Renewal of basic laws and principles for polar continuum theories (Ⅺ)—consistency problems

Some consistency problems existing in continuum field theories are briefly reviewed.Three arts of consistency problems are clarified based on the renewed basic laws for polar continua.The first art discusses the consistency problems between the basic laws for polar continua.The second art discusses the consistency problems between the basic laws for polar continua and for other nonpolar continua.The third art discusses the consistency problems between the basic laws for micropolar continuum theories and the dynamical equations for rigid body.The results presented here can help us to get a deeper understanding the structure of the basic laws for various continuum theories and the interrelations between them.In the meantime,these results obtained show clearly that the consistency problems could not be solved in the framework of traditional basic laws for continuum field theories.     

A THEORY OF CLASSICAL SPACETIME (I)—FOUNDATIONS

Despite its beauty and grandeur the theory of GR still appears to be incomplete in thefollowing ways:(1)It cannot accommodate the asymmetric total energy momentum tensor whoseasymmetry has been shown to exist in the presence of electromagnetism.(2)The law of angular momentum balance as an exact equation is not an automaticconsequence of the field equations as is the case with the law of linear momentum balance.(3)The four degrees of arbitrariness left by the contracted second Bianchi identitymakes a unique solution of the field equations unattainable without extra (unphysical)postulates.To answer the challenge posed by the above assertions we propose in this paper tocomplete Einstein’s theory by postulating the principle fibre bundle P[M,SU(2)]for theunderlying geometry of the 4-dimensional spacetime,where the structre group SU (2) isthe real representation of the special complex unitary group of dimension 2. SU (2) leavesconcurrently invariant the metric form dS~2=g_(αβ)dx~αdx~β and the fundamenta     

Fourier-based incremental homogenisation of coupled unilateral damage–plasticity model for masonry structures

In structural analysis of large masonry structures, nondemanding computation effort, numerical stability and simplified model assembly and meshing often have a higher priority over precise details of local stress or strain responses. This paper presents the development of a Fourier-based incremental homogenisation technique, where the macro–micro transformations of mechanical variables are derived by incremental variational problems to minimise the potential energy in representative volume elements (RVEs) with respect to local fluctuating displacement fields expanded in Fourier series. In addition to the proposed homogenisation technique, a unilateral damage–plasticity constitutive model for mortar joints in the RVE is developed within the framework of thermomechanics, which accounts for the stiffness and strength degradation (or recovery) due to the transverse crack opening/closing in the mortar joints. The numerical solution for the homogenisation problem and the performances of the proposed coupled-damage plastic mode and Fourier-based homogenisation scheme verified by detailed case studies are presented. It has been shown that the computational effort of the analysis with the proposed modelling technique can be considerably reduced by more than 20% as compared with that of the discrete modelling technique.     

Excitation management of (2+1)-dimensional breathers for a coupled partially nonlocal nonlinear Schrödinger equation with variable coefficients

Nonlinear Dynamics - The Akhmediev-breather and Ma-breather solutions of a (2+1)-dimensional variable-coefficient coupled partially nonlocal nonlinear Schrödinger equation with non-localized...     

Development of a fully Lagrangian MPS-based coupled method for simulation of fluid–structure interaction problems

A fully Lagrangian particle-based method is developed for simulating the FSI (Fluid–Structure Interaction) problems corresponding to incompressible fluid flows and elastic structures. First, the developed elastic structure model is verified by static and dynamic tests corresponding to a simple cantilever beam. The simulation results are compared with analytical and other researchers׳ numerical solutions. Then, the structure model is carefully coupled with a fluid model comprising of the so-called PNU-MPS (Pusan-National-University-modified Moving Particle Simulation) method and several recently developed enhanced schemes. The coupled fluid–structure method is applied to a dam break with an elastic gate and a violent sloshing flow with a hanging rubber baffle. The results of simulations are compared with those of the experiments by Antoci et al. (2007) and Idelsohn et al. (2008).     

A rheological equation for anisotropic–anelastic media and simulation of field seismograms

In many cases, geological formations are composed of layers of dissimilar properties whose thicknesses are small compared to the wavelength of the seismic signal, as for instance, a sandstone formation that has intra-reservoir thin mudstone layers. A proper model is represented by an anisotropic (transversely isotropic) and viscoelastic stress–strain relation. In this work, we consider a sandstone reservoir, such as the Utsira formation, saturated with CO₂ and use White’s mesoscopic model to describe the energy loss of the seismic waves. The mudstone layers are assumed to be isotropic, poroelastic and lossless. Then, Backus averaging provides the complex and frequency-dependent stiffnesses of the transversely isotropic (TI) long-wavelength equivalent medium. We obtain the associated wave velocities and quality factors as a function of frequency and propagation direction, while the synthetic seismograms are computed with a finite-element (FE) method in the space-frequency domain. In this way, the frequency-dependent properties of the medium are modeled exactly, without the need of approximations with viscoelastic mechanical models. Numerical simulations of synthetic seismograms show results in agreement with the predictions of the theories and significant differences due to attenuation and anisotropic effects compared to the ideal isotropic and lossless rheology.     

