Some numerical simulations of large deformations of heterogeneous hyperelastic media

Numerical experiments done on a two-dimensional stratified two-phase composite corroborate theoretical results on homogeneization of media capable of large deformations.     

Buckling of thin-walled orthotropic cylindrical shells under uniform external pressure.: Application to corrugated tin cans

The general instability of thin-walled orthotropic circular cylindrical shells under external pressure is investigated. The buckling pressure can be predicted with the use of simple analytical formulae derived from an asymptotic analysis of the corresponding eigenvalue problems. The results predicted by these formulae are compared with finite element solutions and the four types of experimental models investigated by Ross (Thin Walled Structures 1996;26(3):179–93). The comparison proved to be accurate enough for practical purpose except for experimental model 1.     

Finite element simulation of deformation behavior of semi-crystalline polymers with multi-spherulitic mesostructure

Elasto-viscoplastic deformation behavior of semi-crystalline polymer with multi-spherulitic mesostructure was investigated using large deformation finite element homogenization method. Multi-spherulitic mesostructure was modeled in representation volume element (RVE) by Voronoi polygons, and the deformation behavior during tension in different directions was numerically investigated. Mesoscopic stress strain relations were almost similar for different mesoscopic structures except for a quarter spherulite mesoscopic models, and its anisotropy decreased with increase in the number of spherulites in RVE. Although anisotropy in mesoscopic stress strain relation disappeared for enough number of spherulites, highly heterogeneous distribution of local strain and stress was observed in each spherulite. Distribution of lamellar orientation in the spherulite caused the heterogeneity and played an important role in the local deformation field.     

A multiscale extended finite element method for crack propagation

In this paper, we propose a multiscale strategy for crack propagation which enables one to use a refined mesh only in the crack’s vicinity where it is required. Two techniques are used in synergy: a multiscale strategy based on a domain decomposition method to account for the crack’s global and local effects efficiently, and a local enrichment technique (the X-FEM) to describe the geometry of the crack independently of the mesh. The focus of this study is the avoidance of meshing difficulties and the choice of an appropriate scale separation to make the strategy efficient. We show that the introduction of the crack’s discontinuity both on the microscale and on the macroscale is essential for the numerical scalability of the domain decomposition method to remain unaffected by the presence of a crack. Thus, the convergence rate of the iterative solver is the same throughout the crack’s propagation.     

Estimates of effective characteristics of random cell structures in terms of effective characteristics of periodic structures

The bounds of effective characteristics of random cell structures are obtained in terms of effective characteristics of periodic structures.     

Wavelet-based homogenization of unidirectional multiscale composites

The main aim is to present a homogenization algorithm for the multiscale heterogeneous (composite) materials, which is based on the wavelet representation of material properties and the relevant multiscale reduction. It is shown that classical homogenization method used before for two-scale composites (with micro and macro scales) is a special case of general multiresolutional strategy, where a single scale parameter tends to 0. The approach presented is applied to unidirectional wavelet-based homogenization of linear elasticity heterogeneous problem and to wave propagation, which may be applied in conjunction with various discrete numerical methods for efficient modeling of heterogeneous solids, fluids and multiphase media.     

Diffusion with micro-sorption in bentonite: evaluation by molecular dynamics and homogenization analysis

We here give a numerical analysis method of a diffusion problem including sorption chemistry for bentonite clay. Bentonite predominantly consists of the microscopic smectitic clay minerals (mainly montmorillonite and beidellite). Physico-chemical properties of smectite clays such as diffusivity of chemical species and adsorptivity on surface of clay mineral are characterized by crystalline structure of hydrated smectite minerals. To obtain the microscopic properties of the hydrated smectite, the molecular behavior is analyzed by a molecular dynamic (MD) simulation. We understand at least two types of adsorption are formed on the smectite surface; outer sphere complex and inner sphere complex. The inner sphere complex occurs on the edge sites of clay minerals. The amount of mono-layer of cations on the edge surface is considered as the adsorptivity of smectite in the microscopic level. A multiscale homogenization analysis (HA) is applied to extend the microscopic characteristics of the hydrated smectite to the macroscopic behavior. The diffusion and adsorption of a radioactive specie, cesium (Cs), is introduced by this analysis. The calculated results appear to be acceptable.     

均质化制度对Mg-Li合金显微组织和机械性能的影响

研究了超轻镁锂变形合金热处理后的合金显微组织和机械性能。镁锂合金在室温条件下具有非常良好的延展性，Mg—Li—Zn系变形镁合金铸锭经不同温度、时间均匀化退火后的组织、硬度以及冷轧性能进行了研究。结果表明。Mg．9％Li-2％Zn-2％Ca合金在573K温度均匀化退火12h后合金铸锭组织均匀；而对于Mg-9％Li-2％Zn合金，523K温度均匀化退火24h后组织较好。     

炉料搭配和均匀化处理对铸造锌铝合金组织与性能的影响

采用扫描电子显微镜和能谱微区分析,研究了以全新炉料和新旧炉料两种不同炉料搭配方式生产铸造锌铝合金铸件的组织与性能,并对其在铸态和经均匀化处理后的显微组织及成分进行了对比分析。发现采用全新炉料搭配比采用新旧炉料按1∶1搭配的铸造锌铝合金显微组织均匀、力学性能好;在相同条件下,经均匀化处理比铸造状态下的综合性能好。