A material force method for inelastic fracture mechanics

A material force method is proposed for evaluating the energy release rate and work rate of dissipation for fracture in inelastic materials. The inelastic material response is characterized by an internal variable model with an explicitly defined free energy density and dissipation potential. Expressions for the global material and dissipation forces are obtained from a global balance of energy-momentum that incorporates dissipation from inelastic material behavior. It is shown that in the special case of steady-state growth, the global dissipation force equals the work rate of dissipation, and the global material force and J-integral methods are equivalent. For implementation in finite element computations, an equivalent domain expression of the global material force is developed from the weak form of the energy-momentum balance. The method is applied to model problems of cohesive fracture in a remote K-field for viscoelasticity and elastoplasticity. The viscoelastic problem is used to compare various element discretizations in combination with different schemes for computing strain gradients. For the elastoplastic problem, the effects of cohesive and bulk properties on the plastic dissipation are examined using calculations of the global dissipation force.     

Assessment of effect of heat of internal friction on characteristics of structured flow of viscoplastic liquid in a round tube

A structured pressure flow of viscoplastic liquid in an infinite round tube is examined. Energy dissipation is given due consideration; it is assumed that the temperature dependences of the plastic viscosity and the ultimate shear stress are exponential. The solution obtained when the parameter characterizing the rate of production of heat of internal friction is assumed to be small indicates that energy dissipation has a sgnificant effect on the local flow characteristics and the hydraulic-resistance coefficient, for which an expression suitable for engineering calculations is given.     

基于能量耗散分析的混凝土随机疲劳损伤模型

基于微-细观随机断裂模型(MMSF)发展了一类混凝土随机疲劳损伤模型。该模型将MMSF中的微弹簧视为一能量耗散单元并考察了其跨尺度的能量耗散过程。在纳观尺度,引入速率过程理论描述裂纹的扩展速度,并基于裂纹层级模型和自相似假定完成从纳观尺度到微观尺度的过渡。由此建立了微弹簧在疲劳荷载作用下的多尺度耗能描述。此外,为了考虑疲劳加载中混凝土多条裂纹的相互影响,引入了包含损伤扩展效应和损伤愈合效应的疲劳损伤因子来修正耗能表达。通过与相关试验的对比,证明了该模型能反映疲劳荷载作用下混凝土的主要力学行为,如疲劳损伤三阶段特点、疲劳寿命的离散性和疲劳寿命随加载频率的变化趋势等。     

On multiscale significance of Rice’s normality structure

The normality structure proposed by [Rice, J.R., 1971. Inelastic constitutive relations for solids: an integral variable theory and its application to metal plasticity. J. Mech. Phys. Solids 19, 433–455.] provides a minimal framework of multiscale thermodynamics. As shown in this paper, Rice’s multiscale thermodynamic formalism is exactly consistent with Ziegler’s essential notion [Ziegler, H., 1977. An Introduction to Thermomechanics, North-Holland, Amsterdam.] that the entire constitutive response is determined by the knowledge of two scalar potential functions: an energy function and a dissipation function. In Rice’s multiscale thermodynamic formulation, the variational equation relating macroscale and microscale thermodynamic fluxes and forces plays a central role and ensures the equality between microscale and macroscale dissipation rate. The variational equation can be further reformulated into a principle of maximum equivalent dissipation. Based on the variation equation, the transformation from microscale to macroscale is characterized by two linear transformations with the same corresponding matrix.     

Dynamic symmetry breaking and structure-preserving analysis on the longitudinal wave in an elastic rod with a variable cross-section

The longitudinal wave propagating in an elastic rod with a variable cross-section owns wide engineering background, in which the longitudinal wave dissipation determines some important performances of the slender structure. To reproduce the longitudinal wave dissipation effects on an elastic rod with a variable cross-section, a structure-preserving approach is developed based on the dynamic symmetry breaking theory. For the dynamic model controlling the longitudinal wave propagating in the elast...     

Reynolds number dependence of the inertial range scaling of energy dissipation rate and enstrophy in a cylinder wake

The full energy dissipation rate and enstrophy are measured simultaneously using a probe consisting of four X-wires in the intermediate region of a cylinder wake for Taylor microscale Reynolds number in the range of 120–320. Longitudinal and transverse velocity increments are also obtained temporally using Taylor’s hypothesis. The inertial range scaling exponents indicate that the full enstrophy field has a stronger intermittency than does the full dissipation field for all the Reynolds numbers considered. The approximations of the energy dissipation rate and enstrophy based on isotropy are more intermittent than their corresponding true values. While the scaling exponents of the full energy dissipation rate remain approximately constant for different Reynolds numbers, those of the enstrophy decrease slightly and consistently with the increase of Reynolds number. It is conjectured that the scaling of the energy dissipation rate and the enstrophy may be the same when Reynolds number is extremely high, a trend that is consistent with that suggested by Nelkin (Phys Fluids 11:2202–2204, 1999; Am J Phys 68:310–318, 2000).     

