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2011 Vol. 32, No. 3
Published:
论文
217
A rate-dependent constitutive model for aluminum foams and its application to the energy absorption of lightweight sandwich panels with aluminum foam cores
Aluminum foam sandwiches with the excellent mechanical and physical properties as lightweight, high specific stiffness and strength, vibration damping and energy absorption, have been wildly applied in the energy absorption device under impact. In this paper, a transverse isotropic rate-dependent constitutive model for aluminum foam has been developed to capture the feature of strain rate sensitivity. Numerical algorithm for computing the rate-dependent constitutive model in finite element method is presented and coded into the commercial software package ABAQUS/Explicit through the user subroutine interface VUMAT. The numerical stability and reliability of the code are verified using a single element model. The implemented model is then used to study the energy absorption capacity of aluminum foam core sandwich panels subject to impact loading. The effect of strain rate of the foam core is explored. Obtained results show that the energy capacity of the foam core increases and the deformation of bottom panel decreases with the increase of rate sensitivity parameters.
2011 Vol. 32 (3): 217-227 [
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1388
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228
RELATIONSHIP BETWEEN POLYAXIAL STRENGTH AND CONVENTIONAL TRIAXIAL STRENGTH FOR ROCK
In the anisotropic stress condition, the existence of the intermediate principle stress effect on the strength of rock has been verified by a large number of true triaxial tests of rock. Based on analysis of the true triaxial test data of four rock types and the polyaxial strength criterions, the relationship between the polyaxial strength and conventional triaxial strength of rock at the same intermediate principle stress coefficient was studied in this paper. The results indicated that the same function type of the polyaxial strength curves with the conventional triaxial strength curves could be obtained at the same intermediate principle stress coefficient. For the rock types of which the strength features can be described by the Mohr-Coulomb criterion, the influence on the cohesion action of the polyaxial strength of rock is remarkable. The cohesion action will increase firstly and then decrease with the growth of the intermediate principle stress coefficient which hardly influences the friction action of rock strength. The strength effect of different rock types is controlled by the corresponding angle of internal friction. The larger the internal friction angle is, the stronger this effect is. The results also indicated that the strength parameters obtained by the conventional triaxial tests can be directly applied in the polyaxial strength criterion after the intermediate principle stress effect function has been obtained. It will be of the important value for the application of polyaxial strength criterions in the stability analysis of rock engineerings lacking true triaxial test data.
2011 Vol. 32 (3): 228-234 [
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1318
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235
The model of VHCF crack propagation for high strength steel
When fatigue life is beyond 106, the Wöhler S-N curve was always considered to be asymptotic in horizontal axis, but the fatigue behaviour over 106 cycles can not be neglected. Carburized process hardens surface of structure parts in order to improve wear and fatigue resistance. A piezoelectric gigacycle fatigue machine is employed to the tests in VHCF regime with 20KHz frequency and at stress ratio R=0.1, room temperature. The effects of heat and Carburized treatment on VHCF fatigue strength are investigated by test method. The infrared camera is applied to study the energy dissipation during the tests after calibration by blackbody. The cycle of crack initiation can be determined by the temperature increasing within several cycles near end of test. Through Scanning Electron Microscopy (SEM) analysis, the mainly parameters have been obtained to model the crack propagation (CP) based on Paris law, which permits estimating energy dissipation whose power and position are variable with crack propagation. The temperature distribution and evolution of specimen surface can be calculated by the numerical method FEM. The comparison of test and simulation results shows that the model is good agreement with test in the period of crack propagation.
2011 Vol. 32 (3): 235-241 [
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1297
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242
An Inverse Technique for Identification of Dynamic Constitutive Damage Parameters of Brittle Material
The computational inverse technique is proposed for determination of dynamic constitutive model damage parameters of brittle ceramic using the ceramic/window interface velocity profile response under plate impact. The shock wave translating in fly-plate, sample and window is represented by simulation. The relationship of the interface velocity profile response and constitutive parameters is studied. Examples are presented to demonstrate this inverse technique for characterizing the material property from response is very robust. Using the GA and the interface velocity profile response inversely determines constitutive model parameters. This method obtains the need parameters under high strain rates rapidly, which determined difficultly and expensively by traditional method.
