 0 or λ 1 = λ 2 = 0 they reduce to the similar solutions for a Maxwell fluid, a second grade or Newtonian fluid, respectively. Numerical results for helical flow in pipe are presented.

Exact solutions of starting flows for a fractional Burgers’ fluid between coaxial cylinders

This paper deals with the unsteady flows of a viscoelastic fluid between two infinitely long concentric circular cylinders. The fractional calculus approach in the constitutive relationship model of a Burgers’ fluid is introduced. With the help of integral transforms (the Laplace transform and the Weber transform), exact solutions are constructed for the following two problems: (i) when the outer cylinder makes a simple harmonic oscillation; and (ii) when the outer cylinder suddenly begins rotating while the inner cylinder remains stationary. Some previous and classical results can be recovered from the presented results, such as starting solutions for second grade, Maxwell, Oldroyd-B, and Burgers’ fluids.

Statistical volume element method for predicting microstructure–constitutive property relations

There is an inevitable need to establish multilength scale statistical microstructure–constitutive property relations in materials design. In this paper, we have developed a statistical volume element method to analyze, quantify, and calibrate such microstructure–constitutive property relations by statistical means. Statistical volume element simulations are adopted to predict material constitutive properties corresponding to various realizations of random microstructure configurations. A computing framework that links random configuration generators and finite element analysis has been developed. A statistical cause–effect analysis approach is proposed to study the influence of random material microstructure on material constitutive properties. Within the proposed approach, statistically significant microstructure parameters are first identified based on their linear impacts on material constitutive properties. Global sensitivity analysis is then employed to provide a more comprehensive importance ranking of these critical microstructure parameters considering both main and interaction effects. The uncertainties in material constitutive properties due to random microstructure configurations are quantified in terms of distributions, statistical moments, and correlations. The obtained probabilistic constitutive relations are used to calibrate the model parameters in a constitutive relation model following a statistical calibration process. The proposed approach is applied to examine a porous steel alloy material for demonstrative purposes.

Exact Solutions of Rayleigh‐Stokes Problem for Heated Generalized Maxwell Fluid in a Porous Half‐Space

The Rayleigh‐Stokes problem for a generalized Maxwell fluid in a porous half‐space with a heated flat plate is investigated. For the description of such a viscoelastic fluid, a fractional calculus approach in the constitutive relationship model is used. By using the Fourier sine transform and the fractional Laplace transform, exact solutions of the velocity and the temperature are obtained. Some classical results can be regarded as particular cases of our results, such as the classical solutions of the first problem of Stokes for Newtonian viscous fluids, Maxwell fluids, and Maxwell fluids in a porous half‐space.

Exact solutions of the Rayleigh–Stokes problem for a heated generalized second grade fluid in a porous half-space

The Rayleigh–Stokes problem for a generalized second grade fluid in a porous half-space with a heated flat plate is investigated. For the description of such a viscoelastic fluid, a fractional calculus approach in the constitutive relationship model is used. By using the Fourier sine transform and the fractional Laplace transform, exact solutions of the velocity and temperature fields are obtained, from which some classical results can be recovered.