Plastic deformation in mesocomposite materials under dynamic loading as applied to their joining with metals

The paper studies the effect of the amount and distribution pattern of nanoinclusions in a high-strength mesocomposite matrix on its plastic deformation under dynamic loading. The study is performed on mesocomposite specimens shaped as hollow thick-walled cylinders subjected to combined shear/compression loading with an explosive. It is found that homogeneous strain decreases with the growing volume fraction of nanoinclusions. The mechanical texture formed by the distribution of nanoinclusions in mesocomposite bars is shown to influence the deformation and cracking mechanisms. Additionally, the influence of structure is studied by computer simulation. The simulation has revealed that plastic deformation is rotational in the mesocomposite with chaotic structural distribution.     

自由剪切流动中颗粒扩散的自相似特性

为了研究自由剪切流动中颗粒扩散的统计特性,对空间发展模式的三维气固两相射流和时间发展模式的三维气固两相混合层进行了直接数值模拟.其中对气相不可压缩Navier-Stokes方程的求解分别采用有限容积方法和拟谱方法,对离散惯性颗粒的跟踪采用单向耦合的拉格朗日方法.统计结果显示,当流场进入自相似状态后,以流场速度梯度二阶不变量Q为自变量的颗粒数的概率分布函数也呈现出与颗粒尺寸和时间发展无关的自相似特性.     

Evaluating the effects of loading parameters on single-crystal slip in tantalum using molecular mechanics

This study is aimed at developing a physics-based crystal plasticity finite element model for body-centred cubic (BCC) metals, through the introduction of atomic-level deformation information from molecular dynamics (MD) investigations of dislocation motion at the onset of plastic flow. In this study, three critical variables governing crystal plasticity mediated by dislocation motion are considered. MD simulations are first performed across a range of finite temperatures up to 600K to quantify the temperature dependence of critical stress required for slip initiation. An important feature of slip in BCC metals is that it is not solely dependent on the Schmid law measure of resolved shear stress, commonly employed in crystal plasticity models. The configuration of a screw dislocation and its subsequent motion is studied under different load orientations to quantify these non-Schmid effects. Finally, the influence of strain rates on thermal activation is studied by inducing higher stresses during activation at higher applied strain rates. Functional dependence of the critical resolved shear stress on temperature, loading orientation and strain rate is determined from the MD simulation results. The functional forms are derived from the thermal activation mechanisms that govern the plastic behaviour and quantification of relevant deformation variables. The resulting physics-based rate-dependent crystal plasticity model is implemented in a crystal plasticity finite element code. Uniaxial simulations reveal orientation-dependent tension–compression asymmetry of yield that more accurately represents single-crystal experimental results than standard models.     

Discrete element simulation of localized deformation in stochastic distributed granular materials

The deformation in granular material under loading conditions is a problem of great interest currently. In this paper, the micro-mechanism of the localized deformations in stochastically distributed granular materials is investigated based on the modified distinct element method under the plane strain conditions, and the influences of the confining pressure, the initial void ratio and the friction coefficient on the localized deformation and the stability of granular materials are also studied. It is concluded, based on the numerical simulation testing, that two crossed shear sliding planes may occur inside the granular assembly, and deformation patterns vary with the increasing of transverse strain. These conclusions are in good agreement with the present experimental results. By tangential velocity profiles along the direction normal to the two shear sliding planes, it can be found that there are two different shear deformation patterns: one is the fluid-like shear mode and the other is the solid-like shear mode. At last, the influences of various material parameters or factors on localized deformation features and patterns of granular materials are discussed in detail. Supported by the Key Project of the National Natural Science Foundation of China (Grant No. 10532040)     

Strain rate effects on compressive behavior of covalently bonded CNT networks

In this study, strain rate effects on the compressive mechanical properties of randomly structured carbon nanotube (CNT) networks were examined. For this purpose, three-dimensional atomistic models of CNT networks with covalently-bonded junctions were generated. After that, molecular dynamics (MD) simulations of compressive loading were performed at five different strain rates to investigate the basic deformation characteristic mechanisms of CNT networks and determine the effect of strain rate on stress–strain curves. The simulation results showed that the strain rate of compressive loading increases, so that a higher resistance of specimens to deformation is observed. Furthermore, the local deformation characteristics of CNT segments, which are mainly driven by bending and buckling modes, and their prevalence are strongly affected by the deformation rate. It was also observed that CNT networks have superior features to metal foams such as metal matrix syntactic foams (MMSFs) and porous sintered fiber metals (PSFMs) in terms of energy absorbing capabilities.     

