Introduction to asymmetric continuum: dislocations in solids and extreme phenomena in fluids

We present a new approach to the continuum theories: for solids, our version includes the asymmetric stresses, symmetric strains and antisymmetric rotations, while for fluids we take the similar assumptions but related to the respective time rates of these fields. We consider the constitutive relations and the balance laws: those related to the antisymmetric stresses are equivalent and substitute the required relations for the angular moment; a similar approach with rates of these fields is applied for fluids. The stress-dislocation relations are derived and the role of rotation motions in the fracture processes in solids is studied. A new theory of the extreme motion phenomena in fluids is developed.     

Transport in fracture processes: Fragmentation and slip

We present a new development in the asymmetric continuum theory with the shear oscillations (twist motions) and independent spin; these motions (displacement velocities and spin) can be shifted in phase to describe the independent rebound processes. Our approach provides an extension of the asymmetric continuum theory by including the microfragmentation processes with a double transport which may appear in an advanced fracture process under very high load. The related nonlinear equations, leading to soliton solutions, are derived.     

Asymmetric continuum and anisotropy

We present a relation between stress moments and antisymmetric part of stresses and the related constitutive law joining those stresses with the particle/point rotations. Correspondence of the asymmetric continuum theory to the micromorphic theory is considered. An extension of the asymmetric continuum theory for the case of 2D anisotropy for antisymmetric stresses leads us to the problems of friction anisotropy and fracture pattern.     

Symmetropy of earthquake patterns: asymmetry and rotation in a disordered seismic source

We demonstrate that the idea of symmetropy can be used for quantification of earthquake patterns. The symmetropy can be considered as a measure of asymmetry. A pattern is richer in asymmetry when the symmetropy is smaller. The specific results of its applications are obtained as follows. In a discrete model of a seismic source with self-organized criticality, the spatial patterns of earthquakes during critical states and sub-critical states are distinguished by the behaviour of the symmetropy: sub-critical patterns show that the symmetropy is approximately a constant but this has various values during critical states. The critical patterns show asymmetric property without any asymmetric force from the outside and without asymmetric intracellular rule. We show that the emergence of asymmetric patterns is a generic feature of dynamic ruptures in our model. Such a generic asymmetry results from the model which is an inherently discrete system consisting of finite-sized cells. These cells may represent geometrical disordered fault zones. We further discuss rotational motions that generate seismic rotational waves. In micromorphic continuum theory, such rotations are attributed to dynamic ruptures in disordered systems. We note that the concept of disorder in this theory is expressed by a set of finite-sized microstructures and is consistent with the concept of disorder modelled in the present study. Thus, we suggest that the spatially asymmetric patterns of earthquakes might be related to the rotational motions, because both come from dynamic ruptures in a discrete fault zone without a well-defined continuum limit.     

Fluid theory with asymmetric molecular stresses: Difference between vorticity and spin equations

We present a new development in fluid theory, incorporating into it the velocity and spin fields; special attention is given to the structure of transport.The theory includes asymmetric molecular stresses and independent rotation velocity, i.e., spin. Our approach is based on our former studies on the asymmetric continuum theory with the balance and constitutive laws for displacement velocity and independent rotation motion, and points out the role of a related characteristic length unit. It is assumed that the vorticity caused by velocities can induce a spin transport counterpart. Thus, under certain conditions, an additional transport term due to rotational velocity fields may be incorporated to the velocity transport, which may lead to the vortex fields included directly into the theory.     

Edge-driven convection

We consider a series of simple calculations with a step-function change in thickness of the lithosphere and imposed, far-field boundary conditions to illustrate the influence of the lithosphere on mantle flow. We consider the effect of aspect ratio and far-field boundary conditions on the small-scale flow driven by a discontinuity in the thickness of the lithosphere. In an isothermal mantle, with no other outside influences, the basic small-scale flow aligns with the lithosphere such that there is a downwelling at the lithospheric discontinuity (edge-driven flow); however, the pattern of the small-scale flow is strongly dependent on the large-scale thermal structure of a much broader area of the upper mantle. Long-wavelength temperature anomalies in the upper mantle can overwhelm edge-driven flow on a short timescale; however, convective motions work to homogenize these anomalies on the order of 100 million years while cratonic roots can remain stable for longer time periods. A systematic study of the effect of the boundary conditions and aspect ratio of the domain shows that small-scale, and large-scale flows are driven by the lithosphere. Edge-driven flow produces velocities on the order of 20 mm/yr. This is comparable to calculations by others and we can expect an increase in this rate as the mantle viscosity is decreased.     

