三维Cosserat连续体模型与微结构尺寸相关效应的有限元分析

分析了三维Cosserat连续体理论中的应力应变特征,推导了三维Cosserat连续体的有限元方程,基于ABAQUS计算软件提供的用户单元子程序(UEL)接口编写了弹性Cosserat连续体三维20节点有限元程序,并分析了微悬臂梁自由端的挠度问题和微杆扭转问题。通过与基于经典连续体理论的解析解及有限元数值计算结果进行比较,表明所发展的三维Cosserat连续体有限元能有效地模拟微结构尺寸相关效应问题,即随着微结构尺寸与材料内部长度参数的接近,基于Cosserat连续体有限元分析得到的微梁的挠度以及微杆的转角与经典连续体的解析解及有限元解相比越来越小;反之,Cosserat连续体有限元的计算结果与经典连续体的解析解及有限元数值解较为一致。     

Recursive super-convergence computation for multi-dimensional problems via one-dimensional element energy projection technique

This paper presents a strategy for computation of super-convergent solutions of multi-dimensional problems in the finite element method (FEM) by recursive application of the one-dimensional (1D) element energy projection (EEP) technique. The main idea is to conceptually treat multi-dimensional problems as generalized 1D problems, based on which the concepts of generalized 1D FEM and its consequent EEP formulae have been developed in a unified manner. Equipped with these concepts, multi-dimensional problems can be recursively discretized in one dimension at each step, until a fully discretized standard finite element (FE) model is reached. This conceptual dimension-by-dimension (D-by-D) discretization procedure is entirely equivalent to a full FE discretization. As a reverse D-by-D recovery procedure, by using the unified EEP formulae together with proper extraction of the generalized nodal solutions, super-convergent displacements and first derivatives for two-dimensional (2D) and three-dimensional (3D) problems can be obtained over the domain. Numerical examples of 3D Poisson’s equation and elasticity problem are given to verify the feasibility and effectiveness of the proposed strategy.     

三维编织复合材料渐进损伤的非线性数值分析

基于考虑纤维束相互挤压的八边形纤维束截面单胞模型,引入周期性位移边界条件,采用 细观非线性有限元方法,建立了三维四向编织复合材料的渐进损伤拉伸强度模型. 该模型考 虑了增强体纤维束纵向非线性剪切应力-应变关系,采用Hashin型损伤失效准则定义了纤维 束的典型损伤类型,并根据纤维束和纯基体相应损伤类型所造成的材料性能退化,模拟了不 同编织角试件各类损伤产生、扩展及材料最终破坏的整个过程. 模型数值结果与实验数据吻 合较好,证明了该模型的合理有效性. 探讨了组分材料剪切非线性、损伤对材料宏观非线性 本构行为的影响,结果表明：随着编织角增大,纤维束剪切非线性效应和累积损伤对材料非 线性力学行为的影响明显增强.     

Ride comfort evaluation for road vehicle based on rigid-flexible coupling multibody dynamics

In the present research two different whole vehicle multibody models are established respectively, including rigid and rigid-flexible coupling multibody vehicle models. The former is all composed by rigid bodies while in the later model, the flexible rear suspension is built based on the finite element method (FEM) and mode superposition method, in which the deformations of the components are considered. The ride simulations with different speeds are carried out on a 3D digitalized road, and the weighted root mean square (RMS) of accelerations on the seat surface, backrest and at the feet are calculated. The comparison between the responses of the rigid and rigid-flexible coupling multibody models shows that the flexibility of the vehicle parts significantly affects the accelerations at each position, and it is necessary to take the flexibility effects into account for the assessment of ride comfort.     

3D numerical simulation on fluid-structure interaction of structure subjected to underwater explosion with cavitation

In the underwater-shock environment,cavitation occurs near the structural surface.The dynamic response of fluid-structure interactions is influenced seriously by the cavitation effects.It is also the difficulty in the field of underwater explosion.With the traditional boundary element method and the finite element method(FEM),it is difficult to solve the nonlinear problem with cavitation effects subjected to the underwater explosion.To solve this problem,under the consideration of the cavitation effects and fluid compressibility,with fluid viscidity being neglected,a 3D numerical model of transient nonlinear fluid-structure interaction subjected to the underwater explosion is built.The fluid spectral element method(SEM) and the FEM are adopted to solve this model.After comparison with the FEM,it is shown that the SEM is more precise than the FEM,and the SEM results are in good coincidence with benchmark results and experiment results.Based on this,combined with ABAQUS,the transient fluid-structure interaction mechanism of the 3D submerged spherical shell and ship stiffened plates subjected to the underwater explosion is discussed,and the cavitation region and its influence on the structural dynamic responses are presented.The paper aims at providing references for relevant research on transient fluid-structure interaction of ship structures subjected to the underwater explosion.     

