Elastoplastic constitutive modeling under the complex loading driven by GRU and small-amount data

In this paper, a data-driven method to model the three-dimensional engineering structure under the cyclic load with the one-dimensional stress-strain data is proposed. In this method, one-dimensional stress-strain data obtained under uniaxial load and different loading history is learned offline by gate recurrent unit (GRU) network. The learned constitutive model is embedded into the general finite element framework through data expansion from one dimension to three dimensions, which can perform stress updates under the three-dimensional setting. The proposed method is then adopted to drive numerical solutions of boundary value problems for engineering structures. Compared with direct numerical simulations using the J2 plasticity model, the stress-strain response of beam structure with elastoplastic materials under forward loading, reverse loading and cyclic loading were predicted accurately. Loading path dependent response of structure was captured and the effectiveness of the proposed method is verified. The shortcomings of the proposed method are also discussed.     

Optimal Design of Viscoelastic Structures under Forced Steady-State Vibration

ABSTRACT

ABSTRACT With minimum dynamic response as the design criterion, we derive by means of variational analysis a general set of equations governing optimal design of one-dimensional, viscoelastic structures acted on by harmonically varying external loading. The equations are specialized to problems of minimizing transverse vibrational response of beams by attaching optimal, nonuniform cover layers made of a solid, viscoelastic material on the beams. Several numerical solutions to such problems are presented.     

梯度饱和土瞬态响应分析

基于Biot多孔介质理论,建立了饱和土体在动载荷作用下的一维回传射线矩阵法的计算列式,其中考虑了土体的非均匀性、惯性、黏滞以及固体颗粒和流体的可压缩性.利用计算结果与已有结果相比较,二者相吻合,验证了算法的正确性.作为数值算例,考虑饱和土的物理力学性质沿深度方向按幂函数连续变化,利用数值Laplace逆变换求解了在冲击性载荷作用下的位移,应力和孔隙压力等物理量的瞬态响应,重点分析讨论了材料非均匀性对饱和土介质动力特性的影响.      

基于非局部塑性模型的应变局部化理论分析及数值模拟

通过求解一个第二类Fredholm方程,得到了基于非局部塑性软化模型的应变局部化问题理论解,结果表明,只有在当采用过非局部修正形式的非局部塑性软化模型才能得到应变局部化解,且得到的塑性应变分布和荷载响应依赖于所引入的特征长度及过非局部权参数。通过一维应变局部化有限元数值解,验证了非局部理论的引入能克服计算结果的网格敏感...     

A three-dimensional phenomenological model for martensite reorientation in shape memory alloys

In this work, we propose a macroscopic phenomenological model that is based on the classical framework of thermodynamics of irreversible processes and accounts for the effect of multiaxial stress states and non-proportional loading histories. The model is able to account for the evolution of both twinned and detwinned martensite. Moreover, reorientation of the product phase according to loading direction is specifically accounted for. Towards this purpose the inelastic strain is split into two contributions deriving, respectively, from creation of detwinned martensite and reorientation of previously existing martensite variants. Computational tests demonstrate the ability of the model to simulate the main aspects of the shape memory response in a one-dimensional setting and some of the features that have been experimentally found in the case of multiaxial non-proportional loading histories. Experimental non-proportional loading paths have also been simulated and a good qualitative agreement between numerical and experimental response is observed.     

A simple and effective nonlinear elastic one-dimensional model for the structural analysis of masonry arches

In this paper the static response of a masonry arch is studied by way of a one-dimensional nonlinear elastic model in which masonry is regarded as a material with bounded tensile and compressive strengths. By following an approach analogous to that followed in the theory of bending of elastic beams, the equilibrium problem for the arch leads to a free-boundary, nonlinear differential problem. An approximate solution to such problem can be pursued by means of an ad hoc iterative procedure, illustrated in detail herein. The results obtained in three case studies are compared with some numerical and experimental results available in the literature. In addition, the case of an actual arch undergoing spreading of the springings is considered, and the distribution and possible evolution of the cracking pattern discussed.     

