Insight into the physics of foam densification via numerical simulation

Foamed materials are increasingly finding application in engineering systems on account of their unique properties. The basic mechanics which gives rise to these properties is well established, they are the result of collapsing the foam microstructure. Despite a basic understanding, the relationship between the details of foam microstructure and foam bulk response is generally unknown. With continued advances in computational power, many researchers have turned to numerical simulation to gain insight into the relationship between foam microstructure and bulk properties. However, numerical simulation of foam microscale deformation is a very challenging computational task and, to date, simulations over the full range of bulk deformations in which these materials operate have not been reported. Here a particle technique is demonstrated to be well-suited for this computational challenge, permitting simulation of the compression of foam microstructures to full densification. Computations on idealized foam microstructures are in agreement with engineering guidelines and various experimental results. Dependencies on degree of microstructure regularity and material properties are demonstrated. A surprising amount of porosity is found in fully-densified foams. The presence of residual porosity can strongly influence dynamic material response and hence needs to be accounted for in bulk (average) constitutive models of these materials.     

Constitutive equations for martensitic reorientation and detwinning in shape-memory alloys

A crystal-inelasticity-based constitutive model for martensitic reorientation and detwinning in shape-memory alloys (SMAs) has been developed from basic thermodynamics principles. The model has been implemented in a finite-element program by writing a user-material subroutine. We perform two sets of finite-element simulations to model the behavior of polycrystalline SMAs: (1) The full finite-element model where each finite element represents a collection of martensitic microstructures which originated from within an austenite single crystal, chosen from a set of crystal orientations that approximates the initial austentic crystallographic texture. The macroscopic stress-strain responses are calculated as volume averages over the entire aggregate: (2) The Taylor model (J. Inst. Metals 62 (1938) 32) where an integration point in a finite element represents a material point which consist of sets of martensitic microstructures which originated from within respective austenite single-crystals. Here the macroscopic stress-strain responses are calculated through a homogenization scheme.Experiments in tension and compression were conducted on textured polycrystalline Ti-Ni rod initially in the martensitic phase by Xie et al (Acta Mater. 46 (1998) 1989). The material parameters for the constitutive model were calibrated by fitting the tensile stress-strain response from a full finite-element calculation of a polycrystalline aggregate to the simple tension experiment. With the material parameters calibrated the predicted stress-strain curve for simple compression is in very good accord with the corresponding experiment. By comparing the simulated stress-strain response in simple tension and simple compression it is shown that the constitutive model is able to predict the observed tension-compression asymmetry exhibited by polycrystalline Ti-Ni to good accuracy. Furthermore, our calculations also show that the macroscopic stress-strain response depends strongly on the initial martensitic microstructure and crystallographic texture of the material.We also show that the Taylor model predicts the macroscopic stress-strain curves in simple tension and simple compression reasonably well. Therefore, it may be used as a relatively inexpensive computational tool for the design of components made from shape-memory materials.     

Adhesion and friction of an elastic half-space in contact with a slightly wavy rigid surface

The paper deals with the estimation of the pressure distribution, the shape of contact and the friction force at the interface of a flat soft elastic solid moving on a rigid half-space with a slightly wavy surface. In this case an unsymmetrical contact is considered and justified with the adhesion hysteresis. For soft solids as rubber and polymers the friction originates mainly from two different contributions: the internal friction due to the viscoelastic properties of the bulk and the adhesive processes at the interface of the two solids. In the paper the authors focus on the latter contribution to friction. It is known, indeed, that for soft solids, as rubber, the adhesion hysteresis is, at least qualitatively, related to friction: the larger the adhesion hysteresis the larger the friction. Several mechanisms may govern the adhesion hysteresis, such as the interdigitation process between the polymer chains, the local small-scale viscoelasticity or the local elastic instabilities. In the paper the authors propose a model to link, from the continuum mechanics point of view, the friction to the adhesion hysteresis. A simple one-length scale roughness model is considered having a sinusoidal profile. For partial contact conditions the detached zone is taken to be a mode I propagating crack. Due to the adhesion hysteresis, the crack is affected by two different values of the strain energy release rate at the advancing and receding edges respectively. As a result, an unsymmetrical contact and a friction force arise. Additionally, the stability of the equilibrium configurations is discussed and the adherence force for jumping out of contact and the critical load for snapping into full contact are estimated.     

Uniqueness in the water-wave problem for bodies intersecting the free surface at arbitrary anglesL'unicité du problème des ondes de surface pour les corps qui intersectent la surface libre sous des angles arbitraires

This Note deals with the linearized water-wave problem involving a surface-piercing cylinder in water of infinite depth. A solution to this problem is proved to be unique for all values of the radian frequency when the cylinder intersecting the free surface at arbitrary angles is subjected to certain geometric arrangements. To cite this article: N. Kuznetsov, C. R. Mecanique 332 (2004).     

