Numerical computation and analytical estimation of stress-intensity factors for strips with multiple edge cracks

In this paper, stress-intensity factors for a two-dimensional problem are determined. Strips with multiple symmetrical edge cracks in tension are investigated. A simple analytical estimation is compared to numerical results. The influence of penetration of the crack faces and mixed-mode loading on the numerical results is investigated. A simple method to estimate stress-intensity factors for strips with multiple edge cracks is proposed.     

Separating forces in blade coating of viscous and viscoelastic liquids

Coating of viscous and viscoelastic liquids is examined both theoretically and experimentally. A single simple geometry, a blade over a rotating roll, is considered. A perturbation solution to the Navier-Stokes equations yields a lubrication theory with first order corrections for curvature and inertia. A numerical solutions by the Finite Element Method (FEM) is compared to the analytical solutions. For Newtonian fluids, agreement between these mathematical models, and data on blade loading, is quite good.The effect of a non-Newtonian viscosity is explored by adopting a purely viscous power law model. The zeroth-order (lubrication) equations are solved by the method of Steidler and Horowitz, and predictions for coating thickness and blade loading agree quite well with those obtained from a FEM solution of the full equations of motion for a power law fluid. Data on blade loading, obtained using a strongly elastic polymer solution, are compared to these mathematical models, and discrepancies are noted.     

基于耦合算法的三维复杂结构冲击动力学特性

光滑粒子流体动力学-有限元耦合算法（SPH-FEM）较好地结合了SPH和FEM的优势,近年来逐渐被引入冲击动力学相关问题研究中。然而早期的研究对象多为单一材料的简单结构,所取得的研究成果距离实际工程应用仍有一定差距。为此,在总结前人工作的基础上,对SPH-FEM耦合算法进行适当改进,通过引入复合材料损伤模型,对复合材料蒙皮结构飞行器舱段结构进行建模计算,分析其在爆炸冲击激励下的冲击动力学特性。将数值计算结果与试验结果进行对比分析,验证该算法和模型的有效性和准确性,初步实现SPH-FEM的工程实际应用。最后总结了复合材料蒙皮结构飞行器在爆炸冲击激励下的一系列结构动态响应规律,以期为航天飞行器结构设计与防护提供参考。     

Method of analysis of mathematical models of media under complex loading

A method of analysis of constitutive models of media with complex loading trajectories is proposed. It is based on a comparison of data from laboratory experiments and corresponding results of numerical calculations. In previous laboratory experiments, nearly homogeneous complex loading with continuous rotation of the principal axes of the strain tensor and loading with broken strain trajectories was performed. Numerical calculations for the types of loading corresponding to the experiments performed are based on the constitutive equations of the model. The numerical results obtained and data of the laboratory experiments are compared. The hypoplastic model of a geomedium is analyzed. Analysis shows that the model is a satisfactory qualitative and quantitative approximation of data from laboratory experiments on complex loading of geomaterials. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 5, pp. 133–142, September–October, 1999.     

A finite-strain model for anisotropic viscoplastic porous media: II – Applications

In Part I of this work, we have proposed a new model based on the “second-order” nonlinear homogenization method for determining the effective response and microstructure evolution in viscoplastic porous media with aligned ellipsoidal voids subjected to general loading conditions. In this second part, the new model is used to analyze the instantaneous effective behavior and microstructure evolution in porous media for several representative loading conditions and microstructural configurations. First, we study the effect of the shape and orientation of the voids on the overall instantaneous response of a porous medium that is subjected to principal loading conditions. Secondly, we study the problem of microstructure evolution under axisymmetric and simple shear loading conditions for initially spherical voids in an attempt to validate the present model by comparison with existing numerical and approximate results in the literature. Finally, we study the possible development of macroscopic instabilities for the special case of ideally-plastic solids subjected to plane-strain loading conditions. The results, reported in this paper, suggest that the present model improves dramatically on the earlier “variational” estimates, in particular, because it generates much more accurate results for high triaxiality loading conditions.     