The reduction of spatial aliasing by long hot-wire anemometer probes

 Experiment and numerical analysis are presented to demonstrate that a hot-wire anemometer probe reduces spatial aliasing of turbulent velocity fluctuations because of the filtering property of the probe sensing element. The experiment focuses on the one-dimensional turbulent velocity spectrum and utilizes a long sensing length hot-wire probe to exaggerate the effect of the sensing element on the turbulent field. The numerical analysis utilizes a model of the hot-wire probe from Wyngaard (1968) along with isotropic turbulence relations to obtain an equation for the hot-wire response in a turbulent velocity field. The model can be used to determine the effect of hot-wire length on the one and three-dimensional turbulent spectra. The experimental study demonstrates that the finite length, hot-wire probe filters out energy in the high wave number region of the one-dimensional spectrum thereby verifying its ability to reduce spatial aliasing. Interestingly, the study also shows that energy in the low wave numbers of the one-dimensional spectrum is attenuated. The numerical study of the hot-wire probe demonstrates that this low wave-number attenuation is purely an artifact of the one-dimensional spectrum and not an effect of the hot-wire probe. Received: 20 May 996 / Accepted: 14 November 1996     

Numerical simulations of shock wave propagation in condensed multiphase materials

We propose to find out numerical solutions of a travelling shock wave in condensed mixtures by using a direct numerical simulation. Condensed multiphase materials under shock wave conditions are mechanically characterized by a unique pressure and a unique velocity. In this study, the mixture is considered as a collection of grains separated by interface between each material: this problem of interfaces is solved by a diffuse interface method. The results will be compared to existing one-dimensional numerical models, analytical solutions and also experimental data. The volume fraction (or the phase temperature) is not measured in experiments and it is then important to verify the behaviour of a phase quantity through various methods. A non-monotonous evolution of the volume fraction is obtained with analytical solution as well as numerical simulation.      

求解含缺陷一维周期结构动力响应的高效算法

基于周期结构的动力特性和群理论,建立了一种高效求解含缺陷一维周期结构动力响应的数值方法。在求解结构动力响应时,高效求解结构对应的线性代数方程组最为关键。采用凝聚技术,可减小结构对应线性代数方程组的规模。基于周期结构动力系统中线性代数方程组的特性,通过一个小规模含缺陷结构和一维周期结构的响应分析,可得到含缺陷一维周期结构的动力响应。同理,一维周期结构的动力响应可通过一系列小规模结构的响应分析得到,且小规模结构的动力响应可基于群理论高效求解。数值算例表明,本文算法有较高的求解效率。     

A model and numerical study for coiling of Kelvin-type viscoelastic filament

Coiling problems of elastic rope and viscous jet have been fully studied both experimentally and theoretically, but very few studies exist for viscoelastic material. In this paper, a system of one-dimensional two-point boundary nonlinear equations for Kelvin material coiling is presented. The equations are solved numerically by continuation method. It is found that the coiling frequency depends on the dimensionless retardation time and other continuation parameters involving inertia and gravity. The multivaluedness of the solution is observed in the numerical study.     

Wave propagation and dispersion in microstructured wool felt

On the basis of the experimental data of the piano hammers study the one-dimensional constitutive equation of the wool felt material is proposed. This relation enables deriving a nonlinear partial differential equation of motion with third order terms, which takes into account the elastic and hereditary properties of a microstructured felt. This equation of motion is used to study pulse evolution and propagation in the one-dimensional case. Thorough analysis both of the linear and nonlinear problems is presented. The physical dimensionless parameters are established and their importance in describing the dispersion effects is discussed. It is shown that both normal and anomalous dispersion types exist in wool felt material. The dispersion analysis shows also that for the certain ranges of physical parameters negative group velocity will appear. The initial value problem is considered and the analysis of the numerical solution describing the strain wave evolution is provided. The influence of the material parameters on the form of a propagating pulse is demonstrated and explained.     

