Unsteady Rotating Flows of a Viscoelastic Fluid with the Fractional Maxwell Model Between Coaxial Cylinders

The fractional calculus is used in the constitutive relationship model of viscoelastic fluid. A generalized Maxwell model with fractional calculus is considered. Based on the flow conditions described, two flow cases are solved and the exact solutions are obtained by using the Weber transform and the Laplace transform for fractional calculus.The project supported by the National Natural Science Foundation of China (10272067, 10426024), the Doctoral Program Foundation of the Education Ministry of China (20030422046) and the Natural Science Foundation of Shandong University at Weihai. The English text was polished by Keren Wang.     

General irreducible representations for constitutive equations of elastic crystals and transversely isotropic elastic solids

By means of the combined invariance restrictions due to material frame-indifference and material symmetry, the present paper provides general reduced forms for non-polynomial elastic constitutive equations of all 32 classes of crystals and transversely isotropic solids.Project supported by National Natural Science Foundation and National Postdoctoral Science Foundation of China.     

Constitutive relation of weakly anisotropic polycrystal with microstructure and initial stress

Man (Nondestr Test Eval 15:191–214, 1999) derived the constitutive relation of a weakly-textured orthorhombic aggregate of cubic crystallites with effects of microstructure and initial stress. In this paper, a computational expression on the integration is given. Then, by means of the computational expression, the general constitutive relation of a weakly-textured anisotropic polycrystal with the consideration of microstructure and initial stress is derived. As special cases of our general constitutive relation, two constitutive relations are given for an isotropic polycrystal and a weakly-textured anisotropic aggregate of cubic crystallites. The acoustoelastic tensor of the reference cubic crystal is derived to determine the material constants of the polycrystal. Two examples are given for understanding the physical meaning of the texture coefficients and the constitutive relations. The project supported by the National Natural Science Foundation of China (10562004, 10662004), the Natural Science Foundation of Jiangxi of China (0512021), the Science Foundation of Jiangxi Educational Department of China([2006]3), and the Foundation of Training Academic and Technical Header for Main Majors of Jiangxi of China.     

Stokes＇ first problem for a viscoelastic fluid with the generalized Oldroyd-B model

The flow near a wall suddenly set in motion for a viscoelastic fluid with the generalized Oldroyd-B model is studied. The fractional calculus approach is used in the constitutive relationship of fluid model. Exact analytical solutions of velocity and stress are obtained by using the discrete Laplace transform of the sequential fractional derivative and the Fox H-function. The obtained results indicate that some well known solutions for the Newtonian fluid, the generalized second grade fluid as well as the ordinary Oldroyd-B fluid, as limiting cases, are included in our solutions. The project supported by the National Natural Science Foundation of China (10272067), the Doctoral Program Foundation of the Education Ministry of China (20030422046), the Natural Science Foundation of Shandong Province, China (Y2006A14) and the Research Foundation of Shandong University at Weihai. The English text was polished by Keren Wang.     

A quasi-flow constitutive model with strain-rate dependence

In this paper, the proposed is a quasi-flow constitutive model with strain-rate sensitivity for elastic plastic large deformation. The model is based on the Quasi-flow Corner theory, and is suitable for the sheet metal forming process simulation with a variable punch machine velocity. Uniaxial tensile tests and deep-drawing tests of a circular blank with square punch are carried out and numerically simulated. The consistency between the experimental and the numerically simulated results shows the validity of the present new constitutive model. The project supported by the Scientific Foundation of National Outstanding Youth of China (10125208), the National Natural Science Foundation of China (19832020), and the National Education Committee of China     

Stress-strain field near the notch tip of a rubber sheet

Analized in this paper is the elastostatic field near a notch tip in a rubber-like thin sheet. The asymptotic equations for the notch tip field are derived based on the constitutive relation given by Ref. [1]. Near field solutions are obtained in regions that decreases and increases in size as the notch tip is approached. Their singular character depends on the constitutive parameters as well as the angle of notch that is evaluated numerically. The project supported by the National Natural Science Foundation of China     

Poincaré-cartan integral invariants of Birkhoffian systems

Based on modern differential geometry, the symplectic structure of a Birkhoffian system which is an extension of conservative and nonconservative systems is analyzed. An integral invariant of Poincaré-Cartan’s type is constructed for Birkhoffian systems. Finally, one-dimensional damped vibration is taken as an illustrative example and an integral invariant of Poincaré’s type is found.     

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. This research was funded by the National Natural Science Foundation of China (No. 59739180) and the Foundation of National Key Laboratory of Coastal and Offshore Engineering of Dalian University of Technology (No. 9701).     

A constitutive equation of elastic-visco-plasticity for polymers

The rheological behavior and a constitutive relationship of elastic-visco-plasticity for polymers are investigated in this paper. Several sets of experiments have been carried out to determine the material constants and to test the validity of constitutive formulation. It is shown that the theoretical profiles are in good agreement with experimental results. The rheological characteristic and the strain-rate effect of model are analyzed by computer simulation.The project is supported by the National Natural Science Foundation of China     

Constitutive relation of discontinuous reinforced metal-matrix composites

A micromechanical model is developed to simulate the mechanical behaviors of discontinuous reinforced composites. The analysis for a representative unit cell is based on the assumption of a periodic array of aligned reinforcements. The minimum energy principle is used to determine the unknown coefficients of the displacement field of the unit cell. The constitutive behavior of composites is studied to obtain the relationship between the main variables of matrix and reinforcements. It is concluded that the flow strength of composites is strongly influenced by volume fraction, aspect ratio of reinforcement, and the strain hardening exponent of matrix. An analytical constitutive relation of composites is obtained. The predicted results are in agreement with the existing experimental and numerical results. The project supported by the National Natural Science Foundation of China (19704100) and National Science Foundation of Chinese Academy of Sciences (KJ951-1-20)     