相变复合波在伪弹性TiNi合金薄壁管中的传播

相变可以改变材料的性质,从而严重影响波在介质中传播的结构。采用考虑静水压力和偏应力联合作用的增量型相变本构模型,研究了在拉(压)-扭联合作用下半无限长TiNi合金薄壁管内相变复合波的传播规律。基于广义特征理论分析了相变复合波的特征波速及简单波解的基本性质。利用数值方法研究了两种典型情况下管内相变耦合波传播的规律,管内传播的应力路径和波的结构与初始状态及加载幅值有关,展现出和普通弹塑性材料截然不同的性质。     

On the implementation of a multi-surface kinematic hardening plasticity and its applications

This paper is concerned with an application of the multi-surface plasticity in solid mechanics and geotechnical problems. The model is of a von-Mises type with associated flow rule, originally proposed by Montans. The Mroz translation rule is implemented to the movements of the yield surfaces and the fully implicit scheme with radial mapping method is applied in numerical computations. Algorithmic consistent tangent modulus with numerical integration algorithm of constitutive equations is extracted. The model is developed in the class of kinematic hardening models, so the ‘Masing’ rule is preserved. The model is able to consider the plastic strain accumulation in constant axial stress state, such as ratcheting. The implementation is validated by means of a simple deformation path of combined extension and compression test, a pure shear test with pseudo-random loading, a test which demonstrates the capabilities of the model in simulation of cyclic loading and ratcheting, a cyclic shear test in saturated undrained sand and finally, the analysis of a plate with holes, which presents the shear band using the multi-surface plasticity model.     

Singular loadings in elasticity problems and singular solutions of the corresponding integral equations

The method of singular integral equations is an efficient method for the formulation and numerical solution of plane and antiplane, static and dynamic, isotropic and anisotropic elasticity problems. Here we consider three cases of singular loadings of the elastic medium: by a force, by a moment and by a loading distribution with a simple pole. These loadings cause corresponding singularities in the right-hand side function and in the unknown function of the integral equation. A method for the numerical solution of the singular integral equation under the above singular loadings is proposed and the validity of this equation at the singular points is investigated.     

Elastoplastic constitutive modeling under the complex loading driven by GRU and small-amount data

In this paper, a data-driven method to model the three-dimensional engineering structure under the cyclic load with the one-dimensional stress-strain data is proposed. In this method, one-dimensional stress-strain data obtained under uniaxial load and different loading history is learned offline by gate recurrent unit (GRU) network. The learned constitutive model is embedded into the general finite element framework through data expansion from one dimension to three dimensions, which can perform stress updates under the three-dimensional setting. The proposed method is then adopted to drive numerical solutions of boundary value problems for engineering structures. Compared with direct numerical simulations using the J2 plasticity model, the stress-strain response of beam structure with elastoplastic materials under forward loading, reverse loading and cyclic loading were predicted accurately. Loading path dependent response of structure was captured and the effectiveness of the proposed method is verified. The shortcomings of the proposed method are also discussed.     

Analysis of cracked magnetoelectroelastic composites under time-harmonic loading

This paper presents a numerical model for the analysis of cracked magnetoelectroelastic materials subjected to in-plane mechanical, electric and magnetic dynamic time-harmonic loading. A traction boundary integral equation formulation is applied to solve the problem in combination with recently obtained time-harmonic Green’s functions (Rojas-Diaz et al., 2008). The hypersingular boundary integral equations appearing in the formulation are first regularized via a simple change of variables that permits to isolate the singularities. Relevant fracture parameters, namely stress intensity factors, electric displacement intensity factor and magnetic induction intensity factor are directly evaluated as functions of the computed nodal opening displacements and the electric and magnetic potentials jumps across the crack faces. The method is checked by comparing numerical results against existing solutions for piezoelectric solids. Finally, numerical results for scattering of plane waves in a magnetoelectroelastic material by different crack configurations are presented for the first time. The obtained results are analyzed to evaluate the dependence of the fracture parameters on the coupled magnetoelectromechanical load, the crack geometry and the characteristics of the incident wave motion.     