球对称形式物质点法及其在水下爆炸中的应用

利用物质点法求解三维远场水下爆炸冲击响应问题时,爆炸冲击波到达结构物之前传播过程的计算会消耗大量的计算资源,影响求解效率。针对这一问题,并考虑到水下爆炸冲击波在自由场中的传播特点,提出了一维球对称形式的物质点法,对球形炸药水下爆炸过程进行了数值模拟,并与Cole公式以及DYNA计算结果进行了比较,结果吻合较好,验证了一维球对称形式物质点法的正确性。在此基础上,提出了基于物质点法的重映射算法,将爆炸冲击波在自由场中的传播过程在一维球对称模型中进行计算,并将计算结果映射到三维模型中,以便继续完成计算过程,有效避免了计算资源在冲击波传播过程计算上的消耗。     

Three-dimensional constitutive model for shape memory alloys based on microplane model

A new model for the behavior of polycrystalline shape memory alloys (SMA), based on a statically constrained microplane theory, is proposed. The new model can predict three-dimensional response by superposing the effects of inelastic deformations computed on several planes of different orientation, thus reproducing closely the actual physical behavior of the material. Due to the structure of the microplane algorithm, only a one-dimensional constitutive law is necessary on each plane. In this paper, a simple constitutive law and a robust kinetic expression are used as the local constitutive law on the microplane level. The results for SMA response on the macroscale are promising: simple one-dimensional response is easily reproduced, as are more complex features such as stress-strain subloops and tension-compression asymmetry. A key feature of the new model is its ability to accurately represent the deviation from normality exhibited by SMAs under nonproportional loading paths.     

Non-isothermal oscillations of pseudoelastic devices

The non-linear dynamic response of a pseudoelastic oscillator embedded in a convective environment is studied taking into account the temperature variations induced, during oscillations, by the latent heat of transformation and by the heat exchange with the surroundings. The asymptotic periodic response under harmonic excitation is characterized by frequency-response curves in terms of maximum displacement, maximum and mean temperature. The periodic thermomechanical response is computed by a multi-component harmonic balance method implemented within a continuation algorithm that enables to trace out multivalued frequency-response curves. The accuracy of the results is checked by comparison with the results of the numerical integration of the basic equations governing the dynamics of the system. The response is investigated for various excitation amplitude levels and in various material parameters ranges. The resulting picture of the mechanical response shows, in some cases, features similar to other hysteretic oscillators, while, in other cases, points out peculiar behaviors. It turns out that the temperature variations induced by the phase transformations influence the mechanical response and that the results obtained under the simplifying assumption of isothermal behavior can be rather different from those obtained in a fully thermomechanical setting.     

Constitutive model for flake graphite cast iron automotive brake discs: induced anisotropic damage model under complex loadings

The present paper details an elasto-viscoplastic constitutive model for automotive brake discs made of flake graphite cast iron. In a companion paper (Augustins et al. in Contin Mech Thermodyn, 2015), the authors proposed a one-dimensional setting appropriate for representing the complex behavior of the material (i.e., asymmetry between tensile and compressive loadings) under anisothermal conditions. The generalization of this 1D model to 3D cases on a volume element and the associated challenges are addressed. A direct transposition is not possible, and an alternative solution without unilateral conditions is first proposed. Induced anisotropic damage and associated constitutive laws are then introduced. The transition from the volume element to the real structure and the numerical implementation require a specific basis change. Brake disc simulations with this constitutive model show that unilateral conditions are needed for the friction bands. A damage deactivation procedure is therefore defined.     