Investigation of calculation method for anti-penetration of reactive power steel fiber concrete (RPC)

为了解决评估超高强活性粉末钢纤维混凝土的抗侵彻能力问题，根据混凝土在弹体侵彻过程中的介质状态及能量的分配关系，揭示了侵彻近区耗散能量结构与破碎区之间的比例尺度关系。由于近区介质的运动特性变形接近一维应变状态，受力类似于流体动力学状态，据此推导并简化了具有宽广的适用范围的侵彻计算公式，认为侵彻的深度主要由弹体的质量、形状、速度及靶体的强度、密度、断裂韧度、变形波速决定。通过多次的实弹试验，验证了公式的可靠性，得到了RPC的抗侵彻能力是普通混凝土的3倍的结论。     

A coupled model for simulation of the gas–liquid two-phase flow with complex flow patterns

A new model coupling two basic models, the model based on interface tracking method and the two-fluid model, for simulating gas–liquid two-phase flow is presented. The new model can be used to simulate complex multiphase flow in which both large-length-scale interface and small-length-scale gas–liquid interface coexist. By the physical state and the length scale of interface, three phases are divided, including the liquid phase, the large-length-scale-interface phase (LSI phase) and the small-length-scale-interface phase (SSI phase). A unified solution framework shared by the two basic models is built, which makes it convenient to perform the solution process. Based on the unified solution framework, the modified MCBA–SIMPLE algorithm is employed to solve the Navier–Stokes equations for the proposed model. A special treatment called “volume fraction redistribution” is adopted for the special grids containing all three phases. Another treatment is proposed for the advection of large-length-scale interface when some portion of SSI phase coalesces into LSI phase. The movement of the large-length-scale interface is evaluated using VOF/PLIC method. The proposed model is equivalent to the two-fluid model in the zone where only the liquid phase and the SSI phase are present and to the model based on interface tracking method in the zone where only the liquid phase and the LSI phase are present. The characteristics of the proposed model are shown by four problems.     

An enhanced beam-theory model of the mixed-mode bending (MMB) test—Part I: Literature review and mechanical model

The paper presents a mechanical model of the mixed-mode bending (MMB) test used to assess the mixed-mode interlaminar fracture toughness of composite laminates. The laminated specimen is considered as an assemblage of two sublaminates partly connected by an elastic–brittle interface. The problem is formulated through a set of 36 differential equations, accompanied by suitable boundary conditions. Solution of the problem is achieved by separately considering the two subproblems related to the symmetric and antisymmetric parts of the loads, which for symmetric specimens correspond to fracture modes I and II, respectively. Explicit expressions are determined for the interfacial stresses, internal forces, and displacements.     

VECTOR ANALYSIS OF SPATIAL MECHANISMS——(Ⅲ) Kinematics of Spatial Mechanisms

The instantaneous kinematics for the spatial mechanismsconsidered in Parts1 and2 are established via straightfor-ward vector algebra.     

VECTOR ANAYLYSIS OF SPATIAL MECHANISM——(IV)Dynamics of Spatial Mechanisms

The standard dynamical problems of the previous four spatial mechanisms are here solved by the method of vector equations.The procedure is completely independent of the transfer matrices due to the changes of reference frame from one connecting pair to the next, as used by Yang and Bagci[1][2].     

Bubbles in liquids with phase transition—part 2: on balance laws for mixture theories of disperse vapor bubbles in liquid with phase change

We study averaging methods for the derivation of mixture equations for disperse vapor bubbles in liquids. The carrier liquid is modeled as a continuum, whereas simplified assumptions are made for the disperse bubble phase. An approach due to Petrov and Voinov is extended to derive mixture equations for the case that there is a phase transition between the carrier liquid and the vapor bubbles in water. We end up with a system of balance laws for a multi-phase mixture, which is completely in divergence form. Additional non-differential source terms describe the exchange of mass, momentum and energy between the phases. The sources depend explicitly on evolution laws for the total mass, the radius and the temperature of single bubbles. These evolution laws are derived in a prior article (Dreyer et al. in Cont Mech Thermodyn. doi:10.1007/s00161-0225-6, 2011) and are used to close the system. Finally, numerical examples are presented.     

ON LARGE DEFORMATION UNILATERAL CONTACT PROBLEM WITH FRICTION (I)—INCREMENTAL VARIATIONAL EQUATIONS

Based on the theory and technique of nonlinear geometric field theory of continuum, a more general incremental variational equation for elastic and plastic large deformation in co-moving coordinate is established in this paper. An expression for two and three-dimensional continua is derived, and the incremental variational equation for large deformation of changing boundary contact and the variational inequality in rate form are obtained, which provides the theoretical basis for the computation of elastic-plastic large deformation contact problem with friction.     

ON THE STABILITY OF DISTORTED LAMINAR FLOW (I)—BASIC IDEAS AND THEORY

This paper suggests a hydrodynamic stability theory of distorted laminar flow, and presents a kind of distortion profile of mean velocity in parallel shear flow. With such distortion profiles, the new theory can be used to investigate the stability behaviour of parallel shear flow, and thus suggests a new possible approach to instability. The Project Supported by National Natural Science Foundation of China.     

A Gurson-type criterion for porous ductile solids containing arbitrary ellipsoidal voids—I: Limit-analysis of some representative cell

Gurson (1977)'s famous model of the behavior of porous ductile solids, initially developed for spherical cavities, was extended by Gologanu et al., 1993, Gologanu et al., 1994, Gologanu et al., 1997 to spheroidal, both prolate and oblate voids. The aim of this work is to further extend it to general (non-spheroidal) ellipsoidal cavities, through approximate homogenization of some representative elementary porous cell. As a first step, we perform in the present Part I a limit-analysis of such a cell, namely an ellipsoidal volume made of some rigid-ideal-plastic von Mises material and containing a confocal ellipsoidal void, loaded arbitrarily under conditions of homogeneous boundary strain rate. This analysis provides an estimate of the overall plastic dissipation based on a family of trial incompressible velocity fields recently discovered by Leblond and Gologanu (2008), satisfying conditions of homogeneous strain rate on all ellipsoids confocal with the void and the outer boundary. The asymptotic behavior of the integrand in the expression of the global plastic dissipation is studied both far from and close to the void. The results obtained suggest approximations leading to explicit approximate expressions of the overall dissipation and yield function. These expressions contain parameters the full determination of which will be the object of Part II.