A plasticity model for pressure-dependent anisotropic cellular solids

The initial and subsequent yield surfaces for an anisotropic and pressure-dependent 2D stochastic cellular material, which represents solid foams, are investigated under biaxial loading using finite element analysis. Scalar measures of stress and strain, namely characteristic stress and characteristic strain, are used to describe the constitutive response of cellular material along various stress paths. The coupling between loading path and strain hardening is then investigated in characteristic stress–strain domain. The nature of the flow rule that best describes the plastic flow of cellular solid is also investigated. An incremental plasticity framework is proposed to describe the pressure-dependent plastic flow of 2D stochastic cellular solids. The proposed plasticity framework adopts the anisotropic and pressure-dependent yield function recently introduced by Alkhader and Vural [Alkhader M., Vural M., 2009a. An energy-based anisotropic yield criterion for cellular solids and validation by biaxial FE simulations. J. Mech. Phys. Solids 57(5), 871–890]. It has been shown that the proposed yield function can be simply calibrated using elastic constants and flow stresses under uniaixal loading. Comparison of stress fields predicted by continuum plasticity model to the ones obtained from FE analysis shows good agreement for the range of loading paths and strains investigated.     

A computational homogenization approach for the yield design of periodic thin plates. Part II : Upper bound yield design calculation of the homogenized structure

In the first part of this work (Bleyer and de Buhan, 2014), the determination of the macroscopic strength criterion of periodic thin plates has been addressed by means of the yield design homogenization theory and its associated numerical procedures. The present paper aims at using such numerically computed homogenized strength criteria in order to evaluate limit load estimates of global plate structures. The yield line method being a common kinematic approach for the yield design of plates, which enables to obtain upper bound estimates quite efficiently, it is first shown that its extension to the case of complex strength criteria as those calculated from the homogenization method, necessitates the computation of a function depending on one single parameter. A simple analytical example on a reinforced rectangular plate illustrates the simplicity of the method. The case of numerical yield line method being also rapidly mentioned, a more refined finite element-based upper bound approach is also proposed, taking dissipation through curvature as well as angular jumps into account. In this case, an approximation procedure is proposed to treat the curvature term, based upon an algorithm approximating the original macroscopic strength criterion by a convex hull of ellipsoids. Numerical examples are presented to assess the efficiency of the different methods.     

Anisotropic strain hardening behavior in simple shear for cube textured aluminum alloy sheets

Finite element (FE) simulations of the simple shear test were conducted for 1050-O and 6022-T4 aluminum alloy sheet samples. Simulations were conducted with two different constitutive equations to account for plastic anisotropy: Either a recently proposed anisotropic yield function combined with an isotropic strain hardening law or a crystal plasticity model. The FE computed shear stress–shear strain curves were compared to the experimental curves measured for the two materials in previous works. Both phenomenological and polycrystal approaches led to results consistent with the experiments. These comparisons lead to a discussion concerning the assessment of anisotropic hardening in the simple shear test.     

A homogenized Reissner–Mindlin model for orthotropic periodic plates: Application to brickwork panels

This paper describes a new procedure for the homogenization of orthotropic 3D periodic plates. The theory of Caillerie [Caillerie, D., 1984. Thin elastic and periodic plates. Math. Method Appl. Sci., 6, 159–191.] – which leads to a homogeneous Love–Kirchhoff model – is extended in order to take into account the shear effects for thick plates. A homogenized Reissner–Mindlin plate model is proposed. Hence, the determination of the shear constants requires the resolution of an auxiliary 3D boundary value problem on the unit cell that generates the periodic plate. This homogenization procedure is then applied to periodic brickwork panels.A Love–Kirchhoff plate model for linear elastic periodic brickwork has been already proposed by Cecchi and Sab [Cecchi, A., Sab, K., 2002b. Out-of-plane model for heterogeneous periodic materials: the case of masonry. Eur. J. Mech. A-Solids 21, 249–268 ; Cecchi, A., Sab, K., 2006. Corrigendum to A comparison between a 3D discrete model and two homogenised plate models for periodic elastic brickwork [Int. J. Solids Struct., vol. 41/9–10, pp. 2259–2276], Int. J. Solids Struct., vol. 43/2, pp. 390–392.]. The identification of a Reissner–Mindlin homogenized plate model for infinitely rigid blocks connected by elastic interfaces (the mortar thin joints) has been also developed by the authors Cecchi and Sab [Cecchi A., Sab K., 2004. A comparison between a 3D discrete model and two homogenised plate models for periodic elastic brickwork. Int. J. Solids Struct. 41/9–10, 2259–2276.]. In that case, the identification between the 3D block discrete model and the 2D plate model is based on an identification at the order 1 in the rigid body displacement and at the order 0 in the rigid body rotation.In the present paper, the new identification procedure is implemented taking into account the shear effect when the blocks are deformable bodies. It is proved that the proposed procedure is consistent with the one already used by the authors for rigid blocks. Besides, an analytical approximation for the homogenized shear constants is derived. A finite elements model is then used to evaluate the exact shear homogenized constants and to compare them with the approximated one. Excellent agreement is found. Finally, a structural experimentation is carried out in the case of masonry panel under cylindrical bending conditions. Here, the full 3D finite elements heterogeneous model is compared to the corresponding 2D Reissner–Mindlin and Love–Kirchhoff plate models so as to study the discrepancy between these three models as a function of the length-to-thickness ratio (slenderness) of the panel. It is shown that the proposed Reissner–Mindlin model best fits with the finite elements model.     