Numerical simulation of quasi-brittle fracture using damaging cohesive surfaces

The cohesive surface methodology is used in a numerical study of fracture of concrete. The traction vs. separation response is governed by an isotropic damage law in which damage evolves according to a prescribed one-dimensional linear or exponential softening law. Cohesive surfaces are immersed in the continuum to allow for a maximum freedom of crack path selection. The single edge notched four point shear beam and the double edge notched tensile bar are used to study: (i) the influence of the tangential cohesive response on the development of the fracture path and (ii) the mesh alignment sensitivity. It is shown that in the present formulation, the tangential cohesive response has a minor influence on both crack path and global characteristics. Mesh alignment does have a significant influence on the outcome of the numerical analysis.     

Instability analysis and simulation of water infiltration into an unsaturated elasto-viscoplastic material

A linear instability analysis was performed in order to investigate which variables have a significant effect on the onset of the instability of an unsaturated viscoplastic material subjected to water infiltration. It was found that the onset of the growing instability of the material system mainly depends on the specific moisture capacity, the suction, and the hardening parameter. Then, in order to simulate the water infiltration process of a one-dimensional unsaturated soil column, a multiphase coupled elasto-viscoplastic finite element analysis was performed based on the theory of porous media. The results of the numerical simulations are discussed with respect to the effect of the specific moisture capacity and the initial suction on the development of volumetric strain. We found that rapid transitions from unsaturated to saturated states and higher levels of initial suction lead to the contractive behavior of the material and instability. The instability detected by the numerical results is consistent with the theoretical results obtained through the linear instability analysis.     

Local and global nonlinear dynamics of thermomechanically coupled composite plates in passive thermal regime

Unified 2D continuum formulation of the nonlinear dynamic problem for a von Kármán shear indeformable symmetric cross-ply composite plate in a thermomechanical environment is presented, along with the ensuing reduction procedure ending up to a three-mode discretized model with unknown transverse displacement and membrane/bending temperatures. Systematic numerical analyses in the case of thermal dynamics passively entrained by the solely active mechanical excitations allow to unveil the main features of the nonlinear response, while highlighting fundamental aspects associated with the thermomechanical coupling. Local and global dynamics of a single-layer orthotropic plate are investigated under varying in-plane/transverse excitations or thermal property of the material. Comparison with the response provided by partially coupled models and the uncoupled mechanical oscillator enables to identify situations in which thermomechanical coupling affects the nonlinear response even in the solely passive thermal setting and to frame the relevant effects within known literature results.     

水介质初始参数设置对水下爆炸载荷的影响

针对数值计算中水介质初始参数设置对水下爆炸载荷特性的影响开展了深入分析。基于参考状态参数确定了水介质状态方程形式;从热力学角度分析了常用的两种初始参数设置方式,提出了一种按等温假设设置初始参数的方式,并对LS-DYNA中INITIAL_EOS_ALE关键字给出的参数设置结果进行了分析;采用LS-DYNA程序进行一维球形装药水下爆炸数值计算,分析了3种设置方式下爆炸载荷特性的差异,并与已有研究成果进行了对比。结果表明:当仅改变水介质内能项时,参数按等容过程变化,流场压力源于外界传热,与实际深水环境严重不符;INITIAL_EOS_ALE关键字给出的参数设置结果与仅改变水介质密度（等内能过程）接近,水温变化规律与真实环境不符;按等内能过程和等温过程设置初始参数时,水下爆炸载荷特性计算结果基本相同,与已有成果吻合;综合分析认为,按等温形式进行初始参数设置方式较优。研究成果可为水下爆炸尤其是深水爆炸数值仿真提供参考。     

Numerical simulation of aerated powder consolidation

When a fine powder is dumped into a silo, the gas trapped by the particles will slowly escape by diffusing through the material. The corresponding uneven gas pressure distribution creates a body force that is taken into account through Darcy's law. By using spatial averaging, the formulation, even though essentially one-dimensional in space, includes effects due the geometry of the container. An efficient and robust numerical scheme based on a differential algebraic equation formulation is proposed and implemented. Various computational results are presented and discussed to establish the validity of the approach.