Constitutive branching analysis of cylindrical bodies under in-plane equibiaxial dead-load tractions

Finite homogeneous deformations of hyperelastic cylindrical bodies subjected to in-plane equibiaxial dead-load tractions are analyzed. Four basic equilibrium problems are formulated considering incompressible and compressible isotropic bodies under plane stress and plane deformation condition. Depending on the form of the stored energy function, these plane problems, in addition to the obvious symmetric solutions, may admit asymmetric solutions. In other words, the body may assume an equilibrium configuration characterized by two unequal in-plane principal stretches corresponding to equal external forces. In this paper, a mathematical condition, in terms of the principal invariants, governing the global development of the asymmetric deformation branches is obtained and examined in detail with regard to different choices of the stored energy function. Moreover, explicit expressions for evaluating critical loads and bifurcation points are derived. With reference to neo-Hookean, Mooney-Rivlin and Ogden-Ball materials, a broad numerical analysis is performed and the qualitatively more interesting asymmetric equilibrium branches are shown. Finally, using the energy criterion, a number of considerations are put forward about the stability of the computed solutions.     

延性单晶非均匀变形的三维有限元模拟

对延性单晶在拉伸载荷作用下的应变局域化和颈缩等非均匀变形过程进行了三维有限元数值模拟。将相关晶体塑性本构模型及一种新的数值积分方法补充到ABAQUS6.1商用有限元软件中。该方法的特点是，利用晶体塑性的动力学方程，获得一个关于晶体弹性变形梯度的演化方程，采用半隐式积分方案进行求解。本文推导出一种新的应力变本构矩阵。按此方式更新本构矩阵，计算速度和计算稳定性大大提高。加载方式，边界条件和变形程度等因素影响着滑移系的启动状况，这是平面模型所不能预测的。本文利用三维有限元方法模拟了不同取向下滑移系的启动状况，全面地考虑了FCC单晶材料12个可能滑移系在变形过程中的启动状况，合理地模拟了FCC面心立方单晶沿不同取向加载时晶轴旋转导致的应变局域化和颈缩等非均匀变形过程。     

多孔硅橡胶有限变形的粘弹性行为

针对孔隙度较大（孔隙度大于50％）的硅橡胶材料在有限变形时的粘弹性行为，从建立描述材料粘弹性特征的松驰函数和变形特征的应变能函数出发，提出了适合多孔隙、可压硅橡胶材料的非线性粘弹性力学行为的本构关系，松驰函数和应变能函数可解耦为等容和体积变形两部分，并引入了拟时间的概念来反映变形对材料特征时间的影响，利用硅橡胶材料的单轴压缩松驰实验与材料模型进行了对比，讨论了多孔硅橡胶的等容变形和体积变形对应力松驰的影响。     

具有非线性homologous变形约束的桁架结构形态分析

研究了具有非线性homologous变形约束条件的桁架结构形态分析问题。在已有的线性homologous变形约束桁架形态分析的基础上,将结构的节点分成三类:homologous变形约束节点,形状可变节点和边界点。运用Moore-Penrose广义逆矩阵性质,将基础方程组解的存在条件表示为包含形状可变节点未知坐标的非线性方程组,为采用Newton-Raphson方法求解非线性方程组,对AA (A为任意矩阵,A 为A的Moore-Penrose广义逆矩阵)求偏导数,找到了满足保型要求的形态,给出的桁架算例说明了本文方法的有效性。     

微梁与基底间的毛细粘附作用

在表面微型机械结构的制造过程中,强的毛细相互作用常常使得组成这些结构的微桥、微梁与基底粘附而导致失效。而在微尺度实验中,微桥与微梁又是微尺度材料常数和性能检测的常用的试件样式,如果实验中加载端与被检测的微尺度试件发生毛细粘附,将直接影响检测数据的准确性。本文应用微悬臂梁试件,讨论微梁与基底间的毛细粘附作用,并通过能量原理计算其粘附力的大小和试件几何尺寸、粘附面距离、粘附液体特性之间的关系。最后应用微散斑干涉,检测粘附平衡态时微桥和微梁的粘附力以及由毛细粘附所导致的弯曲变形,并与理论计算结果进行比较。     

