Experimental and numerical investigations of the deformation of soft materials under tangential loading

The surface ‘tensile test’, in which tangential loads are applied through surface mounted adhesive tapes, is a viable method for the assessment of mechanical properties of soft materials, particularly biological soft materials in vivo. In the present work the deformation pattern and force–displacement relationship in the surface tensile test were experimentally investigated using surface displacement analysis (SDA) and numerically simulated using finite element modelling. The experimental and FE results showed close agreement using silicone rubber as a model material. The force–displacement relationship was found to be dependent on the tape separations. SDA measurements and FE simulation showed that the displacement and strain fields were not uniform and the distribution pattern varies with tape separation. A combined experimental–numerical approach to inversely extract material properties using multiple tests with different length scales is proposed and assessed using a model material.     

麦秸秆的力学性能及加筋滨海盐渍土的抗压强度研究

为开展天然草本纤维材料防腐前后的力学性能及加筋滨海盐渍土的抗压强度增长规律研究,本文探讨了麦秸秆的微结构特征及防腐方法、测试并对比了防腐前后的麦秸秆的质量增加率、吸水率、极限拉力和极限延伸率,证实用SH胶浸泡麦秸秆不仅能起到防腐作用,还可提高麦秸秆的力学性能。完成了不同加筋长度、不同加筋率及浸胶后呈不同状态麦秸秆的加筋滨海盐渍土无侧限抗压强度试验,结果证实：掺加长10mm麦秸秆优于掺加长20 mm麦秸秆;适宜加筋率为0.3%~0.4%;掺加浸泡SH胶后呈潮湿状态的麦秸秆优于掺加浸泡SH胶后呈干燥状态的;麦秸秆加筋盐渍土的抗压强度高于素盐渍土。初步的研究结果表明,麦秸秆适宜作加筋材料使用。     

Behavior of cell aggregates under force-controlled compression

In this paper we study the mechanical behavior of multicellular aggregates under a cycle of compressive loads and releases. Some analytical properties of the solution are discussed and numerical results are presented for a compressive test under constant force imposed on a cylindrical specimen and for a cycle of compressions and releases. We show that a steady loaded configuration is achieved. The analytical determination of the steady state value allows to obtain mechanical parameters of the cellular structure that cannot be obtained on the basis of creep tests at constant stress.     

The Effect of Edge Compliance on the Contact between a Spherical Indenter and a High-Aspect-Ratio Rectangular Fin

In the last two decades, significant progress has been made on developing new nanoscale mechanical property measurement techniques including instrumented indentation and atomic force microscopy based techniques. The changes in the tip-sample contact mechanics during measurements uniquely modify the displacement and force sensed by a measurement sensor and much effort is dedicated to correctly retrieve the sample mechanical properties from the measured signal. It turns out that in many cases, for the sake of simplicity, a simple contact mechanics model is adopted by overlooking the complexity of the actual contact geometry. In this work, a newly developed matrix formulation is used to solve the stress and strain equations for samples with edge geometries. Such sample geometries are often encountered in today’s nanoscale integrated electronics in the form of high-aspect-ratio fins with widths in the range of tens of nanometers. In the matrix formulation, the fin geometries can be easily modeled as adjacent overlapped half-spaces and the contact problem can be solved by a numerical implementation of the conjugate gradient method. This method is very versatile in terms of contact geometry and contact interaction, either non-adhesive or adhesive. The discussion will incorporate a few model examples that are relevant for the nanoscale mechanics investigated by intermittent contact resonance AFM (ICR-AFM) on low-k dielectric fins of high-aspect-ratio. In such ICR-AFM measurements, distinct dependence of the contact stiffness was observed as a function of the applied force and distance from the edges of the fins. These dependences were correctly predicted by the model and used to retrieve the mechanical changes undergone by fins during fabrication and processing.     

Predicting the Dynamic Compressive Strength of Carbonate Rocks from Quasi-Static Properties

In this study, the split Hopkinson pressure bar testing method was used to quantify the dynamic strength characteristics of rocks with short cylindrical specimens. Seventy dynamic compression tests were conducted on 10 different carbonate rocks with the split Hopkinson pressure bar apparatus. Experimental procedure for testing dynamic compressive strength and elastic behaviour of rock material at high strain rate loading is presented in the paper. Pulse-shaper technique was adopted to obtain dynamic stress equilibrium at the ends of the sample and to provide nearly a constant strain rate during the dynamic loading. In addition to dynamic tests, the physical properties covering bulk density, effective porosity, P-wave velocity and Schmidt hardness of rocks, and mechanical properties such as quasi-static compressive strength and tensile strength were determined through standard testing methods. Multiple linear regression analyses were carried out to investigate the variation of dynamic compressive strength depending on physical and mechanical properties of rocks and loading rate. A three parameter model was found to be simple and provided the best surface fit to data. It was found that dynamic compressive strength of rocks increases with increase in loading rate and/or increase in rock property values except porosity. Statistical tests of regression results showed that quasi-static compressive strength and Schmidt hardness are most significant rock properties to adequately predict the dynamic compressive strength value among the other properties. However, P-wave velocity, quasi-static tensile strength of rocks could also be used to estimate the dynamic compressive strength value of rocks, as well, except the bulk density and effective porosity.     

