Research on nonlinear constitutive relationship of permanent deformation in asphalt pavements

To predict correctly the rut depths in asphalt pavements, a new nonlinear viscoelastic-elastoplastic constitutive model of permanent deformation in asphalt pavements is presented. The model combines a generalized Maxwell model with an elastoplastic one. Then from the creep theory, the linear and nonlinear constitutive equations of the generalized Maxwell model are obtained. From the nonlinear finite element method for the rutting of the asphalt pavement, the rut depths of 4 asphalt-aggregate mixtures are obtained. And the results are compared with the ones from the finite element method by SHRP and the experiments by SWK/UN. The results in this paper are better than the ones by SHRP, and agree with the ones of the experiment by SWK/UN. This shows that the nonlinear viscoelastic-elastoplastic constitutive model, which is presented in this paper for the rutting of the asphalt pavement, is effective. The properties, such as nonlinear elasticity, plasticity, viscoelasticity and nonlinear viscoelasticity, which affect the rutting of an asphalt pavement, can be shown in the model. And the characteristics of the permanent deformation of the asphalt pavement can be presented entirely in the model.     

Plastic Strain Localization and Its Stages in Al-Mg Alloys

The paper describes an experimental technique based on the use of a Vic-3D contactless digital optical system and digital image correlation for research in the mechanical behavior of a solid and its plastic deformation with space-time inhomogeneities. Using this technique, we analyze the evolution of inhomogeneous strain and local strain rate fields in AMg2m alloy at constant uniaxial tension rates. The analysis reveals quasi-periodic strain field homogenization in jerky flow: alternating phases of active local plastic flow (shear banding) and macroscale strain levelling. Also analyzed are the parameters of localized microscale plastic flow such as the height and width of shear bands, their velocity, and coefficient of plastic strain inhomogeneity. From a series of mechanical tests, the influence of the specimen geometry and loading rate on these parameters is estimated.     

Influence of multiscale localized plastic flow on stress-strain patterns

The paper considers the influence of multiscale plastic flow localization on rotational deformation modes and σ-? curves by analyzing the entropy production and equation of state of a deformed solid. It is shown that if the rotational deformation modes are fully self-consistent, the σ-? curve changes monotonically. If not, the curve reveals jerks or serrations due to nonlinear wave relaxation of stresses associated with macroscale non-compensated material rotations. At high loading rates, the rotational deformation modes attain self-consistency by the mechanism of dynamic rotations.     

A conservative level-set based method for compressible solid/fluid problems on fixed grids

A three-dimensional Eulerian method is presented for simulating dynamic systems comprising multiple compressible solid and fluid components where internal boundaries are tracked using level-set functions. Aside from the interface interaction calculation within mixed cells, each material is treated independently and the governing constitutive laws solved using a conservative finite volume discretisation based upon the solution of Riemann problems to determine the numerical fluxes. The required reconstruction of mixed cell volume fractions and cut cell geometries is presented in detail using the level-set fields. High-order accuracy is achieved by incorporating the weighted-essentially non-oscillatory (WENO) method and Runge–Kutta time integration. A model for elastoplastic solid dynamics is employed formulated using the tensor of elastic deformation gradients permitting the equations to be written in divergence form. The scheme is demonstrated using selected one-dimensional initial value problems for which exact solutions are derived, a two-dimensional void collapse, and a three-dimensional simulation of a confined explosion.     

Collective properties of defects,multiscale plasticity,and shock induced phenomena in solids

A statistically based approach is developed for the construction of constitutive equations that provides linkages between defect-induced mechanisms of structural relaxation, thermally activated plastic flow, and material response to extreme loading conditions. The collective properties of defects have been studied to establish the interaction of multiscale defect dynamics and plastic flow, and to explain the mechanisms leading to the universal self-similar structure of shock wave fronts. Pn explanation for structural universality of the steady-state plastic shock front (the four power law) and the self-similarity of shock wave profiles under reloading (unloading) is proposed. Structural characterization under transition from thermally activated dislocation glide to nonlinear dislocation drag effects is developed in terms of scaling invariants (effective temperatures) related to mesodefect induced morphology formed during the different stages of plastic deformation.     

Development of dislocation-based unified material model for simulating microstructure evolution in multipass hot rolling

Dynamic recrystallization and recovery are two competing processes. Both may continue after hot deformation, such as during passes in multipass hot rolling processes, reducing dislocation density of materials and allowing larger plastic deformation to be achieved. The main objective of this research is to develop a set of mechanism-based unified viscoplastic constitutive equations which model the evolution of dislocation density, recrystallization and grain size during and after hot plastic deformation. This set of constitutive equations are determined for a C-Mn steel using an evolutionary programming (EP) optimization technique and implemented into the commercial finite element (FE) solver ABAQUS for process simulations. Numerical procedures to simulate multipass rolling are developed. FE analysis is carried out to simulate the evolution of grain size, dynamic/static recrystallization and recovery, and to rationalize their effects on the viscoplastic flow of the material in a two-pass hot rolling process.     