混凝土动力本构模型的基础理论与建模应用综述

混凝土结构分析问题中动力荷载下混凝土的动力本构模型研究日益重要。为对建立混凝土动力本构关系的基础理论有系统的认知和了解其应用,对其进行了总结,简述了在建立混凝土动本构方面的应用,对混凝土动力本构模型的理论发展趋势作了展望。并对当前混凝土动力本构模型的应用做了概括评述,并指出了混凝土动力本构的可行研究方向,为建立混凝土动力本构模型提供指导。     

瑞利阻尼矩阵对深厚场地地震反应的影响分析

介绍场地时域分析基本理论和几种常见的阻尼矩阵确定方法,并基于有限差分方法,采用实际地震记录,考虑输入地震动强度和频谱特性,分别选择5种不同的瑞利阻尼矩阵形式,比较分析其对深厚场地时域动力反应的影响。结果表明:不同阻尼矩阵对加速度和反应谱均有影响,影响程度和输入地震动的频谱特性有关;当土层基频接近输入地震动卓越频率时,只根据土层基频确定阻尼矩阵是可行的,但当输入地震动卓越频率高于或远高于土层基频时,该方法会严重低估地表加速度峰值和反应谱谱值,时域分析中阻尼的确定应综合考虑土层特性和地震动频谱特性。     

Seismic analysis of two‐way asymmetric building systems under bi‐directional seismic ground motions

An approximation approach of seismic analysis of two‐way asymmetric building systems under bi‐directional seismic ground motions is proposed. The procedures of uncoupled modal response history analysis (UMRHA) are extended to two‐way asymmetric buildings simultaneously excited by two horizontal components of ground motion. Constructing the relationships of two‐way base shears versus two‐way roof translations and base torque versus roof rotation in ADRS format for a two‐way asymmetric building, each modal pushover curve bifurcates into three curves in an inelastic state. A three‐degree‐of‐freedom (3DOF) modal stick is developed to simulate the modal pushover curve with the stated bifurcating characteristic. It requires the calculation of the synthetic earthquake and angle β. It is confirmed that the 3DOF modal stick is consistent with single‐degree‐of‐freedom modal stick in an elastic state. A two‐way asymmetric three‐story building was analyzed by UMRHA procedure incorporating the proposed 3DOF modal sticks. The analytical results are compared with those obtained from nonlinear response history analysis. It is shown that the 3DOF modal sticks are more rational and effective in dealing with the assessment of two‐way asymmetric building systems under two‐directional seismic ground motions. Copyright © 2007 John Wiley & Sons, Ltd.     

从二维地转风到三维涡旋运动

给出了大气三维涡旋运动基本态所满足的简洁的偏微分方程. 大气涡旋运动存在低压辐合上升和高压辐散下沉的基本状况，基本态的三维速度场可以用流函数和对流速度势分解，且具有螺旋结构. 当Reynolds数Re→∞时，涡旋运动就化为地转风，涡旋运动近似就化为地转风近似.     

Perturbation theory in low rate seismology

Summary In the case of low frequency motions in an elastic continuum, first-order perturbation theory can be used to estimate the effect of real-world deviations from the ideal model. Although the effects are often small, some interesting results can be found fairly easily. In spite of the simplicity in the structure of the formalism, nontrivial applications lead to remarkably complicated results.     

Rotation and strain seismology

Asymmetric continuum theory points to the equal roles of the rotation motions and those related directly to shear or confining strains. The strain motions could be quite independent or mutually related with the eventual phase shifts, while the displacements have only a mathematical sense; a real displacement may appear along the fracture slip only. Formally, any deformation could be presented as related to the displacements; however, its origin in a fracture source should be considered either as belonging to an individual process or to complex correlated events; in these cases, the confining, shear and rotation strains can be related mathematically to the different displacement fields. Some of these related deformations could be emitted from a source with a phase shift, while the observed displacements (deduced from records) result as a sum of these independent displacements. An important influence on a source process and on the premonitory micro-events has the material defects, their distribution, and mobility. The defect arrays lead to a concentration of stresses and their local reorganization. Thus, in this paper, we consider the induced stresses and strains related to defect content and to its modification and redistribution. Moreover, an important role in understanding the complex correlated events in a source plays the release?Crebound mechanism. The release?Crebound mechanism in an earthquake source processes leads to a possible direct or phase-shifted correlations between the emitted motions; in this aspect, a propagation of the coupled strain and rotation waves is discussed. In particular, we consider the point fracture events as related either to a confining load or/and to the shear and rotation processes; we discuss the related effects and their meaning when discussing the fault plane mechanism and emitted waves. In some important seismic regions, we have the recording system which permits to record the strains and rotations. However, we should point that the wordwide seismological network is not adequate to record the complex strain deformations released in the fracture processes and remains quite insufficient to understand the global stress changes and related strain waves of a very low period. Consideration on a recording mechanism of the long displacement waves indicates the insufficiencies of the present global recording system and points that recording of the global strain and rotation waves is an important and urgent task.     

