利用内聚力模型(CZM)模拟弹粘塑性多晶体的裂纹扩展

采用内聚力模型（CZM）,模拟多晶体中起裂于晶界的二维平面应变裂纹扩展．结果表明,弹粘塑性体中,初始裂纹尖端不会最先开裂．晶体本构的率敏感指数表征了塑性变形和内聚力区耗散两种机制的相互竞争．率敏感指数越大,塑性耗散能越大,内聚力区粘着能越小,使材料的塑性变形越容易,内聚力区诱发的破坏越不易;率敏感指数越小,材料响应越接近弹塑性性质,塑性耗散能减小,粘着能增大,外力功易转化为内聚力区的粘着能,使内聚力单元更易分离．增大内聚力区结合强度或临界张开位移使晶内和晶界的三轴应力度减小,即提高内聚力区韧性也使基体材料抗孔洞损伤能力提高．     

Heat transfer in a visco-elastic fluid past a stretching sheet with viscous dissipation and internal heat generation

This paper deals with the study of heat transfer characteristics in the laminar boundary layer flow of a visco-elastic fluid over a linearly stretching continuous surface with variable wall temperature subjected to suction or blowing. The study considers the effects of frictional heating (viscous dissipation) and internal heat generation or absorption. An analysis has been carried out for two different cases of heating processes namely: (i) Prescribed surface temperature (PST) and (ii) Prescribed wall heat flux (PHF) to get the effect of visco-elastic parameter for various situations. Further increase of visco-elastic parameter is to decrease the skin friction on the sheet. The solutions for the temperature and the heat transfer characteristics are obtained in terms of Kummers function. Received: June 16, 2004; revised: February 8, 2005     

On the interrelation between dissipation and chemical energies in modeling shape memory alloys

We use the principle of maximum dissipation for thermo-mechanically coupled modeling of poly-crystalline shape memory alloys (SMA). This modeling scheme demands approaches for both Helmholtz free energy and dissipation. For time-independent processes, dissipation is usually modeled by the norm of the internal variable's rate times a factor. We show that for SMAs this factor is not an additional modeling parameter. In contrast, it can be calculated from the Helmholtz free energy. This reduces the number of model parameters and provides furthermore an interesting effect of the model which allows to display the material behavior in an even more realistic manner. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Fracture Mechanics of Rubber Material

This contribution presents an approach based on the material force method which allows to evaluate the fracture sensitivity of rubber material. In order to account for the rate–independent dissipation of filled elastomers subjected to low rates, an endochronic plasticity formulation is introduced. It is shown how configurational forces under consideration of material body forces correspond with the elastic and dissipative energy and how they can be related to energy release rates measured in test configurations. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Rate-dependent incremental variational formulation of ferroelectricity

The paper presents continuous and discrete variational formulations for the treatment of the non-linear response of piezoceramics under electrical loading. The point of departure is a general internal variable formulation that determines the hysteretic response of the material as a generalized standard medium in terms of an energy storage and a rate–dependent dissipation function. Consistent with this type of standard dissipative continua, we develop an incremental variational formulation of the coupled electromechanical boundary value problem. We specify the variational formulation for a setting based on a smooth rate–dependent dissipation function which governs the hysteretic response. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Evolution of a regular precession of a solid body carrying a visco-elastic disk

The motion of inertia is studied of a system consisting of an axisymmetric solid body with fixed point and a homogeneous visco-elastic disk lying in the equatorial plane of the ellipsoid of inertia of the solid body (the center of disk coincides with the fixed point). In the case of a solid disk immobilized relative to the solid body the system accomplishes a regular precession (the case of Euler motion of a symmetric solid body with a fixed point /1/). The deformation of the disk is taking place in the plane of the disk, and is accompanied by energy dissipation is the cause of the regular precession finishing by steady rotation about the vector of the moment of momentum of the system /2/.     