First-principles constitutive equation for suspension rheology

Using mode-coupling theory, we derive a constitutive equation for the nonlinear rheology of dense colloidal suspensions under arbitrary time-dependent homogeneous flow. Generalizing previous results for simple shear, this allows the full tensorial structure of the theory to be identified. Macroscopic deformation measures, such as the Cauchy-Green tensors, thereby emerge. So does a direct relation between the stress and the distorted microstructure, illuminating the interplay of slow structural relaxation and arbitrary imposed flow. We present flow curves for steady planar and uniaxial elongation and compare these to simple shear. The resulting nonlinear Trouton ratios point to a tensorially nontrivial dynamic yield condition for colloidal glasses.     

稀薄气体流动非线性耦合本构关系研究进展

临近空间高超声速飞行器流场蕴含着复杂的非线性流动机理与丰富的热化学非平衡流动现象, 基于Newton摩擦定律和Fourier热传导定律的Navier-Stokes(N-S)方程不足以描述高超声速飞行器从连续流到稀薄流的多尺度非平衡现象。非线性耦合本构关系(nonlinear coupled constitutive relations, NCCR)作为一种全新的本构方程体系, 在严格满足热力学熵条件的基础上, 巧妙地构建了应力与热流的非线性表达形式。然而, NCCR方程的强非线性耦合特性是求解过程的一大难题。为了克服这一技术瓶颈, 提出了混合迭代算法, 为实现NCCR方程的高效稳定求解提供了坚实的理论基础。在该理论研究的基础上, 考虑到原始NCCR方程对热通量演化方程的简化处理, 降低了方程的计算精度, 提出了改进的NCCR+方程。该方程在强激波压缩区域和膨胀区域表现出比传统NCCR方程更高的计算精度与更强的非平衡流动模拟能力。同时, 为了解决临近空间高超声速空气动力学的多尺度与多物理效应耦合难题, 提出了NCCR与转动非平衡的耦合计算模型, 拓展了NCCR方程在双原子气体中的模拟能力。为了揭示稀薄气体效应与真实气体效应的耦合作用机理, 进一步建立了NCCR与热化学反应的耦合计算方法。大量研究结果表明, 考虑多物理效应的NCCR方程在低Kn下能够恢复到与N-S方程一致的解。随着Kn的增加, 流场的非平衡程度逐渐增强, 其结果与N-S方程差异显著, 而与DSMC方法计算结果和实验数据具有更好的一致性。      

A dynamic deformation model of an elastoplastic porous medium

A closed system of equations is obtained for dynamic deformation of an elastoplastic Prandtl-Reiss porous medium. The heterogeneous approach makes it possible to describe the properties of such media in a wide range of loading rates within the theory of plastic flow with the kinematic simplification. The hydrodynamic deformation theory of porous media [1, 2] has been first correctly generalized to the case of including the deviator components of the stress tensor of the medium. The well-known functions of the model are determined from analyzing the fundamental deformations of the corresponding spherical cells.Institute of Theoretical and Applied Mechanics, Siberian Branch, Russian Academy of Sciences. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 46–53, July, 1992.     

Nonlinear dynamic response and active vibration control for piezoelectric functionally graded plate

The nonlinear dynamic response and active vibration control of the piezoelectric functionally graded plate are analyzed in this paper. Based on higher-order shear plate theory and elastic piezoelectric theory, the nonlinear geometric and constitutive relations of the piezoelectric functionally graded plate are established, and then the nonlinear motion equations of the piezoelectric functionally graded plate are obtained through Hamilton's variational principle. The nonlinear active vibration control of the structure is carried out with adoption of the negative velocity feedback control algorithm. By applying finite difference method, the whole problem is solved by using iterative method synthetically. In numerical examples, the effects of mechanical load, electric load, the volume fraction and the geometric parameters on the dynamic response and vibration control of the piezoelectric FGM plate are investigated.     

Nonlinear rheological models for structured interfaces

The GENERIC formalism is a formulation of nonequilibrium thermodynamics ideally suited to develop nonlinear constitutive equations for the stress-deformation behavior of complex interfaces. Here we develop a GENERIC model for multiphase systems with interfaces displaying nonlinear viscoelastic stress-deformation behavior. The link of this behavior to the microstructure of the interface is described by including a scalar and a tensorial structural variable in the set of independent surface variables. We derive an expression for the surface stress tensor in terms of these structural variables, and a set of general nonlinear time evolution equations for these variables, coupling them to the deformation field. We use these general equations to develop a number of specific models, valid for application near equilibrium, or valid for application far beyond equilibrium.     

Correlation between jerky flow and jerky dynamics in a nanoscratch on a metallic glass film

Chaos has been well understood in dynamic system, however, how the chaotic behavior occur in jerky flow in material, is still not clear, and is lack of specific chaotic attractor. Here the jerky evolution of lateral force and the stair-like fluctuation of lateral displacement are observed for Ni62 Nb38(at.%) metallic glass film during nanoscratch process. This jerky flow is investigated by using the largest Lyapunov exponent, Kolmogorov entropy and fractal dimension, and chaotic behavior of lateral force-time and normal displacement-lateral displacement sequences is verified. In addition to time series analysis, it is found that jerk equation can be used to describe the jerky flow of the metallic-glass film during nanoscratch. More importantly, unambiguous chaotic attractor is presented by jerky dynamics using "jerk"-singularities, namely the total change rate of lateral force relative to scratch time. These reveal an inner connection between jerky flow and jerky dynamics in nanoscratch of a metallic-glass film.     