2011 Vol. 32 (3): 242-248 [
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1165
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249
A Modified Wavelet-Galerkin Method for Computations in Structural Mechanics with Strong Nonlinearity
To avoid the undesired jump or wiggle phenomenon near the boundary points when the wavelet-based method is employed to solve a boundary-value problem, this paper presents a set of modified scaling base functions through the interval extension of an unknown continuous function defined in a finite interval on the basis of the Taylor series expansion associated with the arbitrary boundary conditions. After that, an approximate scheme of the function is proposed by the modified scaling base functions. According to the generalized-Gaussian-quadrature method in wavelet analysis, which was developed by the last two authors of this paper, the expansion constants in the approximation of arbitrary nonlinear term of the unknown function can be explicitly expressed in finite terms of the expansion ones of the approximation of the unknown function. Once the wavelet-Galerkin method on the basis of the approximation is employed to solve the nonlinear differential equation with the nonlinear term(s) of a finite beam structure with arbitrary boundary conditions, it is found that the solution has the closure property and the virtue of easy implement in calculation of solving a strong nonlinear problem. The numerical results obtained in solving two cases of large deflected beams with different nonlinear characterization, i.e., either integer order or non-integer order nonlinear terms or both, indicate that this approach has high accuracy.
2011 Vol. 32 (3): 249-257 [
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661
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258
Free vibration analysis of rotating composite thin-walled closed-section beams with SMA fibers
The free vibration model of a rotating composite thin-walled closed-section beams with SMA fiber actuation is presented in this paper. The structural modeling is split into two parts: a two-dimensional analysis over the cross section, and a linear analysis of a beam along the beam span. The two-dimensional cross-sectional analysis is based on the force- deformation relationships equations, accounting for the presence of active SMA fibers distributed along the cross-section of the beam. Hamilton’s principle is employed to derive the equations of motion and associated boundary conditions of the beams. The model includes anisotropy, pitch and precone angle. The Galerkin method is employed in order to solve the coupled differential equations. Numerical results are obtained for two cantilevered box beam: Circumferentially Uniform Stiffness(CUS) and Circumferentially Antisymmetric Stiffness (CAS), the effects of the volume fraction of the SMA fiber, the martensitic residual strain, the fiber orientation, pitch and precone on the natural frequencies associated with coupled vibration modes are investigated.
2011 Vol. 32 (3): 258-276 [
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710
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简报
277
Study of Rising Fracture Toughness of Human Dentin with the Cohesive Zone Modeling
Objective To study the fracture toughness of human dentin for crack propagation along and perpendicular to the tubular orientation, respectively and identify the anisotropic cracking resistance curve of human dentin. Methods Cohesive zone model and finite element analysis were adopted to study the fracture behavior of human dentin. Results The results show that the fracture toughness of human dentin increase with crack propagation in a certain range, i.e., human dentin exhibits rising crack growth resistance curve. However, the fracture toughness for cracking along the tubular direction is higher than that in its orthogonal direction. Conclusion Human dentin exhibits anisotropic crack resistance behavior. This study indicates that the results based on cohesive zone modeling agree reasonably well with reported experimental results.
2011 Vol. 32 (3): 277-281 [
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1277
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344
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282
An approximate solution for the effective elastic moduli of differential method
Ehelby tensor in view of the entire differential method of ‘extraction- accession’ during the process of change in modulus variation is less. Then, an approximate explicit expression of the differential method is established. The simple form of approximate solution is facilitating to calculation. The expression can be fit for sphere and stochastic short fiber. Its result approximates to the experimental result. It can have a better application in the practical engineering.