Rheology of semiconcentrated fibre suspension in the Oldroyd-B fluid

The constitutive equation for a semiconcentrated fibre suspension in the Oldroyd-B fluid has been derived from a statistical model of such a suspension by employing the molecular theory for polymeric liquids. To circumvent theoretical difficulties in viscoelastic fluid mechanics, several simplified models are used to account for the interactions of fibres and polymer molecules. Some of material functions are calculated in terms of the constitutive equation. The project Supported by the University of Melbourne of Australia, the National Natural Science Foundation of China and Zhejiang Province     

Constitutive relations of damaged viscoelastic materials including chemical reaction

Chemical reactions and damage are important in the study of constitutive laws for some engineering materials, such as polymers and their composites. In this paper, we have derived a general form of constitutive laws for damaged viscoelastic materials including chemical reactions by the use of irreversible thermodynamics and the Hamilton principle. The experimental results have been obtained for ageing solid propellant materials and compared with the theoretical model. Good agreement is found between the theory and experiments.The project supported by National Natural Science Foundation of China.     

Mechanical model of multi-crack rockmass and its engineering application

On the basis of Betti's theorem, the constitutive relation of multicrack rockmass which considers the effect of crack-closure is developed in this paper. Meanwhile, based on mathematical elasticity, the paper gives an analytical formula for the compression transmitting coefficient and the shearing transmitting coefficient. A damage evolution equation of rock-mass is presented and an engineering application is given as well. The project supported by the National Natural Science Foundation of China (59493600 and 59939190)     

A finite element model for numerical simulation of thermo-mechanical frictional contact problems

Two kinds of variational principles for numerical simulation of heat transfer and contact analysis are respectively presented. A finite element model for numerical simulation of the thermal contact problems is developed with a pressure dependent heat transfer constitutive model across the contact surface. The numerical algorithm for the finite element analysis of the thermomechanical contact problems is thus developed. Numerical examples are computed and the results demonstrate the validity of the model and algorithm developed. The project supported by the National Key Basic Research Special Foundation (G1999032805), the National Natural Science Foundation of China (50178016, 10225212) and the Foundation for University Key Teacher by the Ministry of Education of China     

Elastic-plastic constitutive relation of particle reinforced composites

In this paper, a systematic approach is proposed to obtain the macroscopic elastic-plastic constitutive relation of particle reinforced composites (PRC). The strain energy density of PRC is analyzed based on the cell model, and the analytical formula for the macro-constitutive relation of PRC is obtained. The strength effects of volume fraction of the particle and the strain hardening exponent of matrix material on the macro-constitutive relation are investigated, the relation curve of strain versus stress of PRC is calculated in detail. The present results are consistent with the results given in the existing references. The project supported by the National Natural Science Foundation of China (No. 19704100) and National Science Foundation of Chinese Academy of Sciences (Project KJ951-1-20).     

Integral constitutive equations of elastic-plastic materials

In this paper the integral constitutive equations of elastic-plastic materials are studied. The endochronic theory can be deduced from this theory. It is shown that the endochronic should be selected compatible with the yield function of the calssical plasticity and this can be considered as a principle of selecting endochronic. Applying this principle the appropriate endochronics of the plastically compressible materials and the orthotropic materials are derived. The second approximate theory of the integral constitutive equation is also discussed in this paper.This paper was reported by the National Natural Science Foundation of China.     

A constitutive model and elastoplastic analysis of structures under cyclic loading

A constitutive model for cyclic plasticity is briefly outlined. Then the model is implemented in a finite element code to predict the response of cyclic loaded structural components such as a double-edge-notched plate, a grove bar and a nozzle in spherical shell. Comparision with results from other theories and experiments shows that the results obtained by using the present model are very satisfactory.The Project Supported by National Natural Science Foundation of China.     

A micromechanics constitutive model for pure dilatant martensitic transformation of ZrO2-containing ceramics

A new micromechanics constitutive model for pure dilatant transformation plasticity of structure ceramics is proposed in this paper. Based on the thermodynamics, micromechanics and microscalet→m transformation mechanism analysis of the TZP and PSZ ZrO₂-containing ceramics, an analytic expressions of the Helmholtz and complementary free energy of the constitutive element for the case of pure dilatant transformation is derived for the first time in a self-consistent manner. By the analysis of energy dissipation in the forward and reverse transformations, the micromechanics constitutive law is derived in the framework of Hill-Rice's internal variable constitutive theory. The project is supported by the National Natural Science Foundation of China.     

Plane surface suddenly set in motion in a viscoelastic fluid with fractional Maxwell model

The fractional calculus approach in the constitutive relationship model of viscoelastic fluid is introduced. The flow near a wall suddenly set in motion is studied for a non-Newtonian viscoelastic fluid with the fractional Maxwell model. Exact solutions of velocity and stress are obtained by using the discrete inverse Laplace transform of the sequential fractional derivatives. It is found that the effect of the fractional orders in the constitutive relationship on the flow field is significant. The results show that for small times there are appreciable viscoelastic effects on the shear stress at the plate, for large times the viscoelastic effects become weak. The project supported by the National Natural Science Foundation of China (10002003), Foundation for University Key Teacher by the Ministry of Education, Research Fund for the Doctoral Program of Higher Education