On the homogeneous nucleation and propagation of dislocations under shock compression

The dynamic response of crystalline materials subjected to extreme shock compression is not well understood. The interaction between the propagating shock wave and the material’s defect occurs at the sub-nanosecond timescale which makes in situ experimental measurements very challenging. Therefore, computer simulation coupled with theoretical modelling and available experimental data is useful to determine the underlying physics behind shock-induced plasticity. In this work, multiscale dislocation dynamics plasticity (MDDP) calculations are carried out to simulate the mechanical response of copper reported at ultra-high strain rates shock loading. We compare the value of threshold stress for homogeneous nucleation obtained from elastodynamic solution and standard nucleation theory with MDDP predictions for copper single crystals oriented in the [0 0 1]. MDDP homogeneous nucleation simulations are then carried out to investigate several aspects of shock-induced deformation such as; stress profile characteristics, plastic relaxation, dislocation microstructure evolution and temperature rise behind the wave front. The computation results show that the stresses exhibit an elastic overshoot followed by rapid relaxation such that the 1D state of strain is transformed into a 3D state of strain due to plastic flow. We demonstrate that MDDP computations of the dislocation density, peak pressure, dynamics yielding and flow stress are in good agreement with recent experimental findings and compare well with the predictions of several dislocation-based continuum models. MDDP-based models for dislocation density evolution, saturation dislocation density, temperature rise due to plastic work and strain rate hardening are proposed. Additionally, we demonstrated using MDDP computations along with recent experimental reports the breakdown of the fourth power law of Swegle and Grady in the homogeneous nucleation regime.     

圆杆波导中的一个非线性波动方程及准确周期解

在小变形条件下，采用Cox的非线性应力应变关系，计及横向Possion效应，借助Hamilton变分原理导出了非线性弹性圆杆波导中的纵向波动方程. 利用Jacobi椭圆余弦函数展开法，对该方程与截断的非线性波动方程进行求解，得到了两类非线性波动方程的准确周期解，它们可以进一步退化为孤波解. 关键词： 非线性波 Possion效应 Jacobi椭圆余弦函数     

格子Boltzmann方法模拟自然对流作用下融化传热过程

建立自然对流作用下融化的格子Boltzmann双分布函数模型,根据非线性对流扩散方程的格子Boltzmann模型理论提出一个新的表征融化温度场的分布函数演化方程,并通过变松弛时间方法处理固液两相变热物性传热问题.应用模型对热传导融化及自然对流融化特别固液变热物的融化过程进行模拟.模拟结果与分析解、经典的关联式结果吻合较好,模型的正确性得到了验证.模拟结果表明,自然对流对融化传热过程有着重要的影响,此外固相热传导也对融化传热、融化速率及固液两相温度分布都有一定影响.     

An extended rational thermodynamics model for surface excess fluxes

In this paper, we derive constitutive equations for the surface excess fluxes in multiphase systems, in the context of an extended rational thermodynamics formalism. This formalism allows us to derive Maxwell-Cattaneo type constitutive laws for the surface extra stress tensor, the surface thermal energy flux vector, and the surface mass flux vector, which incorporate a direct coupling to their corresponding bulk fluxes in the adjacent bulk phases. These constitutive laws also incorporate contributions to the time evolution of the surface excess fluxes from spatial inhomogeneities in these flux fields. These phenomenological equations can be used to model the dynamic behavior of complex viscoelastic interfaces in multiphase systems, in the small deformation limit.     

高压、高应变率与低压、高应变率实验的本构关联性

 指出Johnson-Cook（J-C）、Zerilli-Armstrong（Z-A）、Bodner-Parton（B-P）本构方程在一定条件下的适用性,表明对于低压、高应变率实验,单一曲线假定似乎可以采用。通过等效应力、等效应变,可以将不同应力状态下的流动应力函数采用统一的方程描述。然而,这些本构方程的确立,并不包括平面冲击波实验。对适合于平面冲击波实验的Steinberg-Cochran-Guinan（SCG）本构方程,讨论了其方程中所包含的高压与高应变率耦合效应。指出,以剪切模量度量的流动应力具有应变率相关性。基于温度效应的新发现以及直接测量平面冲击波流动应力的新进展,分别用J-C本构及SCG本构方程估算了钨材料在高压、高应变率加载下的流动应力。结果表明,采用J-C本构估算的流动应力仅在压力为10 GPa以下才能与实验数据相近,当压力高于10 GPa时,流动应力只能采用SCG本构估算。也指出了高压、高应变率本构方程与低压、高应变率本构方程所对应的不同物理背景。