Springback simulation and analysis of strong anisotropic sheet metals in U-channel bending process

The springback phenomenon of strong anisotropic sheet metals with U-channel bending as well as deep-drawing is numerically studied in detail by using Updating Lagrange FEM based on virtual work-rate principle, Kirchhoff shell element models and the Barlat-Lian planar anisotropic yield function. Simulation results are compared with a benchamark test. Very good agreement is obtained between numerical and test results. The focus of the present study is on the numerical simulation of the springback characteristics of the strong anisotropic sheet metals after unloading. The effects of the planar anisotropy coefficients and yield function exponent in the B-L yield function on the springback characteristics are discussed in detail. Some conclusions are given. The project supported by the National Natural Science Foundation of China (No. 19832020) and Provincial Natural Science Foundation of Jilin China (No.20000519)     

BEM for modal analysis of 3-D anisotropic structures

The boundary element method for the modal anlysis of free vibration for 3-D anisotropic structures using particular solutions has been developed. The complete polynomials of order two are used to construct the particular solutions for general anisotropic materials. The numerical results for 3-D free vibration analysis of an isotropic cantilever beam by the method presented is in good agreement with the results using the Ritz technique. For anisotropic materials, the numerical results calculated from the proposed method are in good agreement with the results from MSC.NASTRAN. Project supported by the National Natural Science Foundation of China (No. 19872011).     

Boundary element analysis for elastic and elastoplastic problems of 2D orthotropic media with stress concentration

Both the orthotropy and the stress concentration are common issues in modern structural engineering. This paper introduces the boundary element method (BEM) into the elastic and elastoplastic analyses for 2D orthotropic media with stress concentration. The discretized boundary element formulations are established, and the stress formulae as well as the fundamental solutions are derived in matrix notations. The numerical procedures are proposed to analyze both elastic and elastoplastic problems of 2D orthotropic media with stress concentration. To obtain more precise stress values with fewer elements, the quadratic isoparametric element formulation is adopted in the boundary discretization and numerical procedures. Numerical examples show that there are significant stress concentrations and different elastoplastic behaviors in some orthotropic media, and some of the computational results are compared with other solutions. Good agreements are also observed, which demonstrates the efficiency and reliability of the present BEM in the stress concentration analysis for orthotropic media. The project supported by the Basic Research Foundation of Tsinghua University, the National Foundation for Excellent Doctoral Thesis (200025) and the National Natural Science Foundation of China (19902007). The English text was polished by Keren Wang.     

Effect of dentin tubules on the mechanical properties of dentin Part III: Numerical analysis

Imitating a real tooth and the periodontal supporting tissues, we have established a 2D finite element model and carried out a numerical analysis based on the inhomogeneous and anisotropic (IA) stress-strain relation and strength model of dentin proposed in the preceding Parts I and II, and the conventional homogeneous and isotropic (HI) model, respectively. Quite a few cases of loadings for a non-defected and a defected tooth are considered. The numerical results show that the stress level predicted by the IA model is remarkably higher than that by the HI model, revealing that the effect of the dentin tubules should be taken into a serious consideration from the viewpoint of biomechanics. The project supported by the National Natural Science Foundation of China (19525207, 19891180) and the Tsinghua University Fundamental Research Foundation (Jc1999033)     

Analytical derivation of earing in circular cup drawing based on simple tension properties

In the circular cylindrical cup drawing process of sheet materials, an earing profile develops, incurred by the planar anisotropic properties of sheets. Therefore, proper analysis of earing in cup drawing is important to evaluate anisotropic properties and also to control the development of earing. Even though anisotropic properties are commonly measured in the simple tension test, deformation in circular cylindrical cup drawing is in a near plane strain mode (at the flange) so that numerical simulations utilizing yield functions are common practices to analyze earing. In this work, simplified analytical derivation of earing development in circular cylindrical cup drawing is proposed, based on two simple tension anisotropic properties: the yield stress and the r-value. Good performance of the analytical derivation was verified for AA2090-T3, which has strong anisotropy and six ears in cup drawing. Since the current approach directly utilizes measured simple tension data without involving any yield functions, computational cost is significantly lower. Besides, the current derivation can handle any set of detailed anisotropic measurements in the simple tension test, unlike numerical approaches involving yield functions, which need the development of sophisticated yield functions in the first place.     

