Optimization of a metal honeycomb sandwich beam-bar subjected to torsion and bending

In this paper, we analyze a metal honeycomb sandwich beam/torsion bar subjected to combined loading conditions. The cell wall arrangement of the honeycomb core is addressed in the context of maximizing resistance to either bending, torsion, or combined bending and torsion for given dimensions, face sheet thicknesses and core relative density. It is found that the relative contributions of the honeycomb core to torsion and bending resistances are sensitive to the configuration of cell walls and the optimal properties significantly exceed those of stochastic metallic foams as sandwich beam core materials for this configuration.     

Finite element study for conical indentation of elastoplastic micropolar material

Numerous experiments have repetitively shown that the material behavior presents effective size dependent mechanical properties at scales of microns or submicrons. In this paper, the size dependent behavior of micropolar theory under conical indentation is studied for different indentation depths and micropolar material parameters. To illustrate the effectiveness of the micropolar theory in predicting the indentation size effect (ISE), an axisymmetric finite element model has been developed for elastoplastic contact analysis of the micropolar materials based on the parametric virtual principle. It is shown that the micropolar parameters contribute to describe the characteristic of ISE at different scales, where the material length scale regulates the rate of hardness change at large indentation depth and the value of micropolar shear module restrains the upper limit of hardness at low indentation depth. The simulation results showed that the indentation loads increase as the result of increased material length scale at any indentation depth, however, the rate of increase is higher for lower indentation depth, relative to conventional continuum. The numerical results are presented for perfectly sharp and rounded tip conical indentations of magnesium oxide and compared with the experimental data for hardness coming from the open literature. It is shown that the satisfactory agreement between the experimental data and the numerical results is obtained, and the better correlation is achieved for the rounded tip indentation compared to the sharp indentation.     

An approximate solution to the problem of cone or wedge indentation of elastoplastic solids

The model developed in this Note makes it possible to determine the value of the mean indentation pressure usually named hardness from the elastoplastic properties of materials and also the shape of the cone or that of the wedge. The approximation rests upon the definition of a linear elastic solid which has the same indentation pressure as the material actually indented. Cases of cone and wedge indentation are studied. A method to determine the uniaxial stress–strain curve of materials from indentation tests is given. The results are validated using finite element simulations. To cite this article: G. Kermouche et al., C. R. Mecanique 333 (2005).     

Approximate analysis of progressive deformation in honeycomb structures subjected to in-plane loading

Progressive deformation of honeycomb structures subjected to in-plane loading was approximately analyzed by using the collapse modes of hexagonal unit cells. The collapse modes were categorized as freely compressive, restricted compressive, and shear. Moreover, there were five characteristic deformation patterns, namely deformation bands. Average stresses of the collapsing honeycomb models were evaluated in terms of the plastic collapse stress per hinge and total number of hinges of progressively arising deformation bands. The displacements of the models were obtained by multiplying the displacement per cell with the number of collapsed cells. The present method was used to analyze progressive deformation of typical honeycomb structures. The validity of the stress–displacement relations derived for some structures was confirmed by comparing them with finite element method (FEM) results. Our method is much simpler than FEM but just as effective.     

Self-consistent elastoplastic stress solutions for functionally graded material systems subjected to thermal transients

In this work, a self-consistent constitutive framework is proposed to describe the behaviour of a generic three-layered system containing a functionally graded material (FGM) layer subjected to thermal loading. Analytical and semi-analytical solutions are obtained to describe the thermo-elastic and thermo-elastoplastic behaviour of a three-layered system consisting of a metallic and a ceramic layer joined together by an FGM layer of arbitrary composition profile. Solutions for the stress distributions in a generic FGM system subjected to arbitrary temperature transient conditions are presented. The homogenisation of the local elastoplastic FGM behaviour in terms of the properties of its individual phases is performed using a self-consistent approach. In this work, power-law strain hardening behaviour is assumed for the FGM metallic phase. The stress distributions within the FGM systems are compared with accurate numerical solutions obtained from finite element analyses and good agreement is found throughout. Solutions are also given for the critical temperature transients required for the onset of plastic deformation within the three-layered systems.     

