双金属板拉延成形的有限元分析

双金属板拉延成形同时包含几何非线性、塑性、接触、摩擦以及双金属板中组元金属力学性能差异等多种复杂因素。组元金属之间不均匀的塑性变形是导致组元金属在拉延过程中产生缺陷的主要根源。本文基于刚塑性有限元方法，对双金属板的拉延成形过程进行了有限元分析，揭示了组元金属的等效应变分布规律和厚向应变分布规律。本文的研究方法和结论可以为工艺参数的合理选择和优化提供参考和依据。     

Finite elastic deformations of transversely isotropic circular cylindrical tubes

We consider the finite radially symmetric deformation of a circular cylindrical tube of a homogeneous transversely isotropic elastic material subject to axial stretch, radial deformation and torsion, supported by axial load, internal pressure and end moment. Two different directions of transverse isotropy are considered: the radial direction and an arbitrary direction in planes normal locally to the radial direction, the only directions for which the considered deformation is admissible in general. In the absence of body forces, formulas are obtained for the internal pressure, and the resultant axial load and torsional moment on the ends of the tube in respect of a general strain-energy function. For a specific material model of transversely isotropic elasticity, and material and geometrical parameters, numerical results are used to illustrate the dependence of the pressure, (reduced) axial load and moment on the radial stretch and a measure of the torsional deformation for a fixed value of the axial stretch.     

金属板料成形的快速有限元分析

研究了基于形变理论的金属板形成快速有限元分析的方法－反向方法,并实现了计算程序。通过实例的计算结果和实验以及增量方法进行了比较,表明此方法能够定性地分析成形工件中的变形情况。由于计算速度快、建立分析模模型简单,此方法可用于设计早期估计零件的可成形性,以及部分工艺参数对形的影响。     

Finite element modeling of tube hydroforming of polycrystalline aluminum alloy extrusions

Finite element modeling of tube hydroforming requires information about the anisotropy of the extruded aluminum tube. Unlike sheet metals, the complex geometry of extruded tubes makes it difficult, except in extrusion direction, to directly measure material properties. Therefore, polycrystalline models provide a good alternative for calculating the anisotropy of the tube in all directions and under various loading conditions. Using a rate-independent single crystal yield surface and rigid plasticity, a Taylor-type polycrystalline model was developed and implemented into ABAQUS/Explicit finite element (FE) code using VUMAT. The constitutive model was then used to calculate the crystallographic texture evolution during the hydroforming of an extruded aluminum tube. Initial crystallographic texture measured using orientation imaging microscopy (OIM) and uniaxial tensile test data obtained along the extrusion direction were input to this FEA model. In order to efficiently and practically simulate the tube hydroforming process using the polycrystalline model, sensitivity to the number of grain orientation, total simulation time, and number of finite elements were studied. Predicted results agreed very well with experimentally measured strain obtained from tube hydroforming process.     

Finite element analysis of two-temperature generalized magneto-thermoelasticity

A general finite element model is proposed to analyze transient phenomena in thermoelastic solids. Youssef model of two-temperature generalized magneto-thermoelasticity is selected for an homogenous, isotropic, conducting and elastic medium, which is subjected to thermal shock, and a magnetic field with constant intensity acts tangent to the bounding plane. The numerical solution of the nondimensional governing partial differential equations of the problem has been shown graphically.     

Finite element method for the stress analysis of isotropic cylindrical helical spring

This paper presents an efficient two nodes finite element with six degrees of freedom per node, capable to model the total behaviour of a helical spring. The formulation, which includes the shear deformation effects, is based on the assumed forces hybrid approach. The resultant forces approximation verifies exactly the resultant equilibrium equations. The developed model proves its accuracy compared with other elements. This element permits to get the distribution of different stresses along the spring and through the wire surface by only one element.     

Finite element analysis of lift build-up due to aerofoil indicial motion

In this paper the problem of impulsively started aerofoil or suden change of incidence of an aerofoil in incompressible potential flow is investigated. The essence of solution lies in the representation of a timely and spatially varying wake in a largely irrotational potential flow field. This is achieved by representing the wake through velocity potential difference, which seems to be the only way of imposing a velocity difference condition in the finite element context with velocity potentials as the basic unknowns. Superposition is employed to meet various boundary conditions, which is justified by the linearity of the problem. The finite element solutions are compared with those from singularity method.     

