An external meniscus on a thin ovoidal fiber (the case of full wetting)

A complex shape of an external meniscus formed due to the capillary rise of a liquid along a fiber having the ovoidal profile is considered. Within the framework of the asymptotic approach and under the assumption on the complete wetting of the fiber material by the liquid, an analytical solution of the problem is derived. The particular examples of the meniscus configuration are presented in the cases in which the fiber profile has the shape of an ovoid or an ellipse.     

On the role of the process zone in dynamic fracture

The evolution of the fracture process zone and its influence on dynamic crack propagation are investigated using a simple constitutive assumption to model the material in the fracture process zone. The mode III problem of anti-plane shear is examined using a finite difference scheme to obtain the full field solution. Unlike the classical approach of determining the steady state solutions for imposed constant speed of crack propagation, here the fracture criterion is imposed along with the formulation of the boundary-initial value problem and the coupled equations are solved numerically to determine the generation and growth of the fracture process zone as well as the crack tip. The results of the simulation indicate that the constitutive behavior of the process zone material (or equivalently the evolution of the process zone itself) plays a key role in determining the dynamics of fast fracture.     

Viscoelastic computations for reverse roll coating with dynamic wetting lines and the Phan-Thien-Tanner models

The computational modelling of reverse roll coating with dynamic wetting line has been analysed for various non-Newtonian viscoelastic materials appealing to the Phan-Thien-Tanner (PTT) network class of models suitable for typical polymer solutions, with properties of shear thinning and strain hardening/softening. The numerical technique utilizes a hybrid finite element-sub-cell finite volume algorithm with a dynamic free-surface location, drawing upon a fractional-staged predictor-corrector semi-implicit time-stepping procedure of an incremental pressure-correction form. The numerical solution is investigated following a systematic study which allows for parametric variation in elasticity (We-variation), extensional hardening-softening (ε), and solvent fraction (β). Under incompressible flow conditions, linear PTT (LPTT) and exponential PTT (EPTT) models were used to solve the paint strip coatings, under reverse roll-coating configuration. This involves two-dimensional planar reverse roll-coating domains, considering a range of Weissenberg numbers (We) up to critical levels, addressing velocity fields and vortex development, pressure and lift profiles, shear rate, and stress fields. Various differences are observed when comparing solutions for these constitutive models. Concerning the effects of elasticity, increase in We stimulates vortex structures, which are visible at both the downstream meniscus and upstream narrowest nip region, whilst decreasing the peak pressure and lift values at the nip constriction. At low values (ε > 0.5, β = 0.1) of extensional viscosity, the LPTT flow fields were much easier to extract, attaining critical We levels up to unity, in contrast to critical We levels of 0.4 for EPTT solutions. This finding is reversed at higher extensional viscosity levels (ε < 0.5). This trend reveals qualitative agreement with theoretical studies. Noting flow behaviour under EPTT solution, increasing the peak level of strain hardening/softening is found to stimulate vortex activity around the nip region, with a corresponding increase in peak pressure and lift values.     

Extension of the line element-less method to dynamic problems

Meccanica - The line element-less method is an efficient approach for the approximate solution of the Laplace or biharmonic equation on a general bidimensional domain. Introducing generalized...     

A cohesive plastic and damage zone model for dynamic crack growth in rate-dependent materials

Mode I steady-state dynamic crack growth in rate-dependent viscoplastic solids containing damage, under small scale yielding conditions, is analyzed based on a modified cohesive zone model. A multi-scale approach is used to describe the entire non-linear zone consisting of a plastic region and a damage region, each of which has its own constitutive law. Traction in the damage region is characterized by a softening power-law, in terms of the ultimate strength, a softening index and a rate sensitivity factor. In the plastic region, the cohesive law is assumed to be both strain hardening and rate dependent. The critical crack opening displacement at the physical crack-tip controls crack growth. The governing integral equations are derived and solved by a collocation method combined with associated boundary conditions. Numerical results are presented for the traction and opening profiles along the cohesive zone, the fracture energy and lengths of the damage and non-linear zones at different crack speeds and for different material parameters. The importance of factors, such as material softening, plastic deformation, crack speed and viscosity, is identified by parametric studies. In addition, the competition of plastic flow and material damage, and its effect on crack growth, are discussed.     

梁柱简化模型在自立塔塔线体系动态响应中的适用性研究

对输电塔进行合理简化可以提高塔线体系动力学仿真的效率。本文给出自立塔梁柱简化模型的计算方法,并提出利用梁柱简化模型计算方法建立自立塔塔线体系整体模型,同时采用桁梁混合模型建立精细化塔线体系整体模型,对两种模型塔线体系静力特性及振型和固有频率等动力特性进行对比分析。以脱冰工况为例,采用生死单元技术将施加在输电线节点上的集中质量单元杀死来模拟脱冰,实现对塔线体系动力学响应的有限元模拟,研究塔线体系简化模型在动态响应中的适用性。结果表明,两种模型弯曲变形误差小,低阶的振型相同,固有频率值误差小,动力特性基本相同;脱冰工况下,自立塔节点位移和塔材内力时程曲线一致,在提高计算效率的情况下,能有效保证计算精度。     

Deformations and Stresses in Dried Wood

The deformations and the evolution of drying-induced stresses in wood are studied based on a model which takes into account the alteration of mechanical properties of wood in the course of drying. A two-dimensional initial-boundary value problem is solved with the help of the finite element method. An influence of wood anisotropy on the deformation and the stress distributions and evolution of maximal stresses is analysed.     