On the uniqueness of measuring elastoplastic properties from indentation: The indistinguishable mystical materials

Indentation is widely used to extract material elastoplastic properties from the measured force-displacement curves. One of the most well-established indentation techniques utilizes dual (or plural) sharp indenters (which have different apex angles) to deduce key parameters such as the elastic modulus, yield stress, and work-hardening exponent for materials that obey the power-law constitutive relationship. However, the uniqueness of such analysis is not yet systematically studied or challenged. Here we show the existence of “mystical materials”, which have distinct elastoplastic properties yet they yield almost identical indentation behaviors, even when the indenter angle is varied in a large range. These mystical materials are, therefore, indistinguishable by many existing indentation analyses unless extreme (and often impractical) indenter angles are used. Explicit procedures of deriving these mystical materials are established, and the general characteristics of the mystical materials are discussed. In many cases, for a given indenter angle range, a material would have infinite numbers of mystical siblings, and the existence maps of the mystical materials are also obtained. Furthermore, we propose two alternative techniques to effectively distinguish these mystical materials. The study in this paper addresses the important question of the uniqueness of indentation test, as well as providing useful guidelines to properly use the indentation technique to measure material elastoplastic properties.     

Dynamical similarity of multi-block catenary arches and rocking blocks subjected to horizontal base excitation

Nonlinear Dynamics - In this paper, the dynamical similarity of multi-block catenary arches and columns is discussed, which can be used for the simplified design of rocking arches. The basic...     

Linear and non-linear vibration and frequency response analyses of microcantilevers subjected to tip-sample interaction

Despite their simple structure and design, microcantilevers are receiving increased attention due to their unique sensing and actuation features in many MEMS and NEMS. Along this line, a non-linear distributed-parameters modeling of a microcantilever beam under the influence of a nanoparticle sample is studied in this paper. A long-range Van der Waals force model is utilized to describe the microcantilever-particle interaction along with an inextensibility condition for the microcantilever in order to derive the equations of motion in terms of only one generalized coordinate. Both of these considerations impose strong nonlinearities on the resultant integro-partial equations of motion. In order to provide an understanding of non-linear characteristics of combined microcantilever-particle system, a geometrical function is wisely chosen in such a way that natural frequency of the linear model exactly equates with that of non-linear model. It is shown that both approaches are reasonably comparable for the system considered here. Linear and non-linear equations of motion are then investigated extensively in both frequency and time domains. The simulation results demonstrate that the particle attraction region can be obtained through studying natural frequency of the system consisting of microcantilever and particle. The frequency analysis also proves that the influence of nonlinearities is amplified inside the particle attraction region through bending or shifting the frequency response curves. This is accompanied by sudden changes in the vibration amplitude estimated very closely by the non-linear model, while it cannot be predicted by the best linear model at all.     

Two-scale semiempirical theory of turbulent boundary layers and jets

To characterize the turbulence of boundary layers in the energy-bearing interval of wave numbers several turbulence scales are sometimes used (for example, [1, 2]). In particular, the universality of the semiempirical model of turbulence [2] can be extended in this way. A turbulence model with one equation (energy balance of the turbulence) has been constructed and used [3–6] and it has been established that the number of problems that can be solved for a universal choice of the values of the empirical coefficients increases appreciably if not one but two turbulent scales are used. In the present paper, it is shown that the introduction of a second scale makes it possible to take into account the interaction of shear layers in flows with two shear layers (for example, a channel or jet), and also to take into account the influence of turbulence of an external flow on a boundary layer. The interaction of shear layers is taken into account in theories containing a transport equation for the turbulent frictional stress _t (for example, [7]), in which the essence of the interaction reduces to diffusion of _t from layer to layer. In the present paper, a predominant volume interaction effect is assumed. It takes the form of a difference between the interaction of large-scale vortices with a shear deformation motion in flows with one and two shear layers, and also in the presence of turbulence in an external flow.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 8, pp. 17–25, November–December, 1982.     

感性材料与结构分析的两尺度模型

感性材料是一类基于植物仿生思想,利用化学能产生机械能的高能量密度智能材料。与植物感性运动类似,感性材料能够运用细胞半透膜,有选择、可控地将物质传输到体内产生定向变形。感性材料由基体材料中夹杂液体腔组成,液体腔周围有一层包含离子传输通道(离子泵、离子通道、离子协运机制等)的人工合成细胞膜。本文对感性材料的基本建模过程进行描述,建立了多感性驱动单元与结构相互作用的分析模型,并给出了计算结果。在感性单胞层次,通过对细胞膜离子传输过程以及结构力学模型进行耦合计算,再现感性运动中离子传输和基体结构的力学响应情况;通过改变各初始输入参数,研究不同参数对感性材料变形和响应过程的影响。     

Extension to continua of some minimum theorems in elastoplastic theory

Summary A study of the response of a continuum to given loads is carried out assuming a piecewise linear yield locus, normality, non-interacting yield planes and linear strain bardening. Minimum properties are determined for the plastic strain rates in the incremental case and for plastic strains satisfying holonomic and non-holonomic stress-strain laws, thus extending to continua the minimum properties determined elsewhere for discrete structural linear hardening systems.