Validation of small strain properties from recorded weak seismic motions

During the last decade, there has been an increased interest in the computations of surface ground motions from known rock outcrop motions. The main advantage of the procedure is to allow for the actual variation of strength and stiffness properties of heterogeneous soil profiles, eventually accounting for non-linear soil behavior. The main questions raised against the adequacy of such a procedure lie upon the reliability of the computational scheme and in the representativity of the soil constitutive relationship. The present paper addresses both aspects by comparing the motions computed assuming standard assumptions in the state of practice of earthquake engineering. Since until now, the downhole array recorded only weak motions (horizontal peak ground accelerations smaller than 0·04 g), the paper focuses on elastic soil properties. It is demonstrated that a carefully conducted geotechnical survey yields an accurate shear wave velocity profile and that rate-independent soil damping might not be appropriate to represent the soil behavior in the small strain range.     

Bi‐directional coupled tuned mass dampers for the seismic response control of two‐way asymmetric‐plan buildings

This paper proposes bi‐directional coupled tuned mass dampers (BiCTMDs) for the seismic response control of two‐way asymmetric‐plan buildings subjected to bi‐directional ground motions. The proposed BiCTMD was developed from the three‐degree‐of‐freedom modal system, which represents the vibration mode of a two‐way asymmetric‐plan building. The performance of the proposed BiCTMD for the seismic response control of elastic two‐way asymmetric‐plan buildings was verified by investigating the reductions of the amplitudes of the associated frequency response functions. In addition, the investigation showed that the proposed BiCTMD is effective in reducing the seismic damage of inelastic asymmetric‐plan buildings. Therefore, the BiCTMD is an effective approach for the seismic response control of both elastic and inelastic two‐way asymmetric‐plan buildings. Copyright © 2010 John Wiley & Sons, Ltd.     

模拟地震的应变软化的数学模型

本文从弹塑性岩石介质的一般的本构方程出发,考虑断层介质内摩擦系数和内聚力随变形而降低的性质,建立了断层介质的非稳定的本构关系。这些关系可应用于承受任何应力的不同走向和倾角的断层。考虑到复杂的现代构造和非均匀应力场的背景,给出一个用能量表述的非稳定准则,用它来判断包含断层和围岩在内的整个系统的非稳定性的到来。最后按本文提出的模型用有限元方法对两个震例做了初步的分析。     

偶应力理论框架下的弹性波数值模拟与分析

在经典地震学理论框架下,先人发展了数不胜数的地震技术,为社会发展做出了巨大贡献;可是,当前的技术仍有难以逾越的障碍,亟需破局.高铁地震学联合研究组,在河北定兴采集到大量数据;其中可见含有大量的旋转运动分量.由于基于经典连续介质力学推导弹性波动方程时,从理论出发点上就去除了旋转项,且在其理论框架内,介质被视为一个连续的质量体.而事实上,不论是人造还是天然的介质都存在着复杂的内部结构,广义连续介质力学更适合描述具有更加复杂内部结构的情况.于是,我们尝试启用广义连续介质力学理论,推导偶应力理论框架下的弹性波动方程;将其数学表达形式以及数值模拟结果与传统弹性波动方程进行对比.研究探索推导的具非对称性的波动方程所具有的理论意义和应用价值.     

Equations for global monsoons and toroidal circulations in the σ-coordinate system

Summary In a coordinate system in which the ground is always a coordinate surface, climatic equations for axially asymmetric and symmetric atmospheric motions are derived. These are compared with their counterparts in the pressure coordinate system. Some qualitative predictions regarding solutions are given.     

Numerical modelling of bifurcation and localisation in cohesive-frictional materials

Methods are reviewed for analysing highly localised failure and bifurcation modes in discretised mechanical systems as typically arise in numerical simulations of failure in soils, rocks, metals and concrete. By the example of a plane-strain biaxial test it is shown that strain softening and lack of normality in elasto-plastic constitutive equations and the ensuing loss of ellipticity of the governing field equations cause a pathological mesh dependence of numerical solutions for such problems, thus rendering the results effectively meaningless. The need for introduction of higher-order continuum models is emphasised to remedy this shortcoming of the conventional approach. For one such a continuum model, namely the unconstrained Cosserat continuum, it is demonstrated that meaningful and convergent solutions (in the sense that a finite width of the localisation zone is computed upon mesh refinement) can be obtained.     

A generalized continuum method for dynamic analysis of asymmetric tall buildings

The paper presents a continuum method for dynamic analysis of asymmetric tall buildings with uniform cross-section in which the horizontal stiffness is provided by shear walls and columns of arbitrary shape and layout, coupled by horizontal beams. The equations of motions are formulated in variational terms, including axial strain energy. Numerical solutions, obtained by using finite time differences and infinite polynomials, are presented for the response of a twenty-storey building with six shear walls to an impact load and earthquake accelerations. It is shown that omission of the axial deformations results in a substantially distorted pattern of behaviour, some of its effects being:

• 1 Overestimation of the bending stiffness of the coupled shear walls, with corresponding changes in their stiffness ratios.
• 2 Underestimation of the periods of the principal modes, with a corresponding change in the dynamic response.
• 3 Distortion of the magnitude, form, time of onset and coupling of the maximum displacements.
• 4 Pronounced change in the shear force and moment diagrams for the shear walls, the beams and the building as a whole.