Application of moment interaction to the construction of a stable model of graphite crystal lattice

The aim of the present paper is to construct and study a model of pair moment interaction between carbon atoms in the two-dimensional graphite lattice. The carbon atom is modeled by a structure consisting of three rigidly connected mass points located at the vertices of an equilateral triangle. The interaction between mass points is described by a pair force potential, but the total interatomic interaction contains moment components owing to the finite size of the structure modeling the atom. We compute rank 4 tensors characterizing the elastic properties of the graphite crystal lattice constructed on the basis of our model. We determine lattice stability criteria depending on the number of coordination spheres taken into account. We show that this model permits one to ensure stability of the graphite lattice but significantly underestimates the transverse-to-longitudinal interatomic coupling rigidity ratio. We construct a generalized moment potential that permits one to obtain a rigidity ratio consistent with experimental data.     

Static and dynamic analysis of two-dimensional graphite lattices

Plane problems of statics and dynamics of graphite lattice are considered in the linear approximation. Comparative analysis of two models of interatomic interaction is carried out. One of these models is based on pairwise moment interaction, and the other is the Brennermodel where the variation in the angles between the segments connecting the atom under study with three nearest neighbors is additionally taken into account. The lattice tensile and shear rigidity in two directions is studied by straightforward calculations. The propagation of harmonic tensile and shear waves it two directions is considered. In problems of both statics and wave propagation, the results are compared with similar results for the equivalent continuum. It turned out that in the problems of statics, the Brenner model (after averaging) leads to an isotropic momentless continuum, while the model with pair interaction lead to the moment Cosserat continuum. In problems of wave propagation, both of these models give the same qualitative results. The velocities of acoustic parallel extension-compression wave propagation in a lattice are close to the wave velocity in the continuum but do not coincide with it. The difference increases with decreasing wave length and depends on the wave propagation direction. In the case of shear wave propagation in a lattice, the velocity of acoustic shear wave propagation in the pair moment potential model significantly (in the leading terms) depends on the direction of its propagation. The optical short waves are discovered and some of their properties are described.     

Thermal analysis of thin multi-layer metal films during femtosecond laser heating

Multi-layer metals films are widely used in modern engineering applications such as gold-coated metal mirrors used in high power laser systems. A transient heat flux model is derived to analyze multi-layer metal films under laser heating. The two separate system composed of electrons and the lattice is considered to take into account the electron–lattice interaction. The present model predicted the effects of underlying chromium’s thermal properties on temperature rise of the top gold layer. The effects of two adjacent and different metals with different electron–lattice coupling factors are analyzed for the heating mechanism of different lattices. The derived transient model combined with the two different conservation equations for the lattice and electrons are applied for the ultra short-pulse laser heating of a multi-layer film composed of gold and chromium.     

Two-dimensional model of a granular medium

A two-dimensional model of a granular medium is represented as a square lattice composed of elastically interacting round particles with translational and rotational degrees of freedom. In the long-wave approximation, we derive linear partial differential equations describing the propagation and interaction of waves of various types in such a medium. If microrotations of particles in the lattice and the related moment interactions are taken into account, then a microrotation wave (a spin wave) appears in the medium. We establish the one-to-one correspondence between the parameters of the microstructure and the elastic constants of second order. We analyze the dependence of the medium elasticity constants on the grain dimensions. In the continuum approximation, we compare the model proposed here with the model of two-dimensional Cosserat continuum.     

考虑材料各向异性的熔丝制造PLA点阵结构弹性各向同性设计

增材制造技术的兴起激发了国内外学者对结构创新设计的热情. 然而, 增材制造材料的各向异性为结构力学性能的预测与设计带来了一定的困难. 为了准确预测熔丝制造聚乳酸(PLA)材料和点阵结构的弹性性能, 并实现点阵结构的弹性各向同性设计, 首先, 本文采用正交各向异性弹性模型来描述PLA材料的弹性行为, 通过实验和计算得到了正交各向异性模型需要的9个独立的弹性常数. 然后, 设计了一种力学性能可调的二维组合桁架点阵结构, 基于代表体元法, 在不考虑材料各向异性的情况下推导出了其平面内等效弹性性能的解析表达式及弹性各向同性条件. 最后, 根据PLA材料的各向异性调整点阵结构内部杆件的弹性模量和厚度, 并基于代表体元法重新推导出了点阵结构平面内等效弹性性能的解析表达式及其弹性各向同性条件. 研究结果表明, 正交各向异性弹性模型适用于描述熔丝制造PLA材料的弹性行为, 基于该模型能够准确预测PLA材料在任意方向上的弹性模量. 在预测与设计熔丝制造点阵结构的力学性能时需要充分考虑材料的各向异性. 在考虑材料的各向异性之后, 基于代表体元法调整点阵结构的几何尺寸, 能够实现部分点阵结构的弹性各向同性设计.      