Analysis of interlaminar stress and nonlinear dynamic response for composite laminated plates with interfacial damage

By considering the effect of interfacial damage and using the variation principle, three-dimensional nonlinear dynamic governing equations of the laminated plates with interfacial damage are derived based on the general sixdegrees-of-freedom plate theory towards the accurate stress analysis. The solutions of interlaminar stress and nonlinear dynamic response for a simply supported laminated plate with interfacial damage are obtained by using the finite difference method, and the results are validated by comparison with the solution of nonlinear finite element method. In numerical calculations, the effects of interfacial damage on the stress in the interface and the nonlinear dynamic response of laminated plates are discussed.     

A weighted penalty finite element method for the analysis of power-law fluid flow problems

In this paper, a new finite element method for the flow analysis of the viscous incompressible power-law fluid is proposed by the use of penalty-hybrid/mixed finite element formulation and by the introduction of an alternative perturbation, which is weighted by viscosity, of the continuity equation. A numerical example is presented to exhibit the efficiency of the method.The Project Supported by the National Natural Science Foundation of China.     

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     

Dynamic stress concentration around a circular hole due to SH-wave in anisotropic media

A new approach based on complex function to solve the SH-wave scattering problem around a circular hole in anisotropic media is introduced in this paper. It is found that the dynamic stress concentration factor is dependent on the incident wave number and the hole radius. Finally, some numerical results of dynamic stress concentration factor of a circular hole in anisotropic media are given. The Project Supported by National Natural Science Foundation of China     

The scattered energy around a circular hole by SH wave in anisotropic media

A new approach based on complex function for solving the SH-wave scattering problem around a circular hole in an anisotropic media is desribed in this paper. It is found that the scattered energy depends on the incident wave number and the hole radius. Finally, some numerical results of scattered energy of a circular hole in an anisotropic media are given.The project has been supported by National Natural Science Foundation of China.     

Calculation for path-domain independentJ integral with elasto-viscoplastic consistent tangent operator concept-based boundary element methods

This paper presents an elasto-viscoplastic consistent tangent operator (CTO) based boundary element formulation, and application for calculation of path-domain independentJ integrals (extension of the classicalJ integrals) in nonlinear crack analysis. When viscoplastic deformation happens, the effective stresses around the crack tip in the nonlinear region is allowed to exceed the loading surface, and the pure plastic theory is not suitable for this situation. The concept of consistency employed in the solution of increment viscoplastic problem, plays a crucial role in preserving the quadratic rate asymptotic convergence of iteractive schemes based on Newton's method. Therefore, this paper investigates the viscoplastic crack problem, and presents an implicit viscoplastic algorithm using the CTO concept in a boundary element framework for path-domain independentJ integrals. Applications are presented with two numerical examples for viscoplastic crack problems andJ integrals. The project supported by National Natural Science Foundation of China (9713008) and Zhejiang Natural Science Foundation Special Funds No. RC.9601     

Finite element modeling of consolidation of composite laminates

Advanced fiber reinforced polymer composites have been increasingly applied to various structural components. One of the important processes to fabricate high performance laminated composites is an autoclave assisted prepreg lay-up. Since the quality of laminated composites is largely affected by the cure cycle, selection of an appropriate cure cycle for each application is important and must be optimized. Thus, some fundamental model of the consolidation and cure processes is necessary for selecting suitable parameters for a specific application. This article is concerned with the ``flow-compaction' model during the autoclave processing of composite materials. By using a weighted residual method, two-dimensional finite element formulation for the consolidation process of thick thermosetting composites is presented and the corresponding finite element code is developed. Numerical examples, including comparison of the present numerical results with one-dimensional and two-dimensional analytical solutions, are given to illustrate the accuracy and effectiveness of the proposed finite element formulation. In addition, a consolidation simulation of AS4/3501-6 graphite/epoxy laminate is carried out and compared with the experimental results available in the literature. The project supported by the National Natural Science Foundation of China (10272037) The English text was polished by Yunming Chen.     

The completeness and a new derivation of the Stroh formalism of anisotropic linear elasticity

In this paper we present a new, simpler and unified derivation of the Stroh formalism of anisotropic linear elasticity, for both nondegenerate and degenerate cases. It is based on the potential representation and Jordan canonical representation theorems. The completeness of the Stroh formalism is proved in the derivation process itself. This new approach is also extended to piezoelastic problems. Besides, we show that the eigenvalues of the fundamental elastic matrix in planar anisotropic elasticity are always distinct, except for the case of isotropy. The project supported by the National Natural Science Foundation of China (19525207 and 19891180).     

