Improved reverse analysis for material characterization with dual sharp indenters

It was illustrated by the author in the previous work that combinations between material properties and indentation parameters can be used as mixed parameters in dimensionless functions to capture the indentation response of materials to single and dual sharp indenters. These issues are further extended in the present study. A parametric finite element analysis was performed to investigate the conical indentation response of elasto-plastic solids. Frictional effects are studied. Conical indenters of half-included angles from 50° to 88° are considered to examine several fundamental features of instrumented sharp indentation within the frame work of limit analysis. Regarding dimensional analysis, it is found that a Taylor series expansion according to the elastic indentation work-total indentation work ratio W_e/W_t can be used to improve dimensionless functions. Within this context, a new set of dimensionless functions is explicitly constructed for hardness and indentation parameters of single and dual indenters. Based on formulated functions, a reverse analysis with dual sharp indenters, which was previously proposed by the author, is improved to extract mechanical properties of materials.     

A computational study on the instrumented sharp indentations with dual indenters

Finite element analysis was performed to investigate the indentation response of elasto-plastic solids for conical indenters of half included angles of 60° and 70.3°. The interdependence indentation parameters resulting from a single indentation load–depth curve is considered. Regarding dimensional analysis, several dimensionless relationships are constructed as functions of the reduced elastic modulus-loading curvature ratio E¹/C and the strain hardening exponent n. Further, the duality between corresponding parameters with dual indenters is explored. Finally, a new method based on dual indenters is proposed to extract the strain hardening exponent and the reduced elastic modulus of an indented material. The accuracy of this method is verified and discussed with experimental data from the literature and representative materials.     

Universal viscometric functions for dilute polymer solutions

The Gaussian approximation has been shown previously to be excellent for the treatment of hydrodynamic effects in dilute polymer solutions. However, the computational time required to find the viscometric functions in simple shear flow is prohibitively long for chains with a large number of beads. Here we introduce a new approximation which retains the accuracy of the Gaussian approximation but is significantly less computationally intensive. Thus the rheological behavior of long chains may be explored. Extrapolation of results obtained numerically for long chains to the infinite chain length limit is shown to lead to predictions independent of model parameters. As a result, within the context of the approximation introduced here, universal viscometric functions for dilute polymer solutions in simple shear flow under theta conditions are obtained.     

Switchable dry adhesive based on shape memory polymer with hemispherical indenters for transfer printing

Transfer printing based on switchable adhesive is essential for developing unconventional systems, including flexible electronics, stretchable electronics, and micro light-emitting diode (LED) displays. Here we report a design of switchable dry adhesive based on shape memory polymer (SMP) with hemispherical indenters, which offers a continuously tunable and reversible adhesion through the combination of the preloading effect and the thermal actuation of SMP. Experimental and numerical studies reveal the fundamental aspects of design, fabrication, and operation of the switchable dry adhesive. Demonstrations of this adhesive concept in transfer printing of flat objects (e.g., silicon wafers), three-dimensional (3D) objects (e.g., stainless steel balls), and rough objects (e.g., frosted glasses) in two-dimensional (2D) or 3D layouts illustrate its unusual manipulation capabilities in heterogeneous material integration applications.     

A criterion of the continuous spectrum for elasticity and other self-adjoint systems on sharp peak-shaped domains

The spectra of the elasticity and piezo-electricity systems for a solid with a sharp peak point on the boundary, which is free of traction, are not discrete. An algebraic criterion of non-empty continuous spectrum is found for the Neumann problem for rather arbitrary formally self-adjoint elliptic systems of second-order differential equations on a sharp peak-shaped domain. To cite this article: S.A. Nazarov, C. R. Mecanique 335 (2007).     

充液弯管连续/离散模型振动的动刚度解法

由充液弯管三维振动模型切入,应用动刚度法构建了弯管及直管单元的振动求解方法,进而用于组装求解充液管系的振动,可同时适用于含弯管单元的连续模型或只含直管单元的离散模型;通过算例对比,证明动刚度法比传递矩阵法和有限元法在计算效率和精度上有所提升;与充液L型管道振动实验测得的加速度频响曲线对比,验证了本文对于管道组装的计算方法的有效性,此外还分析了连续模型和离散模型的区别及适用范围。     