Viscous Flow Past a Periodic Array of Spheres

Viscous flow past an infinite periodic array of rigid spheres is considered. The hydrodynamic interaction of all the particles in the array is taken into account. An analytical solution of the problem is proposed. The forces exerted by the fluid on the array particles are calculated and an expression for the velocity of fluid filtration through the array is obtained. The results are compared with the previous theoretical and experimental results.     

复杂应力状态下木材力学性能的数值模拟

针对木材复杂的各向异性材料特点,建立了能反映木材正交各向异性弹性、抗拉和抗压强度不等、抗拉或抗剪时发生脆性破坏而受压时发生塑性变形等特性的本构模型。将木材弹性应力—应变关系简化为正交各向异性;选用Yamada-Sun强度准则来判断木材抗压时是否屈服,抗拉或抗剪时是否发生应变软化;通过引入损伤因子和弹性应变能,建立了木材...     

Saturated and unsaturated behaviour modelling of Meuse–Haute/Marne argillite

Poromechanical behaviour modelling of the Callovo–Oxfordian argillite under saturated and partially saturated conditions is proposed using the equivalent stress concept. In comparison with the previous works on this rock, the particular form of the yield criterion and the plastic flow potential proposed here help to better describe the rock behaviour in tension–stress paths. The evolution of the poroelastic parameters due to the induced cracks is also considered in a simple way. Due to its physical nature, different from classical soils, the partially saturated behaviour of this rock could not be correctly described by any of the pre-existing theories usually used for the partially saturated porous media (soils). Based upon experimental results on this rock and developing some ideas proposed by other authors, an extension of the saturated elastic–plastic model in unsaturated field is proposed. The key hypothesis of this extension is the evolution of the Biot’s coefficient as a function of the suction, justified by laboratory results and micromechanical analyses. The predictions of the model in saturated and partially saturated conditions are compared with laboratory results and a good general agreement is found.     

直接施加本质边界条件的FE／EFG耦合算法及其数值实现

提出一种可以直接施加本质边界条件的有限元与无网格Galerkin（FE／EFG）耦合算法。将问题域分成FE和EFG两种类型的子域,采用转换矩阵耦舍两子域的交界面;通过另一转换矩阵将无网格区域本质边界上的名义位移转换成真实位移,从而可在其上直接施加本质边界条件;采用二次转换实现两种转换矩阵之间的协调。提出全域统一采用单元...     

增强六手臂缺失支柱手性拉胀超材料力学性能理论研究

前期研究工作中, 基于有限元分析, 作者发展了一种在大变形范围内具有可调恒定负泊松比的新型增强六手臂缺失支柱手性拉胀超材料. 为了揭示微观结构?力学性能关系, 并进一步指导超材料目标参数设计, 本文在小变形框架下基于能量法建立了表征该拉胀材料等效泊松比和弹性模量的理论模型. 增强六手臂缺失支柱手性拉胀材料由“Z”型手臂元件组成. “Z”型手臂可以被假设为两端简支的欧拉?伯努利梁. 因此, 本文首先推导了两端受集中力和力偶的任意形状欧拉?伯努利梁的应变能. 然后, 考虑平衡条件和变形协调条件进一步给出了材料等效泊松比和弹性模量的理论表达式. 研究表明只有“Z”型梁的内外手臂比为2:1时, 理论表达式才有简洁的形式. 为了更好地利用所推导的理论表达, 基于理论推导, 本文开发了MATLAT图形用户界面 (GUI). 在GUI中输入可描述该超材料几何形状的独立几何参数, 即可直接获取其等效泊松比和弹性模量. 最后, 基于理论结果, 系统讨论了超材料微结构几何参数对其等效力学性能的影响, 并将理论解与有限元计算结果进行了对比. 结果表明, 可以通过调控微结构几何参数获取大范围的目标力学性能.      