Three-dimensional simulation of elastic capsules in shear flow by the penalty immersed boundary method

An improved penalty immersed boundary method (pIBM) has been proposed for simulation of flow-induced deformation of three-dimensional (3D) elastic capsules. The motion of the capsule membrane is described in the Lagrangian coordinates. The membrane deformation takes account of the bending and twisting effects as well as the stretching and shearing effects. The method of subdivision surfaces is adopted to generate the mesh of membrane and the corresponding shape functions, which are required to be C¹ continuous. The membrane motion is then solved by the subdivision-surface based finite element method on the triangular unstructured mesh. On the other hand, the fluid motion is defined on the Eulerian domain, and is advanced by the fractional step method on a staggered Cartesian grid. Coupling of the fluid motion and the membrane motion is realized in the framework of the pIBM. Using the proposed method, deformation of 3D elastic capsules in a linear shear flow is studied in detail, and validations are examined by comparing with previous studies. Both the neo-Hookean membrane and the Skalak membrane are tested. For an initially spherical capsule the tank-treading motion is formed under various dimensionless shear rates and reduced bending moduli. It is found that buckling occurs near the equator of the capsule for small shear rates but near the tips for large shear rates, which is suppressed by including the bending rigidity of the membrane. Effects of the Reynolds number and the membrane density are investigated for an initially spherical capsule. For a non-spherical capsule, with the initial shape of the oblate spheroid or the biconcave circular disk as a model of the red blood cell, the swinging motion is observed due to the shape memory effect. By decreasing the dimensionless shear rate or increasing the reduced bending modulus, the swinging motion is transited into the tumbling motion.     

Transient deformation of thin metal sheets during pulsed laser forming

The transient deformation of thin grade 304 stainless steel metal sheets heated by a single pulse of a CO₂ laser beam is simulated in this paper. The laser beam is assumed to be line-shaped and the problem is treated as three-dimensional thermo-elastoplastic. The temperature field, deformation pattern, stress–strain states and the residual stress distribution of the specimens have been calculated numerically and the transient response of the bending angle has been validated by experiments. Good agreement has been obtained between the numerical simulation and the experiments under various operating conditions. The numerical study reveals that a high temperature gradient exists for a positive bending angle and a low one for a negative angle. It transpires that the mechanisms of pulsed laser forming are dependent mainly upon the laser power, the heating time, the clamping arrangement, as well as the geometry, the thermal properties and the original stress states of the specimen.     

An improved penalty immersed boundary method for fluid–flexible body interaction

An improved penalty immersed boundary (pIB) method has been proposed for simulation of fluid–flexible body interaction problems. In the proposed method, the fluid motion is defined on the Eulerian domain, while the solid motion is described by the Lagrangian variables. To account for the interaction, the flexible body is assumed to be composed of two parts: massive material points and massless material points, which are assumed to be linked closely by a stiff spring with damping. The massive material points are subjected to the elastic force of solid deformation but do not interact with the fluid directly, while the massless material points interact with the fluid by moving with the local fluid velocity. The flow solver and the solid solver are coupled in this framework and are developed separately by different methods. The fractional step method is adopted to solve the incompressible fluid motion on a staggered Cartesian grid, while the finite element method is developed to simulate the solid motion using an unstructured triangular mesh. The interaction force is just the restoring force of the stiff spring with damping, and is spread from the Lagrangian coordinates to the Eulerian grids by a smoothed approximation of the Dirac delta function. In the numerical simulations, we first validate the solid solver by using a vibrating circular ring in vacuum, and a second-order spatial accuracy is observed. Then both two- and three-dimensional simulations of fluid–flexible body interaction are carried out, including a circular disk in a linear shear flow, an elastic circular disk moving through a constricted channel, a spherical capsule in a linear shear flow, and a windsock in a uniform flow. The spatial accuracy is shown to be between first-order and second-order for both the fluid velocities and the solid positions. Comparisons between the numerical results and the theoretical solutions are also presented.     

A conservative level-set based method for compressible solid/fluid problems on fixed grids

A three-dimensional Eulerian method is presented for simulating dynamic systems comprising multiple compressible solid and fluid components where internal boundaries are tracked using level-set functions. Aside from the interface interaction calculation within mixed cells, each material is treated independently and the governing constitutive laws solved using a conservative finite volume discretisation based upon the solution of Riemann problems to determine the numerical fluxes. The required reconstruction of mixed cell volume fractions and cut cell geometries is presented in detail using the level-set fields. High-order accuracy is achieved by incorporating the weighted-essentially non-oscillatory (WENO) method and Runge–Kutta time integration. A model for elastoplastic solid dynamics is employed formulated using the tensor of elastic deformation gradients permitting the equations to be written in divergence form. The scheme is demonstrated using selected one-dimensional initial value problems for which exact solutions are derived, a two-dimensional void collapse, and a three-dimensional simulation of a confined explosion.     