Modeling and numerical simulation of multiscale behavior in polycrystals via extended crystal plasticity

The purpose of this work is to exploit the algorithmic formulation of models for multiscale inelastic materials whose behavior is influenced by the evolution of inelastic microstructure and the corresponding material or internal lengthscales. The models for extended crystal plasticity are based on the formulation of rate potentials whose form is determined by (i) energetic processes via the free energy, (ii) kinetic processes via the dissipation potential, and (iii) the form of the evolution relations for the internal-variable-like quantities upon which the free energy and dissipation potential depend. Examples for these latter quantities are the inelastic local deformation or dislocation densities as GNDs. Different algorithmic implementations are discussed, namely the algorithmic variational approach and the dual mixed approach. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Energy dissipation bounds for hear flows for a model in large eddy simulation

This report gives an upper bound for the time average of the energy dissipation rate, including energy dissipation due to viscous dissipation and turbulent diffusion in a model for the motion of large eddies in a turbulent flow. The bound is only a function of the reference velocity U, the domain diameter L, the eddy size δ, and surprisingly, the Reynolds number.     

Vibrocreep of polymer materials

The vibrocreep of low-density polyethylene (LDP) in uniaxial tension has been investigated in the presence of vibration in the direction of action of the constant load. The material was deformed under nonisothermal conditions owing to heating caused by the dissipation of vibrational energy. Superimposing vibrations leads to a considerable increase in creep rate. It is shown that this increase can not be explained solely in terms of the rise in temperature due to heating of the material; there is also a dynamic creep acceleration effect. Avariant of the vibrocreep approximation with allowance for the dynamic and temperature creep acceleration effects is proposed.Mekhanika Polimerov, Vol. 4, No. 3, pp. 413–420, 1968     

水动力-热动力学的极值定律

本文对水动力学和更普通性的连续介体动力学中以连续方程与运动方程所表达的现有诸经典守恒定律以外,提出另一最大能量消散率定律.这一定律的推论就是应用水力学中培纶格-波丝最小储存能学说. 凡在运动中消散了的机械能皆转化成为热能,储存在物体里.能量之消散当一定时刻一定温度都使产熵增加.所以,从最大能量消散率可引出热力学第二定律的一个新概念,即机械运动的产熵率也总是一个可能的最大值. 文中建议的这个连续介体极值定律,可从变分原理推导出来,重订热力学第二定律则可藉微观分析加以证明.两者合成水动力-热动力学极值定律     

剪切变形下非晶态高聚物的力学行为

基于非平衡态热力学理论，提出了一个适用于不可压材料的新的热粘弹性本构模型．该模型将橡胶弹性理论中的非高斯分子网络模型推广到计及粘性和热效应的情形．通过引入一组二阶张量形式的内变量，建议了一个新的Helmholtz自由能表达式，从而可以用来合理描述内变量的演化规律．根据以上模型，重点研究了热粘弹性材料在简单剪切变形下的力学行为，考察了由于分子链取向分布的变化而产生的“粘性耗散诱导”各向异性，讨论了应变率效应和由于粘性耗散而导致的热软化效应对剪应力的影响．理论预测结果与G’Sell等人的实验数据的定性比较表明了新的本构模型的有效性。     

Time and frequency domain finite element implementation of a fully anisotropic linear visco-elastic model

Consistent time and frequency domain formulations for a fully anisotropic, linear visco-elastic material model are presented. The finite element implementation leads to a complex valued stiffness matrix in the frequency domain. A homogenisation procedure based on unit-cell analyses in the frequency domain is presented to derive input parameters for the material model. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Higher-order energy consistent time integrators for nonlinear thermoviscoelastodynamics

An advantage of the temporal fe method is that higher-order accurate time integrators can be constructed easily. A further important advantage is the inherent energy consistency if applied to equations of motion. The temporal fe method is therefore used to construct higher-order energy-momentum conserving time integrators for nonlinear elastodynamics (see Ref. [1]). Considering finite motions of a flexible solid body with internal dissipation, an energy consistent time integration is also of great advantage (see the references [2, 3]). In this paper, we show that an energy consistent time integration is also advantageous for dynamics with dissipation arising from conduction of heat as well as from a viscous material. The energy consistency is preserved by using a new enhanced hybrid Galerkin (ehG) method. The obtained numerical schemes satisfy the energy balance exactly, independent of their accuracy and the used time step size. This guarantees numerical stability. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

一个关于流动能量耗散率的minimax变分原理

流动耗散率是湍流理论的核心概念之一．Doering-Constantin变分原理刻画了流动耗散率的上确界(最大值)．在该文的研究中,首先基于优化理论的视角,Doering-Constantin的变分原理被改写为一个不可压缩剪切流耗散率的minimax型的变分原理．其次,博弈论中的Kakutani minimax定理给出该变分原理中minimizing和maximizing计算过程可交换的一个充分条件．这个结果不仅从一个新的角度揭示了谱约束的内涵,也为Doering-Constantin变分原理和Howard-Busse统计理论的等价性从博弈论的角度提供了理论基础．     

On Energy Cascades in the Forced 3D Navier–Stokes Equations

We show—in the framework of physical scales and \((K_1,K_2)\)-averages—that Kolmogorov’s dissipation law combined with the smallness condition on a Taylor length scale is sufficient to guarantee energy cascades in the forced Navier–Stokes equations. Moreover, in the periodic case we establish restrictive scaling laws—in terms of Grashof number—for kinetic energy, energy flux, and energy dissipation rate. These are used to improve our sufficient condition for forced cascades in physical scales.     