Prediction of buckling characteristics of carbon nanotubes

In this paper, to investigate the buckling characteristics of carbon nanotubes, an equivalent beam model is first constructed. The molecular mechanics potentials in a C–C covalent bond are transformed into the form of equivalent strain energy stored in a three dimensional (3D) virtual beam element connecting two carbon atoms. Then, the equivalent stiffness parameters of the beam element can be estimated from the force field constants of the molecular mechanics theory. To evaluate the buckling loads of multi-walled carbon nanotubes, the effects of van-der Waals forces are further modeled using a newly proposed rod element. Then, the buckling characteristics of nanotubes can be easily obtained using a 3D beam and rod model of the traditional finite element method (FEM). The results of this numerical model are in good agreement with some previous results, such as those obtained from molecular dynamics computations. This method, designated as molecular structural mechanics approach, is thus proved to be an efficient means to predict the buckling characteristics of carbon nanotubes. Moreover, in the case of nanotubes with large length/diameter, the validity of Euler’s beam buckling theory and a shell model with the proper material properties defined from the results of present 3D FEM beam model is investigated to reduce the computational cost. The results of these simple theoretical models are found to agree well with the existing experimental results.     

Numerical analysis of effective elastic properties of geomaterials containing voids using 3D random fields and finite elements

The purpose of the study is to investigate the influence of porosity and void size on effective elastic geotechnical engineering properties with a 3D model of random fields and finite element. The random field theory is used to generate models of geomaterials containing spatially random voids with controlled porosity and void size. A “tied freedom” analysis is developed to evaluate the effective Young’s modulus and Poisson’s ratio in an ideal block material of finite elements. To deliver a mean and standard deviation of the elastic parameters, this approach uses Monte-Carlo simulations and finite elements, where each simulation leads to an effective value of the property under investigation. The results are extended to investigate an influence of representative volume element (RVE). A comparison of the effective elastic stiffness of 2D and 3D models is also discussed.     

Studying the effect of grain boundaries in dislocation density based crystal-plasticity finite element simulations

A dislocation density based constitutive model for the face centered cubic crystal structure has been implemented into a crystal-plasticity finite element framework and extended to consider the mechanical interaction between mobile dislocations and grain boundaries by the authors [Ma, A., Roters, F., Raabe, D., 2006a. A dislocation density based constitutive model for crystal-plasticity FEM including geometrically necessary dislocations. Acta Materialia 54, 2169–2179; Ma, A., Roters, F., Raabe, D., 2006b. On the consideration of interactions between dislocations and grain boundaries in crystal-plasticity finite element modeling – theory, experiments, and simulations. Acta Materialia 54, 2181–2194]. The approach to model the grain boundary resistance against slip is based on the introduction of an additional activation energy into the rate equation for mobile dislocations in the vicinity of internal interfaces. This energy barrier is derived from the assumption of thermally activated dislocation penetration events through grain boundaries. The model takes full account of the geometry of the grain boundaries and of the Schmid factors of the critically stressed incoming and outgoing slip systems. In this study we focus on the influence of the one remaining model parameter which can be used to scale the obstacle strength of the grain boundary.     

Acoustic simulation using a novel approach for reducing dispersion error

It is well‐known that the traditional finite element method (FEM) fails to provide accurate results to the Helmholtz equation with the increase of wave number because of the ‘pollution error’ caused by numerical dispersion. In order to overcome this deficiency, a gradient‐weighted finite element method (GW‐FEM) that combines Shepard interpolation and linear shape functions is proposed in this work. Three‐node triangular and four‐node tetrahedral elements that can be generated automatically are first used to discretize the problem domain in 2D and 3D spaces, respectively. For each independent element, a compacted support domain is then formed based on the element itself and its adjacent elements sharing common edges (or faces). With the aid of Shepard interpolation, a weighted acoustic gradient field is then formulated, which will be further used to construct the discretized system equations through the generalized Galerkin weak form. Numerical examples demonstrate that the present algorithm can significantly reduces the dispersion error in computational acoustics. Copyright © 2016 John Wiley & Sons, Ltd.     

Study on spline wavelet finite-element method in multi-scale analysis for foundation

A new finite element method （FEM） of B-spline wavelet on the interval （BSWI） is proposed. Through analyzing the scaling functions of BSWI in one dimension, the basic formula for 2D FEM of BSWI is deduced. The 2D FEM of 7 nodes and 10 nodes are constructed based on the basic formula. Using these proposed elements, the multiscale numerical model for foundation subjected to harmonic periodic load, the foundation model excited by external and internal dynamic load are studied. The results show the pro- posed finite elements have higher precision than the tradi- tional elements with 4 nodes. The proposed finite elements can describe the propagation of stress waves well whenever the foundation model excited by extemal or intemal dynamic load. The proposed finite elements can be also used to con- nect the multi-scale elements. And the proposed finite elements also have high precision to make multi-scale analysis for structure.     