Deformation of a fibrous composite with physically nonlinear fibers and microdamageable matrix

The structural theory of short-term microdamage is generalized to a fibrous composite with a microdamageable matrix and physically nonlinear fibers. The basis for the generalization is the stochastic elasticity equations of a fibrous composite with a porous matrix. Microvolumes in the matrix material meet the Huber-Mises failure criterion. The damaged-microvolume balance equation for the matrix is derived. This equation and the equations relating macrostresses and macrostrains of a fibrous composite with porous matrix and physically nonlinear fibers constitute a closed-form system of equations. This system describes the coupled processes of physically nonlinear deformation and microdamage occurring in different components of the composite. Algorithms for computing the microdamage-macrostrain and macrostress-macrostrain relationships are developed. Uniaxial tension curves are plotted for a fibrous composite with linearly hardening fibers __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 1, pp. 38–47, January 2006.     

Short-term microdamage of a physically nonlinear particulate material under a combination of normal and tangential loads

The structural theory of short-term damage is generalized to the case where the undamaged components of a particulate composite deform nonlinearly under loads that induce a compound stress state. The basis for this generalization is the stochastic elasticity equations for a particulate composite with porous components whose skeletons deform nonlinearly. Damage in a microvolume of the material is assumed to occur in accordance with the Huber-Mises failure criterion. Balance equations for damaged microvolume are derived for the physically nonlinear materials of the components. Together with the macrostress-macrostrain relationship for a particulate composite with porous nonlinear components, they constitute a closed-form system of equations. This system describes the coupled processes of physically nonlinear deformation and microdamage. Algorithms for calculating the microdamage-macrostrain relationship and plotting stress-strain curves are proposed. Such curves are plotted for the case where the composite is subjected to a combination of normal and tangential loads, and microdamages occur in the linearly hardened matrix and do not in the linearly elastic inclusions. The stress-strain curves are examined depending on the volume fraction of inclusions and presence of tangential stresses __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 12, pp. 48–57, December, 2006.     

Thermal analysis of the roll in the strip casting process

Coiled strip can be directly produced through the twin-roll strip casting process from the melt by incorporating casting and hot rolling together into a single step. In this unique process, the strip formation from the molten metal critically relies upon the casting rolls. Thus, the design of the rolls is extremely essential. The coupled heat transfer and deformation analysis of the casting roll is carried out in a two-dimensional numerical model, using a finite element program (MARC) to examine the thermal stress and displacement. The effects of several factors such as the nickel overlay thickness on the roll surface, the casting speed, and the roll diameter on thermal characteristics are investigated.     

A Novel Fluid Structure Interaction Experiment to Investigate Deformation of Structural Elements Subjected to Impulsive Loading

This paper presents a novel experimental methodology for the study of dynamic deformation of structures under underwater impulsive loading. The experimental setup simulates fluid–structure interactions (FSI) encountered in various applications of interest. To generate impulsive loading similar to blast, a specially designed flyer plate impact experiment was designed and implemented. The design is based on scaling analysis to achieve a laboratory scale apparatus that can capture essential features in the deformation and failure of large scale naval structures. In the FSI setup, a water chamber made of a steel tube is incorporated into a gas gun apparatus. A scaled structure is fixed at one end of the steel tube and a water piston seals the other end. A flyer plate impacts the water piston and produces an exponentially decaying pressure history in lieu of explosive detonation. The pressure induced by the flyer plate propagates and imposes an impulse to the structure (panel specimen), which response elicits bubble formation and water cavitations. Calibration experiments and numerical simulations proved the experimental setup to be functional. A 304 stainless steel monolithic plate was tested and analyzed to assess its dynamic deformation behavior under impulsive loading. The experimental diagnostic included measurements of flyer impact velocity, pressure wave history in the water, and full deformation fields by means of shadow moiré and high speed photography.