Incorporation of twinning into a crystal plasticity finite element model: Evolution of lattice strains and texture in Zircaloy-2

A crystal plasticity finite element code is developed to model lattice strains and texture evolution of HCP crystals. The code is implemented to model elastic and plastic deformation considering slip and twinning based plastic deformation. The model accounts for twinning reorientation and growth. Twinning, as well as slip, is considered to follow a rate dependent formulation. The results of the simulations are compared to previously published in situ neutron diffraction data. Experimental results of the evolution of the texture and lattice strains under uniaxial tension/compression loading along the rolling, transverse, and normal direction of a piece of rolled Zircaloy-2 are compared with model predictions. The rate dependent formulation introduced is capable of correctly capturing the influence of slip and twinning deformation on lattice strains as well as texture evolution.     

Helical Birods: An Elastic Model of Helically Wound Double-Stranded Rods

We consider a geometrically accurate model for a helically wound rope constructed from two intertwined elastic rods. The line of contact has an arbitrary smooth shape which is obtained under the action of an arbitrary set of applied forces and moments. We discuss the general form the theory should take along with an insight into the necessary geometric or constitutive laws which must be detailed in order for the system to be complete. This includes a number of contact laws for the interaction of the two rods, in order to fit various relevant physical scenarios. This discussion also extends to the boundary and how this composite system can be acted upon by a single moment and force pair. A second strand of inquiry concerns the linear response of an initially helical rope to an arbitrary set of forces and moments. In particular we show that if the rope has the dimensions assumed of a rod in the Kirchhoff rod theory then it can be accurately treated as an isotropic inextensible elastic rod. An important consideration in this demonstration is the possible effect of varying the geometric boundary constraints; it is shown the effect of this choice becomes negligible in this limit in which the rope has dimensions similar to those of a Kirchhoff rod. Finally we derive the bending and twisting coefficients of this effective rod.     

Kelvin结构开孔泡沫材料的弹性性能研究

采用一修正的十四面体结构模型(Kelvin结构模型)对开孔泡沫金属的弹性性能进行研究,对低密度开孔泡沫材料表现出不可压的特性进行了分析。该模型考虑作用在泡沫筋条上的弯矩、剪力和轴向力,以及轴向力的平衡。修正模型的数值计算结果与实验结果及其他模型的结果进行了对比,结果表明修正模型计算的杨氏模量比原有模型的略有提高,筋条截面为星形的修正模型计算的结果与实验比较符合。在密度等同的条件下,筋条截面惯性矩越大的开孔泡沫材料,其弹性模量也越大,而泊松比则越小。Kelvin结构的开孔泡沫材料的泊松比随相对密度的减小而趋于0.5。     

Self-consistent field method in the problem about the effective properties of an elastic composite

This paper is devoted to the calculation of effective elastic properties of a medium containing a random field of ellipsoidal inhomogeneities. It is assumed that the centers of the inclusions (the inhomogeneities) form a random spatial lattice, i.e., the field of inhomogeneities considered is strongly correlated. The interaction between the inhomogeneities is taken into account within the frame-work of the self-consistent field approximation. It hence turns out that the symmetry of the tensor of the elastic properties of the medium is determined by the symmetry of the elastic properties of the inclusion matrix, as well as by the symmetry of the spatial lattice formed by the mathematical expectations of the centers of the inclusions.     