Numerical simulation of deformation and fracture of a material with a polysilazane-based coating

The paper studies the localization of plastic deformation and fracture in a material with a porous coating. A dynamic boundary value problem in the plane strain formulation is solved. The numerical simulation is performed by the finite difference method. The composite structure corresponds to the experimentally observed one and is specified explicitly in the calculation. A generation procedure of the initial finite-difference grid is developed to describe the coating structure with adjustable porosity and geometry of the substrate-coating interface. Constitutive equations for the steel substrate include an elastic-plastic model of an isotropically hardening material. The ceramic coating is described by a brittle fracture model on the basis of the Huber criterion which accounts for crack nucleation in triaxial tension zones. It is shown that the specific character of deformation and fracture of the studied composite results from the presence of local tensile regions in the vicinity of pores and along the coating-substrate interface, in both tension and compression of the coated material. The interrelation between inhomogeneous plastic flow in the steel substrate and crack propagation in the coating is studied.     

Strain distributions and electronic structure of three-dimensional InAs/GaAs quantum rings

This paper presents a finite element calculation for the electronic structure and strain distribution of self-organized InAs/GaAs quantum rings. The strain distribution calculations are based on the continuum elastic theory. An ideal three-dimensional circular quantum ring model is adopted in this work. The electron and heavy-hole energy levels of the InAs/GaAs quantum rings are calculated by solving the three-dimensional effective mass Schr?dinger equation including the deformation potential and piezoelectric potential up to the second order induced by the strain. The calculated results show the importance of strain and piezoelectric effects, and these effects should be taken into consideration in analysis of the optoelectronic characteristics of strain quantum rings.     

可压剪切层线性稳定性特征直接数值模拟

基于伪随机数生成技术促白噪声扰动,以高精度迎风／对称紧致混合差分算法求解二维／三维非定常可压Navier－Stokes方程,揭示了可压自由剪切层初始剪切过程中扰动的线性演化特征,以及该过程对扰动波数和方向的内在选择性,验证了所用算法的有效性,表明线性理论同数值模拟相结合是可压剪切层研究的合理途径之一。     

Finite strain stress fields near the tip of an interface crack between a soft incompressible elastic material and a rigid substrate

We present a numerical study of finite strain stress fields near the tip of an interface crack between a rigid substrate and an incompressible hyperelastic solid using the finite element method (FEM). The finite element (FE) simulations make use of a remeshing scheme to overcome mesh distortion. Analyses are carried out by assuming that the crack tip is either pinned, i.e., the elastic material is perfectly bonded (no slip) to the rigid substrate, or the crack lies on a frictionless interface. We focus on a material which hardens exponentially. To explore the effect of geometric constraint on the near tip stress fields, simulations are carried out under plane stress and plane strain conditions. For both the frictionless interface and the pinned crack under plane stress deformation, we found that the true stress field directly ahead of the crack tip is dominated by the normal opening stress and the crack face opens up smoothly. This is also true for an interface crack along a frictionless boundary in plane strain deformation. However, for a pinned interface crack under plane strain deformation, the true opening normal stress is found to be lower than the shear stress and the transverse normal stress. Also, the crack opening profile for a pinned crack under plane strain deformation is completely different from those seen in plane stress and in plane strain (frictionless interface). The crack face flips over and the tip angle is almost tangential to the interface. Our results suggest that interface friction can play a very important role in interfacial fracture of soft materials on hard substrates.     

Principal component analysis of shear strain effects

Shear stresses are always present during quasi-static strain imaging, since tissue slippage occurs along the lateral and elevational directions during an axial deformation. Shear stress components along the axial deformation axes add to the axial deformation while perpendicular components introduce both lateral and elevational rigid motion and deformation artifacts into the estimated axial and lateral strain tensor images. A clear understanding of these artifacts introduced into the normal and shear strain tensor images with shear deformations is essential. In addition, signal processing techniques for improved depiction of the strain distribution is required. In this paper, we evaluate the impact of artifacts introduced due to lateral shear deformations on the normal strain tensors estimated by varying the lateral shear angle during an axial deformation. Shear strains are quantified using the lateral shear angle during the applied deformation. Simulation and experimental validation using uniformly elastic and single inclusion phantoms were performed. Variations in the elastographic signal-to-noise and contrast-to-noise ratios for axial deformations ranging from 0% to 5%, and for lateral deformations ranging from 0 to 5° were evaluated. Our results demonstrate that the first and second principal component strain images provide higher signal-to-noise ratios of 20 dB with simulations and 10 dB under experimental conditions and contrast-to-noise ratio levels that are at least 20 dB higher when compared to the axial and lateral strain tensor images, when only lateral shear deformations are applied. For small axial deformations, the lateral shear deformations significantly reduces strain image quality, however the first principal component provides about a 1–2 dB improvement over the axial strain tensor image. Lateral shear deformations also significantly increase the noise level in the axial and lateral strain tensor images with larger axial deformations. Improved elastographic signal and contrast-to-noise ratios in the first principal component strain image are always obtained for both simulation and experimental data when compared to the corresponding axial strain tensor images in the presence of both axial and lateral shear deformations.     