Validation of averaged equations for thermal vibrational convection in near-critical fluidsValidation d'équations moyennées pour l'étude de la convection vibrationnelle dans les fluides supercritiques.

Within an averaging approach, the governing equations and effective boundary conditions describing both the average and pulsation motion of a near-critical fluid subjected to high-frequency vibrations are obtained. Vibrations induce the non-homogeneities in average temperature. Owing to these non-homogeneities, the average flows can be generated even in isothermal cavity under weightlessness. These flows are examined for 1D and 2D configurations. The direct numerical simulations fulfilled earlier confirm the averaged model, we obtain the same flow structures by essentially smaller requirements for computational time. To cite this article: A.Vorobev et al., C. R. Mecanique 332 (2004).     

双周期裂纹压电材料反平面剪切问题断裂力学分析

研究压电材料双周期裂纹反平面剪切与平面电场作用的问题．运用复变函数方法，获得了该问题严格的闭合解，并由此给出了裂纹尖端应力强度因子和电位移强度因子的精确公式．数值算例显示了裂纹分布特征对材料断裂行为的重要影响．叠间小裂纹能够对主裂纹的应力和电位移场起着屏蔽作用，相反行间小裂纹却起着放大作用，至于钻石形分布裂纹的影响规律则更为复杂．对于某些特殊情形给予了解答并导出一系列有意义的结果。     

Bifurcations et solutions multiples en cavité 3D différentiellement chaufféeBifurcations and multiple solutions in a differentially heated cubic cavity

In this paper, a differentially heated square/cubic cavity is studied by performing three-dimensional direct numerical simulations. The first bifurcation observed at $\text{R}{}_{\mathrm{a}}\text{≈3.2×10}{}^7$ is due to the 3D vortex structures generated at the end regions of vertical boundary layers near the median plane. The main results of this Note are that the flow returns to a steady state for higher values of the Rayleigh number $\text{R}{}_{\mathrm{a}}$ (7×10⁷ and 10⁸ for example) still exhibiting these 3D vortex structures, and that multiple steady flows which differ by their symmetry properties, are obtained for $\text{R}{}_{\mathrm{a}}\text{=10}{}^8$. However, the flow reverts to unsteadiness for $\text{R}{}_{\mathrm{a}}\text{=3×10}{}^8$. In this latter case, the instability is due to the vertical boundary layers. To cite this article: G. de Gassowski et al., C. R. Mecanique 331 (2003).     

On the fundamental sloshing frequency in the ice-fishing problemSur la fréquence de ballottement principale dans le problème de la glace avec trous pour pêcher

The sloshing problem is considered in a half-space covered by a rigid dock with apertures. The dependence of the fundamental sloshing frequency on the shape of the free surface region is studied. It is proved that the inequality holds between the fundamental eigenvalues corresponding to two different regions if some conditions are fulfilled. These conditions are verified for particular classes of regions of a fixed area in order to demonstrate that the disk yields the maximum of the fundamental eigenvalue for each of these classes. On the other hand, examples of regions are constructed for which the fundamental eigenfrequency is larger than that for the circular aperture of the same area and even as large as one wishes. To cite this article: V. Kozlov, N. Kuznetsov, C. R. Mecanique 330 (2002) 723–728.     

澜沧江某电站左岸地下洞室群围岩稳定性的FLAC~(3D)分析

在岩体结构模型概化的基础上,采用FLAC3D数值分析方法,系统研究了澜沧江某大型水电站大跨度、高边墙地下洞室群开挖完成后围岩的二次应力场、变形场和塑性破坏区的变化特征。总结了地下洞室群围岩应力、变形和破坏区的分布特征和变化规律,为洞室群稳定性评价和工程施工设计提供了基础资料和参考依据。     

高应变率大变形下的聚丙烯/尼龙共混高聚物损伤型本构特性

对两种采用不同相容剂的聚丙烯（PP）和尼龙（PA）共混高聚物材料在大变形下的粘弹性力学行为进行研究,着重考察应变率效应和损伤的演化,从而分析不同的界面分子设计对共混体系材料宏观性能的作用。在准静态及冲击实验研究的基础上,基于ZWT非线性粘弹性模型,并结合了遗传算法,分别得到了能有效描述两种共混高聚物大变形阶段计及损伤的非线性粘弹性本构关系。两种材料在不同加载条件下表现出明显不一致的性能,原因在于其损伤演化的率相关性,且两种材料的大变形机制存在一定的差别,能用ZWT方程进行描述的范围也不一样。