Stable long-term simulation of dynamically loaded elastomers

A well–known problem in long–term simulations of flexible solid bodies is the restriction to small time steps of standard time integrators in order to obtain a stable simulation. One approach is to achieve exact energy conservation while simulating a nonlinear elastic body (see Reference [1] and the references therein). Additionally, total linear and total angular momentum is conserved for a free motion. This approach leads to a qualitatively improved solution, because the approximated time evolution exactly fulfills the same physical laws as the exact time evolution. Incorporating energy dissipation, the energy conserving time integration is extended to an energy consistent time integration. It turned out that such an energy consistent time integration is also of great advantage when computing finite motions of flexible solid bodies with material dissipation (see References [2,3]). This paper points out that an energy consistent time discretisation is also advantageous for dynamic finite deformation thermoviscoelasticity under dynamic loads. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The pseudo‐elastic response of rubberlike solids

In this paper we focus on the mechanical behaviour of filled natural rubber. Filled elastomers under cyclic loading show noticeable differences between the mechanical response under loading and unloading during the first cycles in oscillation tests. We examine the change in material response associated with the Mullins effect and with cavitation, the latter arising from hydrostatic tensile stresses of sufficient magnitude. Then, we focus on constitutive equations using the theory of pseudoelasticity. Specifically, the strain‐energy function depends on a scalar parameter, which provides a means for modifying the form, thereby reflecting stress softening observed during unloading. The dissipation of energy is also accounted for by the use of a dissipation function, which evolves with the deformation history. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Stabilisation faible interne locale de système élastique de Bresse

In [1], Alabau-Boussouira et al. (2011) studied the exponential and polynomial stability of the Bresse system with one globally distributed dissipation law. In this Note, our goal is to extend the results from Alabau-Boussouira et al. (2011) [1], by taking into consideration the important case when the dissipation law is locally distributed and to improve the polynomial energy decay rate. We then study the energy decay rate of the Bresse system with one locally internal distributed dissipation law acting on the equation about the shear angle displacement. Under the equal speed wave propagation condition, we show that the system is exponentially stable. On the contrary, we establish a new polynomial energy decay rate.     

A three-dimensional progressive damage model for fiber reinforced composites with an implicit-explicit integration scheme

This contribution proposes a fully three dimensional “continuum damage model” (CDM) to describe the interlaminar and intralaminar failure mechanisms of transversely isotropic elastic-brittle materials under static loading. The constitutive model is derived from an energy function with independent damage variables for each damage mode. The evolution law is based on energy dissipation within the damage process, taking into account the critical energy release rate to weaken the effect of mesh dependent outcome. The onset of damage can be predicted with Cuntze's failure mode concept [1] as well as with Hashin's failure criteria. In this model linear stress decreasing is assumed. In addition, an implicit-explicit integration scheme, first proposed by Oliver [3] for isotropic damage models, is adapted to increase the stability and robustness of numerical simulations and to decrease the computational cost of material failure analyses. By comparing the results from implicit-explicit integration schemes and standard implicit integration schemes, a high level of agreement is found. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Thermo-visco-elasticity for Norton–Hoff-type models

Our research is directed to a quasi-static evolution of the thermo-visco-elastic model. We assume that the material is subject to two kinds of mechanical deformations: elastic and inelastic. Moreover, our analysis captures the influence of the temperature on the visco-elastic properties of the body. The novelty of the paper is the consideration of the thermodynamically consistent model to describe this kind of phenomena related with a hardening rule of Norton–Hoff type. We provide the proof of existence of solutions to thermo-visco-elastic model in a simplified setting, namely the thermal expansion effects are neglected. Consequently, the coupling between the temperature and the displacement occurs only in the constitutive function for the evolution of the visco-elastic strain.