2D and 3D finite element analysis of crack growth under compressive residual stress field

In the present study, plasticity induced crack closure (PICC) concept and three dimensional (3D) finite element method (FEM) were used to study the effect of compressive residual stress field on the fatigue crack growth from a hole. Furthermore, a new methodology on the basis of a correction factor was presented to increase the PICC precision. The result obtained was compared to two dimensional (2D) FEM, superposition method and Liu’s experimental data. To simulate the elasto-plastic behavior of the material, isotropic hardening was assumed and the Von-Mises yield criterion was implemented. A 3D mesh was built using eight-node hexahedral elements and one half of the specimen was modeled. The simulation results were fairly well correlated with experimental data. Furthermore, the 3D elasto-plastic FEM predicted a slightly smaller fatigue life than a 2D plane stress FEM. Applying the modified PICC method reduces the 3D FEM fatigue life prediction errors.     

血红细胞力学性能的纳米压痕实验和有限元模拟

采用纳米压痕技术和有限元方法研究了血红细胞的生物力学性能. 进行了血红细胞的纳米压痕实验, 得到了血红细胞的材料参数和变形形貌; 在实验基础上, 建立了血红细胞的三维有限元模型, 模拟了血红细胞的压痕载荷-位移曲线, 并考虑了参数效应. 数值模拟结果和实验数据符合很好. 通过改变压头与材料之间的摩擦系数和压头曲率半径等参数, 比较了载荷-位移曲线的变化情况. 研究表明摩擦系数对压痕载荷-位移曲线和应力分布影响很小, 而压头曲率对载荷-位移曲线的影响明显.     

三维五向编织复合材料渐进损伤分析及强度预测

基于材料连续体细观结构单胞,提出了材料的三维渐进损伤分析模型,采用非线性有限元方法并结合均匀化平均思想,首次建立了三维五向编织复合材料的强度预测模型。经研究典型编织角材料在拉伸载荷作用下细观损伤的发生及演化过程,分析了材料的细观失效机理,获得了材料的宏观拉伸应力应变曲线和极限破坏强度,并详细探讨了主要工艺参数编织角对材料宏观力学性能的影响规律。     

12.7 mm弹侵彻不同强度钢靶的数值模拟

针对12.7 mm弹侵彻不同强度钢靶时可能出现子弹保持完整或发生破碎的情况,过去的数值模拟仅限于模拟单一模式的子弹侵彻行为。为了克服这种数值模拟的局限性,开展了模型算法、网格尺寸对模拟结果影响的研究,并将模拟结果与实验结果进行了对比,提出了一种能够用于模拟子弹保持完整或破碎的弹靶模型。研究结果表明,为模拟子弹保持完整状态,子弹和靶板应分别采用基于Lagrange算法的有限元法和光滑粒子算法,而且子弹网格尺寸和靶板粒子间距之比应至少保持在5.3左右,否则弹头会产生与实验结果不符合的异常变形。但是,在模拟子弹发生破碎侵蚀时,该比例的网格/粒子尺寸比会引起计算中止。为了克服该问题,进一步建立了一种弹体表面采用大尺寸网格、内部采用细化小尺寸网格的有限元/光滑粒子法耦合弹靶模型。计算结果表明,改进的弹靶模型可模拟子弹保持完整或者发生破碎的情况。     

Normal flow boundary conditions in 3D circulation models

The problem of enforcing normal transport conditions on 3D velocity fields is considered in the context of ‘wave equation’ finite element models. A procedure for strong enforcement of the transport constraint is given. The procedure is identical for Neumann (transport known) and Dirichlet (pressure known) problems, which are treated reversibly. All local mass and force balance relations are retained in the FEM system. A global mass conservation property is proven for the general 3D, discrete-time case. Examples demonstrate the quality of the solutions and the practicality of the approach. © 1997 John Wiley & Sons, Ltd.     

Numerical failure analysis of a stretch-bending test on dual-phase steel sheets using a phenomenological fracture model

Advanced High Strength Steels (AHSS) are increasingly used in automotive industry due to their superior strength and substantial weight advantage. However, their compromised ductility gives rise to numerous manufacturing issues. One of them is the so-called ‘shear fracture’ often observed on tight radii during stamping processes. Since traditional approaches, such as the Forming Limit Diagram (FLD), are unable to predict this type of fractures, great efforts have been made to develop failure criteria that could predict shear fractures. In this paper, a recently developed Modified Mohr–Coulomb (MMC) ductile fracture criterion (Bai and Wierzbicki, 2010) is adopted to analyze the failure behavior of a Dual Phase (DP) steel sheet during stretch-bending operations. The plasticity and ductile fracture of the present sheet are fully characterized by a Hill’48 orthotropic model and a MMC fracture model, respectively. Finite element models with three different element types (3D, shell and plane strain) were built for a Stretch Forming Simulator (SFS) test (Shih and Shi, 2008), numerical simulations with four different R/t values (die radius normalized by sheet thickness) were performed. It has been shown that the 3D and shell element simulations can predict failure location/mode, the upper die load–displacement responses as well as wall stress and wrap angle at the onset of fracture for all R/t values with good accuracy. Furthermore, a series of parametric studies were conducted on the 3D element model, and the effect of tension level (clamping distance), tooling friction, mesh size and fracture locus on failure modes and load–displacement responses were investigated.     