Stresses and momenta in electromagnetic materials

The notion of energy–momentum, or energy–stress, pertains typically to electromagnetism. Eshelby transferred such a notion into elasticity in 1951 and, afterward, into continuum mechanics, in order to account for the force acting on a material defect. Similarities and differences between the Maxwell tensor of electromagnetism and the Eshelby tensor are shown and commented hereby. Basing on a Lagrangian approach to electromagnetic materials, canonical momenta are shown to emerge in a natural way. On the basis of these canonical quantities, one can introduce the material momentum (or pseudomomentum) along with the classical momentum and the material stress (Eshelby stress) along with the Maxwell stress, which is a Cauchy-like stress.     

血管的应力和零应力位形

针对切开血管段得到的零应力位形，引入包括张开角在内的四个几何参数表示从零应力位形到完整血管的几何变换，按弹性物体有限变形的原理，采用Mooney—Rivlin物质模型，讨论所引入参数与血管中应力，压力和轴向力的定量关系。     

Singularities of meniscus at the V-shaped edge

An understanding of the capillary rise of the meniscus formed on the V-shaped fibers is crucial for many applications. We classified the cases when the meniscus cannot be smooth by analyzing the local behavior of the solutions to the Laplace equation of capillarity near the sharp edge. The V-angle and two contact angles that the meniscus forms on two chemically different sides of the fiber form a 3D phase space. Smooth menisci constitute a special domain in this 3D space. The constructed diagram allows one to separate the solutions with smooth and non-smooth menisci. The obtained criteria were illustrated using chemically inhomogeneous plates, blades, square corners, and Janus V-shaped edges.     

Solution of the Three-Dimensional Thermoelastic Problem in Stresses

A method is proposed for constructing a general solution to the three-dimensional thermoelastic equations in stresses (compatibility conditions and equilibrium equations). This general solution is valid for both an elastic half-space and an elastic layer. The second thermoelastic boundary-value problem for a half-space is studied in detail as an example     

岩石爆破破碎能耗随抵抗线的变化规律

针对爆炸荷载下岩体破碎块度和有用功能耗及能耗利用率问题,运用断裂力学、分形基础理论分析和模型实验等方法,对爆炸荷载下岩体破碎块度和能耗利用率随最小抵抗线的变化规律开展了系统的分析研究。研究结果表明:在模型实验条件下,破碎块度分形维数在1.2～1.7之间,随最小抵抗线增大呈现较好的线性衰减趋势;破碎能耗随最小抵抗线呈现先增加后降低的趋势,爆炸能量利用率在4.57%～12.51%之间,趋势与能耗值一致,模型实验中能耗利用率存在最大值;破碎块度与能耗利用率变化趋势相反,说明在最小抵抗线变化过程中存在一个最佳值,使得破碎块度和能耗利用率均处于最优状态,模型实验中这一最佳值为160 mm,是装药直径的26.7倍。该研究结果可为提高爆炸能利用率理论分析及工程中降低大块率的设计和施工提供理论依据。     

Change in the electrical resistance of the friction zone of metal composites with the addition of a Pb-Sn melt

Volt-ampere characteristics of the sliding zone of steel-base metal composites in a current collection mode are presented. Friction is implemented at a current density of 100 A/cm² for the cases of absence and presence of a Pb-Sn melt in the friction zone. An elementary model of rough surface contact is proposed to assess the relation between the area occupied by the melt and the current density. It is shown that the addition of molten low-melting metals is an effective way to reduce the electrical resistance of the friction zone of sliding electrical contact.     

Analytical dynamic displacement response of rigid pavements to moving concentrated and line loads

This paper presents the formulation of a plate of infinite dimensions (without boundary conditions) on an elastic foundation, subjected to a moving concentrated and line load of constant amplitude and speed, using a triple Fourier transform. The solution is carried out integration by residues. A closed-form solution of displacement field has been obtained for a moving load with subsonic, transonic and supersonic speeds. It is found that the maximum response of the slab occurs beneath the moving load and travels with the load at the same speed. It is also shown that a critical speed exists. If the moving load travels at critical speed, slab displacement becomes infinite in amplitude.     

Asymptotic Analysis of the Stresses in Thin Elastic Shells

. In this paper, we identify the limiting stress tensor of a thin elastic shell whose thickness approaches zero. In the linear case, we use a convergence result established for the displacement field in order to get the convergence of the contravariant components of the linearised stress tensor. In the nonlinear case, the identification of the first Piola‐Kirchhoff stress tensor is made through a formal asymptotic analysis. In both cases, we show that these limiting stress fields depend on the geometry of the shell and on the boundary conditions. (Accepted June 1, 1998)