Effective bending stiffness for plates with microcracks

Summary In this paper, micromechanics methods are applied to characterize the damage of plate structures, both Love-Kirchhoff and Reissner-Mindlin plates, due to microcrack distribution. Analytical expressions for effective stiffness of a damaged plate with distributed microcracks are derived for the first time. The results are compared with the results based on continuum damage theory, and it is found that there are significant differences between the two. It is well known that constitutive relations at the structural level, e.g. curvature/moment relation, and shear/transverse strain relation, are fundamentally different from the constitutive relation at the material level, i.e. stress/strain relations. This is because a priori kinematic assumptions in engineering structural theories pose additional constitutive constraints on the relationships between stress resultant/couple and strain measures. The newly derived effective stiffness formulae for various plates reflect such constitutive constraints, and therefore are consistent with engineering plate theories. They provide an alternative means in structure designs and structure damage evaluations.The work is supported by an Junior Faculty Research Fund (BURNL-07427-11503-EGSLI) to Professor Shaofan Li provided by the senate committee on research of University of California at Berkeley. The authors would like to thank the referees of AAM helpful comments and suggestions.     

Diagrams of critical equilibrium for brittle bodies with sharp flaws

Certain forms of the stress-intensity factors close to the tips of sharp flaws (plane problem) are used as the basis of a method for plotting critical equilibrium diagrams for brittle bodies with flaws in the form of pointed cavity-cracks [5]. Concrete examples are discussed, mainly in the context of such diagrams, for a brittle body weakened by a circular cavity flaw with a crack leaving the edge of the flaw. Determination of the stress-intensity factors for this problem is based on approximate solution of an integral equation by the method of collocations. Plots of some familiar diagrams are also analyzed.Translated from Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, Vol. 11, No. 3, pp. 98–104, May–June, 1970.     

A reconstructed discontinuous Galerkin method for multi-material hydrodynamics with sharp interfaces

Discontinuous Galerkin (DG) methods have been well established for single-material hydrodynamics. However, consistent DG discretizations for non-equilibrium multi-material (more than two materials) hydrodynamics have not been extensively studied. In this work, a novel reconstructed DG (rDG) method for the single-velocity multi-material system is presented. The multi-material system being considered assumes stiff velocity relaxation, but does not assume pressure and temperature equilibrium between the multiple materials. A second-order DG(P₁) method and a third-order least-squares based rDG(P₁P₂) are used to discretize this system in space, and a third-order total variation diminishing (TVD) Runge-Kutta method is used to integrate in time. A well-balanced DG discretization of the non-conservative system is presented and is verified by numerical test problems. Furthermore, a consistent interface treatment is implemented, which ensures strict conservation of material masses and total energy. Numerical tests indicate that the DG and rDG methods are, indeed, the second- and third-order accurate. Comparisons with the second-order finite volume method show that the DG and rDG methods are able to capture the interfaces more sharply. The DG and rDG methods are also more accurate in the single-material regions of the flow. This work focuses on the general multidimensional rDG formulation of the non-equilibrium multi-material system and a study of properties of the method via one-dimensional numerical experiments. The results from this research will be the foundation for a multidimensional high-order rDG method for multi-material hydrodynamics.     

变截面Timoshenko梁的单元刚度矩阵

变截面构件在工程中应用广泛,在对变截面梁进行数值计算时,需要建立变截面梁单元的刚度矩阵。该文采用势能驻值原理,考虑了轴力引起的几何非线性和剪切变形的影响,将梁截面刚度的变化率作为小量,得到了近似到二阶的单元刚度矩阵。在构造位移模式时,从梁的微分平衡方程出发,得到同样近似到二阶、分别以三次和五次多项式表示的剪切和弯曲位移模式。该文还证明了单元刚度矩阵的奇异性,给出了轴压刚度的表达式,定量论证了与某些精确解的误差,表明在一定范围内,该文的结果具有足够的精度。最后以一个计算实例说明该文的单元刚度矩阵具有较快的收敛性。     

Near-wall scaling for turbulent boundary layers with adverse pressure gradient

A new extended inner scaling is proposed for the wall layer of wall-bounded flows under the influence of both wall shear stress and streamwise pressure gradient. This scaling avoids problems of the classical wall coordinates close to flow separation and reattachment. Based on the proposed extended velocity and length scales a universal nondimensional family of velocity profiles is derived for the viscous region in the vicinity of a wall that depend on wall distance and a parameter α quantifying the importance of the streamwise pressure gradient with respect to the wall shear stress in the momentum balance. The performance of the proposed extended scaling is investigated in two different flow fields, a separating and reattaching turbulent boundary layer and a turbulent flow over a periodic arrangement of smoothly contoured hills. Both flows are results of highly resolved direct numerical simulation (DNS). The results show that the viscous assumptions are valid up to about two extended wall units. If the profiles are scaled by the extended inner coordinates, they seem to behave in a universal way. This gives rise to the hope that a universal behavior of velocity profiles can be found in the proposed extended inner coordinates even beyond the validity of the extended viscous law of the wall.      