Un modèle discret du couplage entre les fils dans une structure tisséeA discrete model for the coupling between the yarns in a woven fabric

The coupling between yarns in a piece of fabric has been analysed at the mesoscopic scale, in terms of its impact on the macroscopic unidirectional behaviour. Starting from a discrete model of a woven structure associated to a variational formulation of the equilibrium of the structure, the coupling between both yarns is introduced, the potential energy of which is calculated. The initial shape of the yarn, represented by a planar undulated beam supposed to be periodic, is described by a Fourier series. The coefficients of the series are expressed vs. the contact force exerted at the top of the undulations, and vs. the mechanical properties of the solicited yarn. The contact force is then expressed vs. the mechanical properties of the transverse yarn and vs. the vertical displacement of the contact point. The potential energy of the coupling is then built, assuming the continuity of the displacement at the contact points. The equilibrium shape of the yarn submitted to unidirectional traction is obtained numerically as the minimum of the total potential energy. The simulated traction curve reproduces in a satisfactorily manner the observed behaviour. The respective contributions of the flexional and extensional effects of the yarn are analysed. The consideration of the coupling enhances the rigidity of the response of the yarn; one demonstrates the effect of the geometrical and mechanical parameters of the transverse yarn. To cite this article: B. Ben Boubaker et al., C. R. Mecanique 331 (2003).     

Self-piercing riveting connections using aluminium rivets

The development of the self-piercing riveting (SPR) technology in recent years has broadened the application of the technology in the automobile industry. However, the SPR process currently utilises high-strength steel rivets; and the combination between steel rivets with an aluminium car body makes recycling a challenge. The possibility of replacing a steel self-piercing rivet with an aluminium one has thus been raised as an interesting topic. Within this framework, the objective of the present paper is to provide an experimental database on the riveting process using an aluminium self-piercing rivet. An experimental programme has been carried out, where two similar sheets in aluminium alloy 6060 in three different tempers (temper W, temper T4, and temper T6) have been joined by using a self-piercing rivet in three different alloys, i.e. 6082-T6, 7108-T5, and 7278-T6. The influence of the die shape on the SPR of aluminium sheets using aluminium rivets was also considered. Conventional rivets and dies according to the Boellhoff standards were employed. The test results were exploited in terms of the riveting force–displacement curves and cross-sectional geometries of the riveted joints. The test data were also used to validate a 2D-axisymmetric model, which was originally developed at SIMLab for modelling the riveting process using a steel rivet. Finally, the mechanical behaviour of a riveted connection using an aluminium rivet under quasi-static loading conditions (i.e. combined pure shear and pure opening loads) was experimentally studied and compared with corresponding tests using a steel rivet in terms of force–displacement curves.     

Determination of impact parameters by optical measurement of the impactor displacement

In dynamic materials research, high precision impact displacement, velocity and force measurements are often required. In lower velocity testing apparatus, impact force histories are most often obtained through strain gage, piezoelectric force transducer or accelerometer signals. Velocity and displacement histories are then obtained by integration. Non-contact measurement systems have a number of advantages over these more common mechanical contact methods, and can generally be used at higher impact speeds. In this paper a relatively simple optical technique is presented for recording the impactor displacement history, from which the impact velocity and force histories can be readily obtained for a (quasi-) rigid impactor. The technique is based on the relative displacement of two moiré line gratings: one grating attached to the impacting body and the other serving as stationary reference grating. The technique has proven to be useful for impact speeds of a few m/s to well over 200 m/s. Results of transverse impact experiments on composite laminates are presented.     

Buckling and Post-buckling Behaviour of Prismatic Aluminium Columns Submitted to a Series of Compressive Loads

The buckling and post-buckling behaviour of prismatic aluminium columns from stocky to very slender shapes is investigated. The unconventional, in terms of buckling tests, displacement control of compressive load and a series of loadings provided an enhanced insight into the buckling process. A phenomenon of buckling load drop has been detected in columns of intermediate slenderness, reaching over 20% of the load early critical value. This newly observed occurrence resembles finite disturbance instability, which until recently was commonly believed to only appear in cases of thin walled cylindrical shells, but not columns. The observation is in contradiction to predicted results from the elasto-plastic buckling models of Engesser or Shanley, with constant or growing values of load during the post-buckling process. Further tests on columns of intermediate slenderness, with strain gauges glued at node and anti-node locations of the buckled profiles, revealed that even minute buckling results in fields of highly non-symmetric residual microplastic strain. The results of the present study indicate that running column buckling tests under displacement control is worthy of being adopted as common practice. The envelope of column post-buckling states can be conveniently determined. This information will in turn allow for the quick and reliable estimation of the safety of a column, which has undergone accidental or deliberate damage in the form of limited buckling when under operational load.     