From Discrete Visco-Elasticity to Continuum Rate-Independent Plasticity: Rigorous Results

We show that continuum models for ideal plasticity can be obtained as a rigorous mathematical limit starting from a discrete microscopic model describing a visco-elastic crystal lattice with quenched disorder. The constitutive structure changes as a result of two concurrent limiting procedures: the vanishing-viscosity limit and the discrete-to-continuum limit. In the course of these limits a non-convex elastic problem transforms into a convex elastic problem while the quadratic rate-dependent dissipation of visco-elastic lattice transforms into a singular rate-independent dissipation of an ideally plastic solid. In order to emphasize our ideas we employ in our proofs the simplest prototypical system mimicking the phenomenology of transformational plasticity in shape-memory alloys. The approach, however, is sufficiently general that it can be used for similar reductions in the cases of more general plasticity and damage models.     

On the evolution of lattice deformation in austenitic stainless steels—The role of work hardening at finite strains

In this work, a three dimensional crystal plasticity-based finite element model is presented to examine the micromechanical behaviour of austenitic stainless steels. The model accounts for realistic polycrystal micromorphology, the kinematics of crystallographic slip, lattice rotation, slip interaction (latent hardening) and geometric distortion at finite deformation. We utilise the model to predict the microscopic lattice strain evolution of austenitic stainless steels during uniaxial tension at ambient temperature with validation through in situ neutron diffraction measurements. Overall, the predicted lattice strains are in very good agreement with those measured in both longitudinal and transverse directions (parallel and perpendicular to the tensile loading axis, respectively). The information provided by the model suggests that the observed nonlinear response in the transverse {200} grain family is associated with a competitive bimodal evolution of strain during inelastic deformation. The results associated with latent hardening effects at the microscale also indicate that in situ neutron diffraction measurements in conjunction with macroscopic uniaxial tensile data may be used to calibrate crystal plasticity models for the prediction of the inelastic material deformation response.     

Elastic waves in prestressed bodies interacting with a fluid (survey)

Conclusion The above survey of different studies and analysis of results obtained widiin the framework of linearized three-dimensional theory show that use of the given model makes it possible to account for fluid viscosity and initial stresses in elastic bodies. Both of these factors play a significant role in actual media. The model also permits determination of the effect of fluid viscosity and initial stresses on the wave processes in hydroelastic systems. The use of an approach based on representations of general solutions of linearized problems of aerohydroelasticity for bodies with uniform initial strains and a compressible viscous fluid makes it possible to obtain dispersion relations in a general form diat is invariant relative to different types of elastic potential and valid for arbitrary compressible and incompressible materials. The approach also allows researchers to study the main classes of problems encountered in practice, conduct numerical experiments, and use the results to find new properties, laws, and mechanical effects that are characteristic of the investigated wave processes and reflect the mutual effects of the fields of initial and dynamic stresses, as well as the interaction of elastic bodies with viscous fluids. Translated from Prikladnaya Mekhanika, Vol. 33, No. 6, pp. 3–39, June, 1997.     

Cotransport of Graphene Oxide Nanoparticles and Kaolinite Colloids in Porous Media

Optimising production from heterogeneous and anisotropic reservoirs challenges the modern hydrocarbon industry because such reservoirs exhibit extreme inter-well variability making them very hard to model. Reasonable reservoir models can be obtained using modern geostatistical techniques, but all of them rely on significant variability in the reservoir only occurring at a scale at or larger than the inter-well spacing. In this paper we take a different, generic approach. We have developed a method for constructing realistic synthetic heterogeneous and anisotropic reservoirs which can be made to represent the reservoir under test. The main physical properties of these synthetic reservoirs are distributed fractally. The models are fully controlled and reproducible and can be extended to model multiple facies reservoir types. This paper shows how the models can be constructed and how they have been tested. Reservoir simulation results of a number of generated 3-D heterogeneous and anisotropic models show that heterogeneity, in terms of only the geometric distribution of reservoir properties, has a little effect on oil production from high and moderate quality reservoirs. However, if the effect of heterogeneity on capillary pressure is taken into account, the effect becomes striking, where varying the heterogeneity of reservoirs properties can lead to a 70 % change in the predicted oil production rate and a significant early shift of water breakthrough time. Hence, it is the heterogeneity consequences that are really substantial if not taken into account. These are very significant uncertainties for a hydrocarbon company if the heterogeneity of their reservoir is not well defined.     