粘弹性大变形动力响应的有限元分析

本文基于ＴｏｔａｌＬａｇｒａｎｇｉａｎ增量叠加方法，采用Ｋｉｒｃｈｈｏｆｆ应力增量和Ｇｒｅｅｎ应变增量表示的动力虚功方程和Ｋｉｒｃｈｈｏｆｆ应力－Ｇｒｅｅｎ应变的单积分型本构关系，导出粘弹性大变形的动力变分方程。依此采用Ｎｅｗｍａｒｋ法和八节点轴对称等参数元与二十节点三维等参数元编制了轴对称及三维问题的动力响应计算程序，典型例题的计算结果表明分析符合结构的物理性质。     

Finite element implementation of boundary conditions for the pressure Poisson equation of incompressible flow

In this paper we address the problem of the implementation of boundary conditions for the derived pressure Poisson equation of incompressible flow. It is shown that the direct Galerkin finite element formulation of the pressure Poisson equation automatically satisfies the inhomogeneous Neumann boundary conditions, thus avoiding the difficulty in specifying boundary conditions for pressure. This ensures that only physically meaningful pressure boundary conditions consistent with the Navier-Stokes equations are imposed. Since second derivatives appear in this formulation, the conforming finite element method requires C¹ continuity. However, for many problems of practical interest (i.e. high Reynolds numbers) the second derivatives need not be included, thus allowing the use of more conventional C⁰ elements. Numerical results using this approach for a wall-driven contained flow within a square cavity verify the validity of the approach. Although the results were obtained for a two-dimensional problem using the p-version of the finite element method, the approach presented here is general and remains valid for the conventional h-version as well as three-dimensional problems.     

Site of ductile fracture initiation in cold forging: A finite element model

Ductile fracture occurs due to micro-void nucleation, growth and finally coalescence into micro-crack. In this study a new ductile fracture condition that based on the microscopic phenomena of void nucleation, growth and coalescence was proposed. Using this condition and combining with finite element model to predict the fracture locations in bulk metal forming, the results show that it is in close accordance with observations of some experimental specimens. However, in order to obtaining the high trustiness many experiments have to be carried out.     

Finite element technique to solve the elastic strain for Leonov fluid flow

The finite element method is used to find the elastic strain (and thus the stress) for given velocity fields of the Leonov model fluid. With a simple linearization technique and the Galerkin formulation, the quasi-linear coupled first-order hyperbolic differential equations together with a non-linear equality constraint are solved over the entire domain based on a weighted residual scheme. The proposed numerical scheme has yielded efficient and accurate convective integrations for both the planar channel and the diverging radial flows for the Leonov model fluid. Only the strain in the inflow plane is required to be prescribed as the boundary conditions. In application, it can be conveniently incorporated in an existing finite element algorithm to simulate the Leonov viscoelastic fluid flow with more complex geometry in which the velocity field is not known a priori and an iterative procedure is needed.     

Crystal plasticity finite element modelling of low cycle fatigue in fcc metals

A new dislocation-based model for low cycle fatigue in fcc metals at a length scale smaller than the feature size of the dislocation structures is presented. It uses the crystal plasticity finite element method and dislocation densities as internal variables. Equations for the dipole distance distribution, for the double cross slip mechanism and a new dislocation multiplication law are introduced, which can predict the emergence of vein and channel structures starting from a randomly perturbed dislocation distribution. The characteristics of these structures in copper and aluminium, as well as the mechanical properties, are compared with experiments. Compared with existing density-based theories, the capability to reproduce dislocation patterning is a significant step forward.     

Finite element modeling of micropolar-based phononic crystals

The performance of a Cosserat/micropolar solid as a numerical vehicle to represent dispersive media is explored. The study is conducted using the finite element method with emphasis on Hermiticity, positive definiteness, principle of virtual work and Bloch–Floquet boundary conditions. The periodic boundary conditions are given for both translational and rotational degrees of freedom and for the associated force- and couple-traction vectors. Results in terms of band structures for different material cells and mechanical parameters are provided.     