Investigation of the effects of tensile strain on optical properties of ZnO nanowire

In this paper, the effects of mechanical tensile strain on optical properties of ZnO nanowire before and after embedding ZnS nanowire were investigated by simulation. Finite element modeling (FEM) software package ABAQUS and three-dimensional (3D) finite-difference time-domain (FDTD) methods were furnished to analyze the problems numerically, including the nonlinear mechanical behavior and optical properties of the sample, respectively. The physical deformation model was imported into the FDTD to investigate optical properties of ZnO nanowire under mechanical tensile strain. Besides, the stress-strain curve via tensile experimental was compared with stress-strain curve that was obtained from finite element modeling. The results disclosed that the mechanical strain was demonstrated to play an important role in determining the optical properties of ZnO nanowire such as absorption coefficient and optical density.     

剪切流动条件下液滴变形和断裂的数值模拟

本文采用扩散界面法研究了剪切流动条件下悬浮液滴变形和断裂的动力学机制。控制方程采用考虑表面张力影响的Navier-Stokes-Cahn-Hilliard方程描述。计算网格采用均匀矩形交错网格。采用基于压力增量的近似投影法计算 Navier-Stokes方程,采用完全近似多重网格法计算Cahn-Hilliard方程。稳态液滴变形规律及液滴拉伸断裂过程的计算结果与试验结果符合较好,表明本文模型能够很好的研究液滴变形及断裂机理。     

Single-step scanner-based digital image correlation (SB-DIC) method for large deformation mapping in rubber

The incremental digital image correlation (DIC) method has been applied in the past to determine strain in large deformation materials like rubber. This method is, however, prone to cumulative errors since the total displacement is determined by combining the displacements in numerous stages of the deformation. In this work, a method of mapping large strains in rubber using DIC in a single-step without the need for a series of deformation images is proposed. The reference subsets were deformed using deformation factors obtained from the fitted mean stress-axial stretch ratio curve obtained experimentally and the theoretical Poisson function. The deformed reference subsets were then correlated with the deformed image after loading. The recently developed scanner-based digital image correlation (SB-DIC) method was applied on dumbbell rubber specimens to obtain the in-plane displacement fields up to 350% axial strain. Comparison of the mean axial strains determined from the single-step SB-DIC method with those from the incremental SB-DIC method showed an average difference of 4.7%. Two rectangular rubber specimens containing circular and square holes were deformed and analysed using the proposed method. The resultant strain maps from the single-step SB-DIC method were compared with the results of finite element modeling (FEM). The comparison shows that the proposed single-step SB-DIC method can be used to map the strain distribution accurately in large deformation materials like rubber at much shorter time compared to the incremental DIC method.     

A Lagrangian integration point finite element method for large deformation modeling of viscoelastic geomaterials

We review the methods available for large deformation simulations of geomaterials before presenting a Lagrangian integration point finite element method designed specifically to tackle this problem. In our Ellipsis code, the problem domain is represented by an Eulerian mesh and an embedded set of Lagrangian integration points or particles. Unknown variables are computed at the mesh nodes and the Lagrangian particles carry history variables during the deformation process. This method is ideally suited to model fluid-like behavior of continuum solids which are frequently encountered in geological contexts. We present benchmark examples taken from the geomechanics area.     

基于局部基本解法的静电场仿真分析

将局部基本解方法应用于静电场问题的模拟与分析。局部基本解方法是利用控制方程的基本解,基于局部理论和移动最小二乘原理提出的一种无网格算法。相比于有限元和有限差分等传统网格类方法,该方法仅需离散节点,避免了复杂的网格剖分难题。作为一种半解析数值技术,物理问题的基本解被作为插值基函数建立数值离散模型,从而保证了算法的较高精度。此外,与具有全局离散格式的无网格方法相比,局部基本解法更适用于高维复杂几何和大尺度模拟。二维和三维数值试验表明,该方法具有实施方便灵活,计算精度高和计算速度快等优势。为静电场仿真研究开辟新的途径,拓展了局部基本解方法的应用领域。