OSCILLATORY AND ASYMPTOTIC BEHMIOUR OF A CLASS OF NONLINEAR DIFFERENTIALEQUATIONS OF THIRD ORDER

1IntroductionInthispaperwedealwithoscillatoryandnonoscillatorybehaviourofsolutionsofnonlinearthirdorderdifferentialequationsoftheformwherea,b,cEC([er,co),R),rrER,fEC(R,R)suchthatac2P>0fory/0and7>0isaquotientofoddintegers.From"Theoryofequations"tsee[1],itfollowsthattheequationwithconstantcoefficientsMoreover,allnonoscillatorysolutionsof(1.3)tendtozeroifandonlyifequatioll(l.3)hasanoscillatorysolution.Theseobservationsarefoundtobetruetoalargeextentformoregeneralequationsoftheformwherealb,cE…     

非平衡状态下半导体方程解在H1中的收敛

本文研究具有Dirichlet边界条件的稳态半导体模型，在净复合率R≠0时，对N维半导体方程，论证了奇异摄动问题的解在H^1中弱收敛于退化问题的解；对一维半导体模型，进一步证明了解在H^1中强收敛。     

Modelling the mechanical behaviour of adhesively bonded and sintered hollow-sphere structures

The mechanical properties of periodic hollow-sphere structures are investigated numerically. Young’s modulus and the Poisson ratio are determined in order to describe their linearly elastic behaviour. The initial compressive yield strength is also calculated. The spheres are located at the nodes of a cubic primitive lattice. The cohesion is achieved by an adhesive concentrated in the minimum gap between neighbouring spheres. The geometry of the structure is discretized based on regular hexahedral elements. This approach is much more time-consuming, but it is important in order to achieve a more accurate simulation of the nonlinear behaviour (e.g., plasticity) of such materials. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 42, No. 6, pp. 803–816, November–December, 2006.     

Load-induced oriented damage and anisotropy of rock-like materials

Theoretical model for deformability of brittle rock-like materials in the presence of an oriented damage of their internal structure is formulated and verified experimentally. This model is based on the assumption that non-linearity of the stress–strain curves of these materials is a result of irreversible process of oriented damage growth. It was also assumed that a material response, represented by the strain tensor, is a function of two tensorial variables: the stress tensor and the damage effect tensor that is responsible for the current state of the internal structure of the material. The explicit form of the respective non-linear stress–strain relations that account for the appropriate damage evolution equation was obtained by employing the theory of tensor function representations and by using the results of own experiments on damage growth. Such an oriented damage that grows in the material, described by the second order symmetric damage effect tensor, results in gradual development of the material anisotropy. The validity of the constitutive equations proposed was verified by using the available experimental results for concrete subjected to the plane state of stress. The relevant experimental data for sandstone and concrete subjected to tri-axial state of stress were also used.     

干燥和水饱和花岗岩的动态断裂特性

利用霍布金森压杆实验研究了干燥和水饱和花岗岩试件的动态应力应变关系。实验得到了干燥和水饱和花岗岩试件的平均动态拉断强度，表明水饱和花岗岩试件和干燥花岗岩试件的抗拉强度与加载速率具有不同的关系。对实验中实测试件层裂片的厚度进行了计算分析，对岩石类介质的动态断裂准则提出了初步见解。     

Viscoplastic behaviour of a medium density polyethylene (MDPE): Constitutive equations based on double nonlinear deformation model

The viscoplastic behaviour of a medium density ethylene–butene copolymer (MDPE) is investigated by using samples cut out from thick-walled MDPE pipe. Extensive experimental work has been performed to characterise the nonlinear time-dependent response of such semi-crystalline thermoplastic material. Tests were carried out at 60 °C, on smooth tensile, full axisymmetrically notched creep tensile (FNCT) and double edge notched tensile (DENT) specimens.     

含能材料三轴动态压缩实验的一个计算机模拟方法

在含能材料单轴、受限三轴动态压缩实验的基础上，提出一种将计算机数值模拟和实验数据相结合，估算实验系统中钢筒与试件间的库伦摩擦力，从而正确确定含能材料的动态三轴力学性能（弹性模量Ｅ，泊桑比ν，屈服限Ｙ等）的方法。本方法用于ＴＮＴ炸药受限三轴动态压缩实验，通过建立钢筒－试件的库伦摩擦有限元模型，采用ＡＤＩＮＡ通用程序进行动力分析，估算了摩擦力对实验数据的影响，获得了考虑摩擦力修正后的ＴＮＴ三轴动态压缩响应，为含能材料三轴动态力学性能的确定提供了一种有效的方法。     

Composite and filament models for the mechanical behaviour of elastomeric materials

In this work we present a composite model, which combines the approach of Poisson's function with the filament theory and requires three material parameters. We also suggest the form for a strain-energy function that approximates the constitutive equations of the composite model. Furthermore, a simple asymptotic analysis allows us to reduce the number of material constants to only two, thus, forming a new filament model. The predictive capability of the two models to reproduce the mechanical behaviour of elastomeric materials in deformation experiments is evaluated against the extensive data of Kawabata et al. (Macromolecules 14 (1981) 154). The models give excellent agreement in not only uniaxial and equibiaxial but also non-equibiaxial extension. Although being rather more simplistic in comparison with some successful network models involving non-Gaussian chain statistics, the two models conform much more closely to the classical experimental data of Treloar (Trans. Faraday Soc. 40 (1944) 59).     

CO2 will probably not help to save Venice from the sea

It has been proposed to rise Venice by injecting CO₂ into an aquifer lying 600–800 m below its lagoon. It is shown that because of the prevailing ambient conditions in the aquifer phase change of CO₂ cannot be avoided. The ensuing change of specific volume and compressibility will inhibit a uniform uplift pattern which is needed to avoid cracks in historical buildings. Further, both liquid and gaseous CO₂ produce capillary effects at the contact surface with water in the voids of the reservoir rock and this affects its mechanical response. Hence further non homogeneity in the uplift pattern will be produced. This prevents the use of CO₂ in the proposed conditions.     

Cavity nucleation, growth and stress field in elastic-plastic medium

A finite element method is used to study the cavity nucleation and growth in an elastic-plastic medium. The critical cohesion strength, _c at IPM (interface between second phase particle and matrix) is employed as the criterion of cavity formation. Three different values of _c are taken to examine their influence on the overall mechanical behaviour and process of cavity formation.