On the use of a reduced enhanced solid-shell (RESS) element for sheet forming simulations

A recently proposed reduced enhanced solid-shell (RESS) element [Alves de Sousa, R.J., Cardoso, R.P.R., Fontes Valente, R.A., Yoon, J.W., Grácio, J.J., Natal Jorge, R.M., 2005. A new one-point quadrature enhanced assumed strain (EAS) solid-shell element with multiple integration points along thickness: Part I – Geometrically Linear Applications. International Journal for Numerical Methods in Engineering 62, 952–977; Alves de Sousa, R.J., Cardoso, R.P.R., Fontes Valente, R.A., Yoon, J.W., Grácio, J.J., Natal Jorge, R.M., 2006. A new one-point quadrature enhanced assumed strain (EAS) solid-shell element with multiple integration points along thickness: Part II – Nonlinear Applications. International Journal for Numerical Methods in Engineering, 67, 160–188.] is based on the enhanced assumed strain (EAS) method with a one-point quadrature numerical integration scheme. In this work, the RESS element is applied to large-deformation elasto-plastic thin-shell applications, including contact and plastic anisotropy. One of the main advantages of the RESS is its minimum number of enhancing parameters (only one), which when associated with an in-plane reduced integration scheme, circumvents efficiently well-known locking phenomena, leading to a computationally efficient performance when compared to conventional 3D solid elements. It is also worth noting that the element accounts for an arbitrary number of integration points through thickness direction within a single element layer. This capability has proven to be efficient, for instance, for accurately describing springback phenomenon in sheet forming simulations. A physical stabilization procedure is employed in order to correct the element’s rank deficiency. A general elasto-plastic model is also incorporated for the constitutive modelling of sheet forming operations with plastic anisotropy. Several examples including contact, anisotropic plasticity and springback effects are carried out and the results are compared with experimental data.     

金属板料拉延二次成形的有限元法模拟

建立了二次拉延成形加工的有限元分析计算模型;采用一次成形-回弹计算-二次成形的连续计算过程模拟了实际加工过程;有限元计算采用动力显式计算程序MSC/DYTRAN;用主从面（master surface-slave surface)模型定义板料和模具的接触,摩擦力用库仑定律计算;利用动力松弛法对成形过程中的回弹进行了计算。模拟结果和实际零件比较,证明模型合理,自满稳定,结果可靠,具有良好的应用价值。     

板料三维成形过程的有限元数值模拟

基于有限变形理论建立了三维金属板料成形过程的刚塑性有限元数学模拟,该数学模型采用物质坐标系中的Ｕｐｄａｔｅ－Ｌａｇｒａｎｇｅ描述,等向强化假设,考虑了板料的厚向异性,对于金属板料与模具有摩擦采用近似的库仑摩擦定律以改善计算的收敛性。为简经计算采用薄膜单元,并根据此模型编制程序。     

Finite element study for conical indentation of elastoplastic micropolar material

Numerous experiments have repetitively shown that the material behavior presents effective size dependent mechanical properties at scales of microns or submicrons. In this paper, the size dependent behavior of micropolar theory under conical indentation is studied for different indentation depths and micropolar material parameters. To illustrate the effectiveness of the micropolar theory in predicting the indentation size effect (ISE), an axisymmetric finite element model has been developed for elastoplastic contact analysis of the micropolar materials based on the parametric virtual principle. It is shown that the micropolar parameters contribute to describe the characteristic of ISE at different scales, where the material length scale regulates the rate of hardness change at large indentation depth and the value of micropolar shear module restrains the upper limit of hardness at low indentation depth. The simulation results showed that the indentation loads increase as the result of increased material length scale at any indentation depth, however, the rate of increase is higher for lower indentation depth, relative to conventional continuum. The numerical results are presented for perfectly sharp and rounded tip conical indentations of magnesium oxide and compared with the experimental data for hardness coming from the open literature. It is shown that the satisfactory agreement between the experimental data and the numerical results is obtained, and the better correlation is achieved for the rounded tip indentation compared to the sharp indentation.     

Finite element modeling of tire/terrain interaction: Application to predicting soil compaction and tire mobility

Tire/terrain interaction has been an important research topic in terramechanics. For off-road vehicle design, good tire mobility and little compaction on terrain are always strongly desired. These two issues were always investigated based on empirical approaches or testing methods. Finite element modeling of tire/terrain interaction seems a good approach, but the capability of the finite element has not well demonstrated. In this paper, the fundamental formulations on modeling soil compaction and tire mobility issues are further introduced. The Drucker-Prager/Cap model implemented in ABAQUS is used to model the soil compaction. A user subroutine for finite strain hyperelasticity model is developed to model nearly incompressible rubber material for tire. In order to predict transient spatial density, large deformation finite element formulation is used to capture the configuration change, which combines with soil elastoplastic model to calculate the transient spatial density due to tire compaction on terrain. Representative simulations are provided to demonstrate how the tire/terrain interaction model can be used to predict soil compaction and tire mobility in the field of terramechanics.