Hydroelastic analysis of gravity wave interaction with submerged horizontal flexible porous plate

The present study deals with the surface gravity wave interaction with submerged horizontal flexible porous plate under the assumption of small amplitude water wave theory and structural response. The flexible porous plate is modeled using the thin plate theory and wave past porous structure is based on the generalized porous wavemaker theory. The wave characteristics due to the interaction of gravity waves with submerged flexible porous structure are studied by analyzing the complex dispersion relation using contour plots. Three different problems such as (i) wave scattering by a submerged flexible porous plate, (ii) wave trapping by submerged flexible porous plate placed at a finite distance from a rigid wall and (iii) wave reflection by a rigid wall in the presence of a submerged flexible porous plate are analyzed. The role of flexible porous plate in attenuating wave height and creating a tranquility zone is studied by analyzing the reflection, transmission and dissipation coefficients for various wave and structural parameters such as angle of incidence, depth of submergence, plate length, compression force and structural flexibility. In the case of wave trapping, the optimum distance between the porous plate and rigid wall for wave reflection is analyzed in different cases. In addition, effects of various physical parameters on free surface elevation, plate deflection, wave load on the plate and rigid wall are studied. The present approach can be extended to deal with acoustic wave interaction with flexible porous plates.     

新型格构式钢骨混凝土柱的轴压性能研究

提出了一种由格构式钢骨及钢筋混凝土所组成的新型LSRC(latticed-steel-reinforced-concrete,格构式钢骨约束混凝土)柱.通过对4个试件的轴压试验分析,对比CFTEC(con-crete-filled steel tube with encased concrete,外包混凝土的钢管混凝土...     

The influence of Hall current on the rotating oscillating flows of an Oldroyd-B fluid in a porous medium

In this article, analysis is presented to study the effect of Hall current on the rotating flow of a non-Newtonian fluid in a porous medium taking into consideration the modified Darcy's law. The Oldroyd-B fluid model is used to characterize the non-Newtonian fluid behavior. The governing equations for unsteady rotating flow have been modeled in a porous medium. The analysis includes the flows induced by general periodic oscillations and elliptic harmonic oscillations of a plate. The effect of the various emerging parameters is discussed on the velocity distribution. The analytical results are confirmed mathematically by giving comparison with previous studies in the literature. It is observed that the velocity distribution increases with an increase of Hall parameter. The behavior of permeability is similar to that of the Hall parameter.     

Analyses of dynamic characteristics of a fluid-filled thin rectangular porous plate with various boundary conditions

Based on the classical theory of thin plate and Biot theory, a precise model of the transverse vibrations of a thin rectangular porous plate is proposed. The first order differential equations of the porous plate are derived in the frequency domain. By considering the coupling effect between the solid phase and the fluid phase and without any hypothesis for the fluid displacement, the model presented here is rigorous and close to the real materials. Owing to the use of extended homogeneous capacity precision integration method and precise element method, the model can be applied in higher frequency range than pure numerical methods. This model also easily adapts to various boundary conditions. Numerical results are given for two different porous plates under different excitations and boundary conditions.     

Numerical modelling of the plasticity induced during diffusive transformation. Case of a cubic array of nuclei