鸟撞击叶片时载荷因素的数值模拟分析

鸟与叶片的撞击过程是一个复杂的加载过程。为了将其简化,以建立一个简单且合理的鸟撞击载荷模型,需要分析鸟撞击载荷的各种因素对叶片响应的影响。本文通过计算机数值模拟进行上述工作。以矩形悬臂板模拟实际叶片,以冲击载荷模拟鸟撞击载荷,采用有限元法计算悬臂板在冲击载荷下的非线性瞬态响应。从鸟撞击载荷的冲量、时间因索、空间因素三个方面分析了冲量、加载持续时间、力-时间函数、初始冲击压力、加载位置、载荷的空间分布以及载荷类型等七种因素对叶片响应的影响。本文得出的结论为合理简化鸟撞击加载过程及建立鸟撞击载荷模型提供了参考与依据。     

On the accurate determination of contact compliance for impact test modelling

To model the specimen interaction with supports during an impact test, simple formulas for indentation–contact force relation between a beam specimen and a rigid cylindrical indenter have been derived using a mixed analytical/numerical approach. Two types of boundary conditions for the specimen (i) support by a frictionless rigid foundation and (ii) conventional three-point bending have been considered. The first scheme of loading (the compression indentation test, CIT) is sometimes used for quasi-static estimation of the specimen–striker or specimen–support contact compliance instead of the second scheme, which more closely corresponds to the real loading conditions of the specimen during an impact test. It has been found that the indentation (and, therefore, the contact compliance) of the specimen loaded according to the first scheme is up to 19% higher than for the second one. A simple correction of the results of CIT, which allows to estimate the contact compliance accurately has been proposed. Approximate formulas for the linearized contact compliance have been derived for both schemes of loading using three different methods of linearization. The best result has been obtained by the method of the equality of work done by nonlinear and linearized contact forces. An example of modelling of the three-point-bending test using the computed contact stiffness of the anvil is presented.     

基于近场动力学的单晶冰弹性各向异性数值模拟方法

天然冰材料在变形与破坏行为上的各向异性特征是冰与结构相互作用中产生复杂载荷过程的关键诱因, 而天然冰各向异性的根源则在于单晶冰的各向异性. 目前, 学术界针对单晶冰各向异性的数值模拟方法研究仍较为缺乏. 为了准确再现天然冰材料的特殊力学性质, 本文基于近场动力学理论, 提出了一种单晶冰弹性各向异性的数值模拟方法. 该方法的核心思想是将单晶冰杨氏模量沿不同加载方向的变化规律引入到近场动力学力密度向量的影响函数中. 以前人实验测试得到的杨氏模量值为参考, 通过开展与C轴呈0°, 45°和90°三个加载方向的单晶冰单轴压缩数值模拟实验, 提出了针对该影响函数的修正和辅助参数标定方法, 最终在15°, 30°, 60°和75°等其他四个加载方向进行了验证. 结果表明: 本文提出的针对影响函数的修正与参数标定方法, 能够较为便捷地找到数值模型杨氏模量与参考杨氏模量相一致的影响函数最优解, 即本文提出的基于影响函数的近场动力学数值模拟方法, 能够合理、准确地模拟单晶冰的弹性各向异性行为. 本文研究成果可为后续多晶冰各向异性数值模拟方法的建立提供基础性参考.      

螺旋焊线管局部噘嘴应力集中分析

螺旋焊缝局部噘嘴问题是复杂的三维问题，至今没有现成的安全评定公式可以利用，也难以获得纯粹的理论解。应“西气东输”工程之需，本文利用现有直焊缝理论基础，建立了该问题的力学模型，获得了应力集中因子的显式解，给制订螺旋焊线管几保缺陷的安全评定标准提供了理论基础。利用商用有限元工具ABAQUS对螺旋焊线局部噘嘴进行的系统分析显示，本文提供的理论解具有很强的预测能力。     