Deformation localization and shear band fracture in strong anisotropy sheet tension

The tensile deformation localization and the shear band fracture behaviors of sheet metals with strong anisotropy are numerically simulated by using Updating Lagrange finite element method, Quasi-flow plastic constitutive theory^[1] and B-L planar anisotropy yield criterion^[2]. Simulated results are compared with experimental ones. Very good consistence is obtained between numerical and experimental results. The relationship between the anisotropy coefficientR and the shear band angle θ is found. The project supported by the National Natural Science Foundation of China and the Excellent Youth Teacher Foundation of the State Education Commission of China     

Effect of microstructure on the hardening and softening behaviors of polycrystalline shape memory alloys Part II: Numerical simulation under axisymmetrical loading

Based on the microstructure-based constitutive model established in Part I, a detailed numerical investigation on the role of each microstructure parameter in the kinematical and kinetic evolution of polycrystalline SMA under axisymmetrical tension loading is performed. Some macroscopic constitutive features of stress-induced martensite transformation are discussed. The subject supported by the Research Grant Committee (RGC) of Hong Kong SAR, the National Natural Science Foundation of China and the Provincial Natural Science Foundation of Jiangxi Province of China     

Magnetoelastic bending and stability of current-carrdying coil structures

As a results of magnetoelastic interaction, the mechanical behavior of current-carrying coil structures, such as deformation and instability, is a key problem in the design of strong field magnets. In this paper, a nonlinear mathematical model is presented to described the deformation and buckling of D-type current-carrying coil, based on the Biot-Savart law and the bending theory of curved beams. The bending deformation, the critical value of current for the magnetoelastic buckling of the current-carrying coil, and the effect of the type and number of supports at middle part of the bendling coil on the critical value are quantitatively investigated by a semi-analytical and semi-numerical method. The numerical results are shown to be in good agreement with the experimental data. The project supported by the National Natural Science Foundation of China, the Science Foundation of the State Education Committee of China for Outstanding Teacher in Universities, and the Natural Science Foundation of Gansu Province of China     

A new hybrid stress element method for the analysis of elastoplastic solids

Based on a modified Hellinger/Reissner variational principle which includes the equivalent stress, equivalent plastic strain and non-conforming displacement increments as independent variables, a quadrilateral isoparametric hybrid stress element for the analysis of elastoplastic problem is proposed. By this formulation, the yield criterion and flow rule are satisfied in an average sense and greater accuracy can be obtained by using non-conforming displacement. A numerical example is presented to show that the present model has high accuracy and computational effectiveness.This project is supported by the Natural Science Foundation of the State Education Commission.     

Triangular grid method for stress-wave propagation in 2-D orthotropic materials

A triangular grid method is presented to calculate propagation problems of elastic stress waves in 2-D orthotropic materials. This method is based on the dynamic equilibrium equations of the computational cells formed among the auxiliary triangular grids. The solution is obtained by calculating alternately the nodal displacements and the central point stresses of the spatial grids. The numerical results are compared with the corresponding solutions of the finite element method. Comparisons show that the triangular grid method yields a higher calculational speed than the finite element method. The stress concentrations are investigated from wave-field analyses when the stress wave propagates within an orthotropic plate with a hole. Finally, the presented numerical method is used to study the features of wave propagation and diffraction in a square orthotropic plate with a hole when an impact load is applied to the top of the plate.This work was supported by National Natural Science Foundation of China (Nos. 10025212 and 10232040) and Natural Science Foundation of Liaoning province (No. 20021070).     

P-version hybrid analytical finite element method for plate bending problems

Two sets of trial functions with different variables are constructed for the admissible space of the finite element analysis. The trial functions satisfy the equilibrium differential equation inside elements, while the deflections and rotations on the edges of the elements are approximated by the Peano hierarchical interpolation functions. Then, a generalized variational principle is applied to set up the p-version hybrid analytical finite element method for plate bending problems. The accuracy of finite element computation can be improved by increasing the order of the interpolation polynomials with fixed mesh. In the finite element formulation, to obtain the stiffness matrices and the load vectors, it is only necessary to perform quadrature over the edges of the elements. These matrices and vectors possess an embedding structure. The conformability between the elements can be controlled automatically.This work is supported by the Natural Science Foundation of China and the Aeronautical Science Foundation of China.     

Bueckner's work conjugate integrals and weight functions for a crack in anisotropic solids

The Bueckner work conjugate integrals are studied for cracks in anisotropic elastic solids. The difficulties in separating Lekhnitskii's two complex arguments involved in the integrals are overcome and explicit functional representations of the integrals are given for several typical cases. It is found that the pseudoorthogonal property of the eigenfunction expansion forms presented previously for isotropic cases, isotropic bimaterials, and orthotropic cases, are proved to be also valid in the present case of anisotropic material. Finally, Some useful path-independent integrals and weight functions are proposed. The project supported by the National Natural Science Foundation of China (19891180) and Doctorate Foundation of Xi'an Jiaotong University