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Sommario Si studia la risposta di un generico continuo soggetto ad assegnati carichi quando per il materiale sì assumano le ipotesi di assenza di interazione e di normalità. Introdotto un funzionale delle deformazioni plastiche incrementali e delle deformazioni plastiche soddisfacenti leggi di scorrimento olonomo ed anolonomo, si determinano delle proprietà di minimo che estendono al continuo alcuni teoremi di minimo per sistemi strutturali discreti.

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Study supported by the C.N.R. (Plasticity Group).     

Two-scale analysis of a filament-wound cylindrical structure and application of periodic boundary conditions

A two-scale numerical approach to predict the effective in-plane properties of helical filament-wound thin-walled cylindrical tubes is provided. A meso-scale repeated unit cell (RUC) model for a filament-wound tube is established according to the manufacturing process, in which cross-overs, undulations and overlaps of fibre bundles are described using a bottom-up solid modelling technique. An approach to implement the general periodic boundary conditions in a finite element analysis scheme is also presented. As an application example, the effective in-plane elastic constants of glass fibre/epoxy filament-wound tubes are predicted and the influences of the number of the winding circuits and the shape of the fibre bundles are analyzed and discussed. In addition, the stress/strain distribution in the RUC is obtained which provides the essential information on the stress/strain concentration due to fibre cross-over/undulation/overlap. This then indicates the location where damage will initiate.     

Reconcile the perfectly elastoplastic model to simulate the cyclic behavior and ratcheting

Perfectly elastoplastic constitutive model is modified through a smoothing factor introduced by Liu [Liu, C.-S., 2003. Smoothing elastoplastic stress–strain curves obtained by a critical modification of conventional models. Int. J. Solids Struct. 40, 2121–2145]. The new model allows plasticity to happen in a non-zero-measure yield volume in stress space, rather than that of conventional zero-measure yield surface, and within the yield volume the plastic modulus is varying continuously. It endows a specific strain-hardening rule of flow stress and is able to describe the phenomena of strain hardening, cyclic hardening, the Bauschinger effect, mean-stress relaxation, strain ratcheting, out-of-phase hardening, as well as erasure-of-memory. In order to suppress the over prediction of ratcheting we consider a scalar function of smoothing factor, which can simulate the saturation behavior of uniaxial/multiaxial strain ratcheting. These effects are demonstrated through numerical examples. The existence of stress equilibrium point and limiting surface is a natural result without requiring an extra design. Moreover, the non-linear constitutive equations can be converted into a linear system for augmented stress in the Minkowski space, of which the symmetry group is a proper orthochronous Lorentz group SO_o(5, 1). The augmented stress is a time-like vector, moving on hyperboloids inside the cone. When taking the Prager kinematic hardening rule into account we can simulate some cyclic behaviors of SAE 4340 and grade 60 steels within a certain accuracy through the use of only three material constants and a fixed smoothing factor. To simulate the ratcheting behaviors of SS304 stainless steel we allow the smoothing factor to be an exponential decaying function of λ.     

Analysis of elastic-plastic ball indentation to measure strength of high-strength steels

Ball-indentation experiment ware performed with A723 steel of 100- to 1200-MPa ultimate strength. Results are compared with conventional tension tests and with an elastic-plastic finite-element model of the ball indentation. Finite-element analysis shows the ball-indentation process to be insensitive to friction effects. Comparison of indentation and conventional tests shows that slip-line field analysis closely predicts the ball contact stress. The indentation tests gave an accurate measure of ultimate tensile strength because of the following test procedures: using a large ball size and a fixed ratio of indentation depth to ball size; accounting for directional material properties; accounting for extraneous system deflections.     

An application of Curie’s principle to elastoplastic dynamics

This paper deals with the stability and the dynamics of a harmonically excited elastic–perfectly plastic unsymmetrical oscillator. Stability of the periodic orbits is analytically investigated with a perturbation approach. The occurrence of ratcheting effect is discussed for this system, and is related to the loss of symmetry of the periodic orbit in the phase space. Curie’s principle of symmetry is numerically verified for the symmetrical system with positive damping. Therefore, the observation of ratcheting phenomenon is necessarily associated to a breaking of symmetry in the constitutive behaviour, or in the forcing term. However, the generalized version of Curie’s principle has to be considered when a negative damping is introduced.