Comparison of isotropic hardening and kinematic hardening in thermoplasticity

A coupled thermo-mechanical problem is presented in this paper. The constitutive model is based on thermoplastic model for large strains where both kinematic and isotropic hardening are included. It is shown that a non-associated plasticity formulation enables thermodynamic consistent heat generation to be modeled, which can be fitted accurately to experimental data. In the numerical examples the effect of heat generation is investigated and both thermal softening and temperature-dependent thermal material parameters are considered. The constitutive model is formulated such that pure isotropic and pure kinematic hardening yield identical uniaxial mechanical response and mechanical dissipation. Thus, differences in response due to hardening during non-proportional loading can be studied. Thermally triggered necking is studied, as well as cyclic loading of Cook’s membrane. The numerical examples are solved using the finite element method, and the coupled problem that arises is solved using a staggered method where an isothermal split is adopted.     

基于Fourier级数展开的Laplace数值逆变换

研究了基于Fourier级数展开的Laplace数值逆变换在黏弹性力学问题中的有效应用,这类方法的关键涉及计算参数的选择. 构造了优化模型,对计算参数寻优,以黏弹性层合圆柱薄壳在轴压下的准静态变形以及受突加内压黏弹性圆筒在平面应变条件下的动应力响应为例阐述方法的应用. 结果表明:通过优化模型能有效地确定计算参数;且当反演参数与计算时间的乘积在一定范围内时,Fourier级数展开法均能给出一致的结果,由此,可按与计算时间成反比的关系来确定反演算法中的参数.      

THE APPLICATION OF DISCRETE ELEMENT METHOD IN SOLVING THREE-DIMENTIONAL IMPACT DYNAMICS PROBLEMS

A three-dimensional discrete element model of the connective type is presented. Moreover, a three- dimensional numerical analysis code, which can carry out the transitional process from connective model (for continuum) to contact model (for non-continuum), is developed for simulating the mechanical process from continuum to non-continuum. The wave propagation process in a concrete block (as continuum) made of cement grout under impact loading is numerically simulated with this code. By comparing its numerical results with those by LS-DYNA, the calculation accuracy of the model and algorithm is proved. Furthermore, the failure process of the concrete block under quasi-static loading is demonstrated, showing the basic dynamic transitional process from continuum to non-continuum. The results of calculation can be displayed by animation. The damage modes are similar to the experimental results. The two numerical examples above prove that our model and its code are powerful and efficient in simulating the dynamic failure problems accompanying the transition from continuum to non-continuum. It also shows that the discrete element method (DEM) will have broad prospects for development and application.     

离散元法在求解三维冲击动力学问题中的应用

提出了三维连结型离散模型,建立了可实现连结型模型(用于连续介质)-接触型模型(用于非连续介质)转化的三维离散元计算程序,用来模拟连续介质转变为非连续介质的力学过程．利用该计算程序对冲击载荷下混凝土块体内(连续体情况下)的应力波传播过程进行了数值模拟．将计算结果的数值与LS-DYNA程序计算的结果进行比较,验证了该计算程序的计算精度．在此基础上,模拟了混凝土块体的动态破坏(连续介质向非连续介质转化)过程．其计算结果可用动画显示,得到的破坏形式与由实验得到的破坏形式相近．两个算例说明该离散元模型及其计算程序是模拟计算伴随有连续介质向非连续介质转变的动态破坏问题的有力工具．     

Plasticity and fracture of martensitic boron steel under plane stress conditions

Two series of multiaxial experiments are performed to characterize the mechanical behavior of a hot formed martensitic 22MnB5 boron steel. In the first series, flat specimens of uniform cross-section are subjected to various combinations of tensile and shear loading to characterize the elasto-plastic response. Butterfly-shaped specimens of non-uniform cross-section are used for the second series to study the onset of fracture in the martensitic steel. It is found from the analysis of the experimental results that the planar isotropic Hill’48 yield function along with an associated flow rule provides good estimates of the stress–strain response over a wide range of loading paths. The fracture experiments demonstrate that the crack initiation depends strongly on the loading state. A simple stress triaxiality dependent phenomenological fracture model is calibrated to describe the onset of fracture. Using the proposed plasticity and fracture model, numerical simulations of the fracture of tensile specimens of different notch radii are performed and compared with experiments.