Generalization of the Stefan model to allow for both velocity and temperature jumps

We obtain an expression for the energy dissipation due to an evolving nonmaterial interface across which the mass density, velocity, stress, energy density, heat flux, entropy density, and temperature may be discontinuous. This expression is a sum of three terms: the product of the interfacial mass flux with the interfacial energy release; the scalar product of the interfacial velocity slip with the interfacial friction; and, the product of the interfacial temperature jump, scaled by the interfacial temperature average, with the interfacial heating. When the surface in question is a phase interface, we propose, on the basis of the interfacial dissipation inequality, supplemental relations that determine the interfacial energy release, the interfacial friction, and the interfacial heating constitutively as functions of the interfacial mass flux, the interfacial velocity slip, and the scaled interfacial temperature jump. As a step toward an understanding of the role that such interfacial relations may serve in theories for phase transitions, we investigate a problem involving the solidification of a pure substance in the absence of flow. Received February 17, 1999     

一类平衡大气边界层边界条件研究

基于标准k-ε湍流模型,首先利用湍流粘度方程和剪切应力在整个边界层内恒定的假设,推导出一类耗散率表达式,并根据常用的湍动能入口剖面方程以及平均风速剖面方程,计算获得相应的耗散率方程;然后在输运方程中添加自定义源项,通过已经确定的平均速度方程、湍动能方程、耗散率方程计算得到相应输运方程的自定义源项表达式,并进行空风洞数值模拟,从而得到了一类满足平衡大气边界层的来流边界条件．通过将这种边界条件与由湍流平衡条件得到的边界条件进行比较,表明本方法获得的边界条件更适用．并且,本方法无需考虑修正壁面函数和修正湍流模型常数,因而计算更为简单,可为平衡大气边界层的研究提供一种新的思路．     

Arbitrary normal stress data and a fluid of differential type

A fairly simple generalization of the grade 2 fluid is described. However, unlike the grade 2 fluid, this fluid of differential type can accomodate extremely general viscometric data and still be consistent with commonly held ideas of energy dissipation and stability.     

Development of an approach to constitutive modelling of concrete: Isotropic damage coupled with plasticity

The paper presents an approach to constitutive modelling of concrete using damage mechanics and plasticity theory. The thermodynamic formulation, and parameter identification of a non-local coupled damage-plasticity model are presented in this study. The particular focus is the calibration of model parameters. It is shown that both the local parameters and the parameters governing the non-local interaction can be determined from experimental data reliably and consistently. A novel procedure is developed for parameter identification, using the separation of total dissipation energy into additive parts corresponding to different dissipation mechanisms. The relationship between the local and non-local parameters is also addressed, helping to obtain model responses consistent with the fracture energy of the material. The application of the model and the calibration procedure proposed in this study to the numerical failure analysis of concrete structures is illustrated through a series of real structural tests, showing both the performance of the model and the consistency of the proposed calibration procedure.     

基于胡聿贤谱的带支撑广义Maxwell阻尼隔震结构随机响应分析

工程中通过设置支撑将阻尼器和建筑结构连接, 但常为了简化分析, 将支撑的水平刚度看成无穷大, 即不考虑支撑对耗能结构随机地震响应的影响. 实际上, 考虑有限水平刚度的支撑对耗能结构响应的影响更加符合工程实际, 为考虑支撑影响的广义Maxwell耗能隔震结构在胡聿贤谱地震激励下的响应分析, 提出一种求解随机地震响应的简明解析解法. 将带支撑广义Maxwell阻尼器等效本构关系、隔震结构运动方程以及胡聿贤谱滤波方程联合组成非经典阻尼系统, 运用复模态法对该非经典阻尼系统解耦, 通过不同响应模态获得耗能隔震系统系列响应基于白噪声激励的Duhamel积分表达式; 利用Dirac函数的性质, 将系统系列响应协方差简化为无积分运算的表达式, 根据功率谱密度函数与其协方差函数的Wiener-Khinchin关系, 得到耗能隔震系统系列响应功率谱和地面加速度功率谱, 基于随机振动理论中谱矩的定义, 得到耗能隔震系统系列响应0 ~ 2阶谱矩. 算例通过与虚拟激励法对比分析, 验证所提方法在该耗能隔震系统分析的正确性和高效性, 并讨论了不同支撑刚度对阻尼器减震效果的影响.      

Models for one-variant shape memory materials based on dissipation functions

Some simple models for the macroscopic behavior of shape memory materials whose microstructure can be described as a mixture of two phases are derived on the basis of a free energy and a dissipation function. Keeping a common expression for the free energy, each model is based on a different expression for the dissipation function. Temperature-induced as well as isothermal, adiabatic and convective stress-induced transformations are studied. Attention is paid to closed form solutions, comparison among the models and parameter identification.     