Numerical modeling of PZT-induced Lamb wave-based crack detection in plate-like structures

This paper presents the numerical modeling and simulations of PZT-induced Lamb wave propagation in plate-like structures by using the spectral finite element method. A novel spectral plate finite element, which can efficiently model the three-dimensional (3D) behavior of Lamb waves, is proposed. In the formulation, linear displacement distributions in the thickness direction are assumed for both the PZT layer and the base plate. A way to avoid the thickness locking is proposed and used in the formulations. Two examples, one for the validation of the proposed two-dimensional (2D) spectral finite element and the other for the demonstration of crack detection in plates, are presented and discussed. The contact between the two faces of crack is considered. Numerical results show that (1) only the anti-symmetric mode is prone to thickness locking thus remedy should be made only on this part, (2) the proposed 2D spectral finite element can adequately model the Lamb wave propagation in plate-like structures and the complex scattering for the crack, and (3) crack location can be well determined by a PZT-induced Lamb wave-based diagnosis algorithm.     

Helical coil buckling mechanism for a stiff nanowire on an elastomeric substrate

When a stiff nanowire is deposited on a compliant soft substrate, it may buckle into a helical coil form when the system is compressed. Using theoretical and finite element method (FEM) analyses, the detailed three-dimensional coil buckling mechanism for a silicon nanowire (SiNW) on a polydimethylsiloxane (PDMS) substrate is studied. A continuum mechanics approach based on the minimization of the strain energy in the SiNW and elastomeric substrate is developed. Due to the helical buckling, the bending strain in SiNW is significantly reduced and the maximum local strain is almost uniformly distributed along SiNW. Based on the theoretical model, the energy landscape for different buckling modes of SiNW on PDMS substrate is given, which shows that both the in-plane and out-of-plane buckling modes have the local minimum potential energy, whereas the helical buckling model has the global minimum potential energy. Furthermore, the helical buckling spacing and amplitudes are deduced, taking into account the influences of the elastic properties and dimensions of SiNWs. These features are verified by systematic FEM simulations and parallel experiments. As the effective compressive strain in elastomeric substrate increases, the buckling profile evolves from a vertical ellipse to a lateral ellipse, and then approaches to a circle when the effective compressive strain is larger than 30%. The study may shed useful insights on the design and optimization of high-performance stretchable electronics and 3D complex nano-structures.     

Impact of material processing and deformation on cell morphology and mechanical behavior of polyurethane and nickel foams

The cell morphology and mechanical behavior of open-cell polyurethane and nickel foams are investigated by means of combined 3D X-ray micro-tomography and large scale finite element simulations. Our quantitative 3D image analysis and finite element simulations demonstrate that the strongly anisotropic tensile behavior of nickel foams is due to the cell anisotropy induced by the deformation of PU precursor during the electroplating and heat treatment stages of nickel foam processing. In situ tensile tests on PU foams reveal that the initial main elongation axis of the cells evolves from the foam sheet normal direction to the rolling direction of the coils. Finite element simulations of the hyperelastic behavior of PU foams based on real cell morphology confirm the observation that cell struts do not experience significant elongation after 0.15 tensile straining, thus pointing out alternative deformation mechanisms like complex strut junctions deformation. The plastic behavior and the anisotropy of nickel foams are then satisfactorily retrieved from finite element simulations on a volume element containing eight cells with a detailed mesh of all the hollow struts and junctions. The experimental and computational strategy is considered as a first step toward optimization of process parameters to tailor anisotropy of cell shape and mechanical behavior for applications in batteries or Diesel particulate filtering.     

线性区间有限元静力控制方程的组合解法

区间有限元的静力控制方程常被归结为区间方程组来求解。但实际上两者并不等价。本文根据不确定结构有限元分析的力学背景，直接从问题的基本参量的不确定性出发，将基本区间参量的边界组合与求解区间方程组的有关解法相结合，提出了线性区间有限元静力控制方程的两种组合解法－参量边界全组合法和组合迭代法。可以以较小的计算量获得或逼近位移和应力区间的准确界限。且不受基本参量变化范围的限制。算例分析表明文中方法是实用和可行的。