平行圆管空心板双向抗弯刚度的确定

平行圆管空心板横管方向抗弯刚度的取值问题尚未获得圆满解决.本文通过有限元分析,发现横管方向平均应变仍符合平截面假定;提出了两种基于数值解求其等效刚度的方法,即分别用水平位移按刚度定义计算和用竖向挠庹按挠度-刚度关系式计算,两种方法的结果得到了相互印证;继而经拟合得到了横管与顺管两个方向刚度比的经验公式,简单实用.值得指出,本文提出的等效刚度确定方法简便合理,对解决类似问题有重要的借鉴价值.     

Dynamic elastic stiffness with service generated inhomogeneity for fibrous composites

Following the work on the determination of dynamic elastic constants for the state of affairs around a single inhomogeneous ellipsoid, this work considers a fibrous composite whose inhomogeneity is increased on account of change in porosity or moisture content after the composite has been in service for some time. The added inhomogeneous phase, measured in terms of volume fraction of uniformly suspended particles in composite, is related to velocity measurement(s). The analysis is useful when the volume fraction of one type of inclusion phase is not known a priori.     

A generalized frequency detuning method for multidegree-of-freedom oscillators with nonlinear stiffness

In this paper, we derive a frequency detuning method for multi-degree-of-freedom oscillators with nonlinear stiffness. This approach includes a matrix of detuning parameters, which are used to model the amplitude dependent variation in resonant frequencies for the system. As a result, we compare three different approximations for modeling the affect of the nonlinear stiffness on the linearized frequency of the system. In each case, the response of the primary resonances can be captured with the same level of accuracy. However, harmonic and subharmonic responses away from the primary response are captured with significant differences in accuracy. The detuning analysis is carried out using a normal form technique, and the analytical results are compared with numerical simulations of the response. Two examples are considered, the second of which is a two degree-of-freedom oscillator with cubic stiffnesses.     

Bifurcation and universal unfolding for a rotating shaft with unsymmetrical stiffness

The 1/2 subharmonic resonance bifurcation and universal unfolding are studied for a rotating shaft with unsymmetrical stiffness. The bifurcation behavior of the response amplitude with respect to the detuning parameter was studied for this class of problems by Xiao et al. Obviously, it is highly important to research the bifurcation behavior of the response amplitude with respect to the unsymmetry of stiffness for this problem. Here, by means of the singularity theory, the bifurcation and universal unfolding of amplitude with respect to the unsymmetrical stiffness parameter are discussed. The results indicate that it is a high codimensional bifurcation problem with codimension 5, and the universal unfolding is given. From the mechanical background, we study four forms of two parameter unfoldings contained in the universal unfolding. The transition sets in the parameter plane and the bifurcation diagrams are plotted. The results obtained in this paper show rich bifurcation phenomena and provide some guidance for the analysis and design of dynamic buckling experiments of this class of system, especially, for the choice of system parameters. The project supported by the National Natural Science Foundation of China (19990510), the National Key Basic Research Special Foundation (G1998020316) and Liuhui Center for Applied Mathematics, Nankai University and Tianjin University     

Velocity-defect scaling for turbulent boundary layers with a range of relative roughness

Velocity profile measurements in zero pressure gradient, turbulent boundary layer flow were made on a smooth wall and on two types of rough walls with a wide range of roughness heights. The ratio of the boundary layer thickness (δ) to the roughness height (k) was 16≤δ/k≤110 in the present study, while the ratio of δ to the equivalent sand roughness height (k _s) ranged from 6≤δ/k _s≤91. The results show that the mean velocity profiles for all the test surfaces agree within experimental uncertainty in velocity-defect form in the overlap and outer layer when normalized by the friction velocity obtained using two different methods. The velocity-defect profiles also agree when normalized with the velocity scale proposed by Zagarola and Smits (J Fluid Mech 373:33–70, 1998). The results provide evidence that roughness effects on the mean flow are confined to the inner layer, and outer layer similarity of the mean velocity profile applies even for relatively large roughness.