A study on the behaviour of high-order flux reconstruction method with different low-dissipation numerical fluxes for large eddy simulation

This work focuses on the numerical dissipation features of high-order flux reconstruction (FR) method combined with different numerical fluxes in turbulence flows. The famous Roe and AUSM+ numerical fluxes together with their corresponding low-dissipation enhanced versions (LMRoe, SLAU2) and higher resolution variants (HR-LMRoe, HR-SLAU2) are incorporated into FR framework, and the dissipation interplay of these combinations is investigated in implicit large eddy simulation. The numerical dissipation stemming from these convective numerical fluxes is quantified by simulating the inviscid Gresho vortex, the transitional Taylor–Green vortex and the homogenous decaying isotropic turbulence. The results suggest that low-dissipation enhanced versions are preferential both in high-order and low-order cases to their original forms, while the use of HR-SLAU2 has marginal improvements and the HR-LMRoe leads to degenerated solution with high-order. In high-order the effects of numerical fluxes are reduced, and their viscosity may not be dissipative enough to provide physically consistent turbulence when under-resolved.     

Comparison of the time-temperature superposition of the relaxation modulus and time-to-break of preswollen gels

This paper describes the work carried out to investigate the pore pressures occurring in secondary consolidation. A theoretical approach and an experimental technique was developed in order to conduct the study. By considering compression to occur only due to water leaving the soil it was possible to derive an expression for the dissipation of pore pressure in the secondary phase. By further simplified assumptions which are based on experimental observations, the above general solution was reduced to a simple formula which predicted the observed behaviour of pore water pressures during secondary consolidation.     

Extension du modèle d'échelles mixtes à la diffusivité de sous-maille

In the large-eddy simulation frame for non-isothermal turbulent flow, the Mixed Scale Model is extended to the subgrid diffusivity, in order to dissociate the computation of subgrid viscosity and diffusivity. The identification of the subgrid thermal dissipation term in the subgrid flux transport equation leads to an algebraic expression of the subgrid diffusivity. This diffusive model, as the Smagorinsky one, is weighted by a model based on scale similarity. This expression leads to satisfactory results when applied to a buoyant turbulent flow in a differentially heated cavity.     

A new thermodynamically consistent continuum model for hardening plasticity coupled with damage

A phenomenological model for hardening–softening elasto-plasticity coupled with damage is presented. Specific kinematic internal variables are used to describe the mechanical state of the system. These, in the hypothesis of infinitesimal changes of configuration, are partitioned in the sum of a reversible and an irreversible part. The constitutive equations, developed in the framework of the Generalised Standard Material Model, are derived for reversible processes from an internal energy functional, postulated as the sum of the deformation energy and of the hardening energy both coupled with damage, while for irreversible phenomena from a dissipation functional.Performing duality transformations, the conjugated potentials of the complementary elastic energy and of the complementary dissipation are obtained. From the latter a generalised elastic domain in the extended space of stresses and thermodynamic forces is derived. The model, which is completely formulated in the space of actual stresses, is compared with other formulations based on the concept of effective stresses in the case of isotropic damage. It is observed that such models are consistent only for particular choices of the damage coupling. Finally, the predictions of the proposed model for some simple processes are analysed.     

The fluid hopkinson bar

Experiments in which pressure pulses are propagated in a column of fluid held in a stiff tube are described. A parameter, η, which characterizes the tube stiffness has been defined and a one-dimensional model of the wave propagation which includes dissipation both in the volume of the fluid and at the wall of the containing tube has been developed. It is found that dissipation at the wall dominates dissipation in the fluid volume for pulse lengths long compared to the tube radius. The experimental results delineate practical limits on the ratio of pulse length to tube radius for which the wave propagation can be characterized as one-dimensional. The validity of a one-dimensional representation of pulse transmission and reflection at a solid-fluid interface is also evaluated with the aid of experimental results. Finally, the dissipation model in combination with the experimental results leads to a simple expression for pressure pulse attenuation in terms of a nondimensional physical parameter, Ξ, and tube radius.     

A generalized Brinkman number for non-Newtonian duct flows

When viscous dissipation effects are important in duct flows the Brinkman number is widely used to quantify the relationship between the heat generated by dissipation and the heat exchanged at the wall. For Newtonian laminar fully developed pipe flow the use of the classical expression for this dimensionless group is appropriate, but under different conditions it can lead to misleading conclusions, such as when comparing flows through different cross-section ducts, flow regimes and mainly non-Newtonian flows. In this work a generalized Brinkman number is proposed, based on an energy balance for the power dissipated by friction, that allows proper quantification of viscous heating effects and reduces to the classical definition in laminar Newtonian pipe flow. The advantages of the new definition are shown and expressions are given for generalized Brinkman numbers in the most common cases.