Effect of Network Topology on Relative Permeability

We consider the role of topology on drainage relative permeabilities derived from network models. We describe the topological properties of rock networks derived from a suite of tomographic images of Fontainbleau sandstone (Lindquist et al., 2000, J. Geophys. Res. 105B, 21508). All rock networks display a broad distribution of coordination number and the presence of long-range topological bonds. We show the importance of accurately reproducing sample topology when deriving relative permeability curves from the model networks. Comparisons between the relative permeability curves for the rock networks and those computed on a regular cubic lattice with identical geometric characteristics (pore and throat size distributions) show poor agreement. Relative permeabilities computed on regular lattices and on diluted lattices with a similar average coordination number to the rock networks also display poor agreement. We find that relative permeability curves computed on stochastic networks which honour the full coordination number distribution of the rock networks produce reasonable agreement with the rock networks. We show that random and regular lattices with the same coordination number distribution produce similar relative permeabilities and that the introduction of longer-range topological bonds has only a small effect. We show that relative permeabilities for networks exhibiting pore–throat size correlations and sizes up to the core-scale still exhibit a significant dependence on network topology. The results show the importance of incorporating realistic 3D topologies in network models for predicting multiphase flow properties.     

A lattice Boltzmann model for the compressible Euler equations with second‐order accuracy

In this paper, we propose a new lattice Boltzmann model for the compressible Euler equations. The model is based on a three‐energy‐level and three‐speed lattice Boltzmann equation by using a method of higher moments of the equilibrium distribution functions. In order to obtain second‐order accuracy, we employ the ghost field distribution functions to remove the non‐physical viscous parts. We also use the conditions of the higher moment of the ghost field equilibrium distribution functions to obtain the equilibrium distribution functions. In the numerical examples, we compare the numerical results of this scheme with those obtained by other lattice Boltzmann models for the compressible Euler equations. Copyright © 2008 John Wiley & Sons, Ltd.     

Simultaneous initiation and growth of multiple radial hydraulic fractures from a horizontal wellbore

Multi-stage fracturing is the current preferred method of completion of horizontal wells in unconventional hydrocarbon reservoirs. Its core component consists in simultaneously initiating and propagating an array of hydraulic fractures. We develop a numerical model for the initiation and growth of an array of parallel radial hydraulic fractures. The solution accounts for fracture growth, coupling between elastic deformation and fluid flow in the fractures, elastic stress interactions between fractures and fluid flow in the wellbore. We also take into account the presence of a local pressure drop (function of the entering flow rate) at the connection between the well and the fracture, i.e., a choke-like effect due to current well completion practices, also referred to as entry friction. The partitioning of the fluid into the different fractures at any given time is part of the solution and is a critical indicator of simultaneous (balanced fluid partitioning) versus preferential growth. We validate our numerical model against reference solutions and a laboratory experiment for the initiation and growth of a single radial hydraulic fracture. We then investigate the impact of stress interaction on preferential growth of a subset of fractures in the array. Our results show that a sufficiently large local entry friction provides a strong feedback in the system and thus can counteract elastic stress interaction between fractures, thereby ensuring simultaneous growth. We propose a dimensionless number capturing the competition between stress interaction and local entry friction. This dimensionless number is a function of rock properties, fracture spacing and injection parameters. We verify that it captures the transition from the case of simultaneous growth (entry friction larger than interaction stress) to the case of preferential growth of some fractures (interaction stress larger than entry friction). We also discuss the implication of these results for multi-stage fracturing engineering practices.     

反倾层状岩体斜坡弯曲-拉裂两种失稳破坏之判据探讨

对反倾层状岩体斜坡弯曲-拉裂的失稳破坏判据,已有研究分别基于两种力学模型进行推导,即竖直压杆弹性屈曲稳定和平直梁弯折破坏模型,但对层间错动阻力及挠度产生附加弯矩等因素未加以考虑,不尽合理。在反倾斜坡岩层受力分析基础上,建立考虑了板侧层间错动阻力的下端嵌固、上端自由的斜置等厚弹性悬臂板梁模型,统一地通过瑞利-里兹能量方法,推导了弹性屈曲临界条件和嵌固端弯折破坏临界条件。实例计算及讨论表明,弹性屈曲判据适用于陡立岩层;而中-陡反倾岩层应主要为弯折破坏,但层间的力学性质对弯折临界判据值具有较大影响。