2011 Vol. 32 (3): 282-286 [
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642
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287
STUDY ON THE EFFECTIVE ANTI-PLANE SHEAR MODULUS OF NANO INHOMOGENEITY COMPOSITE MATERIALS
Based on the theory of Gurtin-Murdoch surface/interface model, a rigorous whole-field solution is obtained for the inhomogeneity/matrix/equivalent medium model, in terms of which a generalized self-consistent approach is developed for predicting the effective anti-plane shear modulus of nano composites. Closed-form solution of the effective anti-plane shear modulus was presented. The numerical results reveal that the effective anti-plane shear modulus is size dependent when the size of the inhomogeneity is on the order of nanometer. With the increase of the size of the inhomogeneity, the present solution approaches to the classical results obtained in the linear elasticity theory. In comparison to the effective bulk modulus and shear modulus (isotropic materials), the present effective anti-plane shear modulus of the nano composites is influenced by the size of the inhomogeneity at a smaller range. The interface property and the stiffness of the inhomogeneity play an important role in the effective anti-plane shear modulus of the nano composites.
2011 Vol. 32 (3): 287-292 [
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1197
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293
A constitutive law of cement-based material at large range of confining pressure state
The triaxial compression test and hydrostatic compression test have been performed at first. Based on the experimental data, different mechanism of cement paste has been analyzed. According to thermodynamics theory, a new constitutive law is established and the damage criterion, two plastic mechanisms have been taken into account. This modelling considers also the influence of confining pressure. Numerical simulation shows that this constitutive law for cement-based materials can well explicit the main mechanical behavior at a large range of confining pressure state.
2011 Vol. 32 (3): 293-298 [
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1286
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299
Homogenization Method for Dynamic Problems Based on Continuous Size Field
Abstract: A new topological optimization method of continuum structure for dynamic problems is presented based on con-tinuous size field. Based on homogenization theory, hexagonal microstructure with isotropic behavior is adopted as descrip-tion of the macroscopic material. The proper character of the microcosmic cell is numerically validated to avoid localized modes. The size of the hexagonal cell for the material point instead of element or node is accepted as design variables. Con-tinuity of design variables field is ensured by interpolation of the modified filtering interpolation functions. Checkerboard patterns that are a concern in most topological optimization methods are avoided naturally. Sensitivities of global stiffness matrix, global mass matrix and so on are derived according to calculation method for partial derivative of compound function. Topological optimization models are established where dynamic structural responses are taken as objective and prescribed volume fraction is referred to as constraint conditions. Numerical examples show that the proposed method is feasible and robust in dynamic topological optimization design of continuum structure.
2011 Vol. 32 (3): 299-305 [
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647
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305
A quick method for solving responses of axisymmetric structures subjected to loads of rotational similarity: rotation-superposition method and its application
Based on the principle of superposition, a quick method, rotation-superposition method, for solving responses of axisymmetric structures subjected to loads of rotational similarity is built by coordinate rotation and linear superposition. This paper firstly defines the loads of rotational similarity and derives the calculation formulas. Then an application example is given to prove the validity and efficiency of this method, and relating problems are discussed in the end. The rotation-superposition method ingeniously utilizes the principle of superposition and the axisymmtry of structures. For one structure, only one analysis is necessary, and then the responses under various load conditions can be obtained by brief arithmetical calculations. This method provides a high-efficiency approach for relating multi-case analyses.
2011 Vol. 32 (3): 305-312 [
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600
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319
Application of SPH-FEM Contact Algorithm in Impact Dynamics Simulation
Coupling of smoothed particle hydrodynamics (SPH) and finite element method (FEM) can make full use of the superiority of SPH in dealing with large deformation and the high accuracy and efficiency of FEM. This paper calculates the contact between SPH particles and finite elements using meshless particle contact method, and background particles are assigned in the position of FE nodes. The oblique impact between spheral-nosed projectile and steel target and the normal impact between blunt-nosed projectile and steel target are calculated using the SPH-FEM contact algorithm. The fully variable smoothing lengths algorithm is used in SPH and the EBE algorithm is used in FEM. The numerical results of LS-DYNA and the experimental observations validate the accuracy of the SPH-FEM contact algorithm.
2011 Vol. 32 (3): 319-324 [
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773
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