The experimental work of Taleb and Petit-Grostabussiat [Taleb, L., Petit-Grostabussiat, S., 2002. Elastoplasticity and phase transformations in ferrous alloys: some discrepancies between experiments and modeling. J. Phys. IV 12 (11), 187–194; Taleb, L., Petit, S., 2006. New investigations on transformation induced plasticity and its interaction with classical plasticity. Int. J. Plasticity 22 (1), 110–130] has shown evidence that the evolution of TRansformation Induced Plasticity (TRIP) in a low carbon steel (16MND5) could be significantly influenced by the loading history of the parent phase, for a martensitic as well as a bainitic transformation. Furthermore, estimates from the Leblond model – one of the few micromechanical models currently found in different Finite Element (FE) softwares – have appeared to be in disagreement with experiments in these cases where the parent phase has been strain hardened. This has motivated the development of alternative approaches based on FE computations. This paper presents our first investigations about simulations of diffusive transformations with FE in an idealized case: the parent and the product phase are considered as two homogeneous materials with given elastoplastic properties and density; the transformation takes place at the same instant at predefined elements constituting the nuclei; then it progresses at a uniform rate by changing the material properties of the layer of elements surrounding the nuclei. In the basic configuration of modelling, the volume of discretization stands for a unit cell of a periodic cellular array, with a single central nucleus. In a more complex configuration, which is introduced shortly here and to be presented in details in the paper under preparation [Barbe, F., Quey, R., Taleb, L., Souza de Cursi, E., 2006. Numerical modelling of the plasticity induced during diffusive transformation. Case of a random instantaneous array of nuclei, in preparation], the volume of computation contains few to several nuclei at random locations. For both configurations, results in terms of effective (mean) TRIP as a function of the volume fraction of product phase are in correct quantitative and qualitative agreement with experimental results.     

A new yield function and a hydrostatic stress-controlled void nucleation model for porous solids with pressure-sensitive matrices

A macroscopic yield function for porous solids with pressure-sensitive matrices modeled by Coulomb's yield function was obtained by generalizing Gurson's yield function with consideration of the hydrostatic yield stress of a spherical thick-walled shell and by fitting the finite element results of the yield stresses of a voided cube. The macroscopic yield function is valid for the negative hydrostatic stress as well as for the positive hydrostatic stress. From the yield function, a plastic potential function for the porous solids was derived either for plastic normality flow or for plastic non-normality flow of the pressure-sensitive matrices. In addition, void nucleation was modeled by a normal distribution function with the macroscopic hydrostatic stress regarded as a controlling stress. This set of constitutive relations was implemented into a finite element code abaqus as a user material subroutine to analyze the cavitation and the deformation behavior of a rubber-modified epoxy around a crack tip under the Mode I plane strain conditions. By comparing the cavitation zone and the plastic zone obtained in the analysis with those observed in an experiment, the mean stress and the standard deviation for the void nucleation model could be determined. The cavitation and the deformation behavior of the rubber-modified epoxy were also analyzed around notches under four-point bending. The size and shape of the cavitation zone and the plastic zone were shown to be in good agreement with those observed in an experiment.     

Boundary conditions for stokes flows near a porous membrane

A theoretical development is carried out to model the boundary conditions for Stokes flows near a porous membrane, which, in general, allows non-zero slip as well as normal flow at the surface. Two types of models are treated: an infinitesimally thin plate with a periodic array of circular apertures and a series of parallel slits. For Stokes flows, the mean normal flux and slip velocity are proportional to the pressure difference across the membrane and the average shear stress at the membrane, respectively. The appropriate proportionality constants which depend on the membrane geometry are calculated as functions of the porosity. An interesting feature of the results is that the slip at the membrane has, in general, a direction different from that of the applied shear for these models.     

Ordinary state-based peridynamics for plastic deformation according to von Mises yield criteria with isotropic hardening

This study presents the ordinary state-based peridynamic constitutive relations for plastic deformation based on von Mises yield criteria with isotropic hardening. The peridynamic force density–stretch relations concerning elastic deformation are augmented with increments of force density and stretch for plastic deformation. The expressions for the yield function and the rule of incremental plastic stretch are derived in terms of the horizon, force density, shear modulus, and hardening parameter of the material. The yield surface is constructed based on the relationship between the effective stress and equivalent plastic stretch. The validity of peridynamic predictions is established by considering benchmark solutions concerning a plate under tension, a plate with a hole and a crack also under tension.     

Anisotropic response of high-purity α-titanium: Experimental characterization and constitutive modeling

This paper presents a comprehensive experimental and theoretical investigation of the deformation behavior of high-purity, polycrystalline α-titanium under quasi-static conditions at room temperature. The initial material in this study was a cross-rolled plate with a strong basal texture. To quantify the plastic anisotropy and the tension–compression asymmetry of this material, monotonic tensile and compressive tests were conducted, on samples cut along different directions of the plate. A new anisotropic elastic/plastic model was developed to describe the quasi-static macroscopic response of the aggregate. Key in its formulation is the use of an anisotropic yield criterion that captures strength-differential effects and an anisotropic hardening rule that accounts for texture evolution associated to twinning. A very good agreement between FE simulations using the model developed and uniaxial data was obtained.