Experimental investigation of the transverse mechanical properties of a single Kevlar® KM2 fiber

A new experimental setup is developed to investigate the transverse mechanical properties of Kevlar^® KM2 fibers, which has been widely used in ballistic impact applications. Experimental results for large deformation reveal that the Kevlar^® KM2 fibers possess nonlinear, pseudo-elastic transverse mechanical properties. A phenomenon similar to the Mullins effect (stress softening) in rubbers exists for the Kevlar^® KM2 fibers. Large transverse deformation does not significantly reduce the longitudinal tensile load-bearing capacity of the fibers. In addition, longitudinal tensile loads stiffen the fibers' transverse nominal stress–strain behaviors at large transverse deformation. Loading rates have insignificant effects on their transverse mechanical properties even in the finite deformation range. An analytical relationship between transverse compressive force and displacement is derived at infinitesimal strain level. This relation is used to estimate the transverse elastic modulus of the Kevlar^® KM2 fibers, which is 1.34 ± 0.35 GPa.     

Buckling of embedded microtubules in elastic medium

Motivated by the application of Winkler-like models for the buckling analysis of embedded carbon nanotubes, an orthotropic Winkler-like model is developed to study the buckling behavior of embedded cytoskeletal microtubules within the cytoplasm. Experimental observations of the buckling of embedded cytoskeletal microtubules reveal that embedded microtubules bear a large compressive force as compared with free microtubules. The present theoretical model predicts that embedded microtubules in an elastic medium bear large compressive forces than free microtubules. The estimated critical pressure is in good agreement with the experimental values of the pressure-induced buckling of microtubules. Moreover, due to the mechanical coupling of microtubules with the surrounding elastic medium, the critical buckling force is increased considerably, which well explains the theory that the mechanical coupling of microtubules with an elastic medium increases compressive forces that microtubules can sustain. The model presented in the paper is a good approximation for the buckling analysis of embedded microtubules.     

<Emphasis Type="Italic">In situ</Emphasis> Characterization of Nanomechanical Behavior of Free-standing Nanostructures

The present paper reports the development of an in situ nanotensilometer that enables highly reliable mechanical tensile testing on individual micro-/nano-scale structures. The device features independent measurement of force and displacement histories in the specimen with nanoNewton force and sub-nanometer displacement resolutions, respectively. Moreover, the device is well suited for in situ testing of free-standing micro/nano-structures within a high resolution scanning electron microscope (SEM), which permits continuous high-resolution imaging of the specimen during straining. The device is comprised of two main parts: (a) a three-plate capacitive transducer that doubles up both as an actuator and a force sensor, and (b) a commercially available nanomanipulator that facilitates transportation and positioning of nanoscale structures with sub-nanometer precision. In order to conduct the mechanical tests the ends of the specimen are attached to the probe tips of the device using ion-beam induced deposition. The general capabilities and features of the nanotensilometer are illustrated by presenting results of nanomechanical tensile tests on electrospun polyaniline microfibers.     

圆薄板材料性能随温度变化的大挠度弯曲分析

记入材料性能参数随温度的变化,导出了横向力作用下圆薄板轴对称大挠度弯曲的位移型控 制方程,并利用伽辽金方法求出了圆薄板大挠度弯曲的近似位移解;针对一个简例进行了理 论计算和有限元数值模拟,二者结果一致. 在此基础上分析了圆薄板大挠度弯曲的规律及材 料参数随温度变化的热软化效应,给出了相关结果.     

Simulations of nanowire bend tests for extracting mechanical properties

Mechanical properties of nickel nanowires are characterized based on the numerical simulations of bend tests performed with a customized atomic force microscope (AFM) and scanning electron microscope (SEM). Nickel nanowire specimens are subjected to bending loads by the tip of the AFM cantilever. The experimental force versus bending displacement curves are compared against simulations from finite element analysis and peridynamic theory, and the mechanical properties are extracted based on their best correlations. Similarly, SEM images of fractured nanowires are compared against peridynamic failure simulations. The results of this study reveal that nickel nanowires have significantly higher strengths than their bulk counterparts, although their elastic modulus values are comparable to bulk nickel modulus values.     

Study on energy absorbing composite structure made of concentric NiTi spring and porous NiTi

An energy absorbing composite structure made of a concentric NiTi spring and a porous NiTi rod is investigated in this paper. Both NiTi spring and porous NiTi rod are of superelastic grade. Ductile porous NiTi cylindrical specimens are fabricated by spark plasma sintering. The composite structure exhibits not only high reversible force–displacement relation for small to intermediate loading but also high energy absorbing property when subjected to large compressive load. A model for the compressive force–displacement curve of the composite structure is presented. The predicted curve is compared to the experimental data, resulting in a reasonably good agreement.     

Axisymmetric compressive buckling of multi-walled carbon nanotubes under different boundary conditions

The paper studies the axisymmetric compressive buckling behavior of multi-walled carbon nanotubes (MWNTs) under different boundary conditions based on continuum mechanics model. A buckling condition is derived for determining the critical buckling load and associated buckling mode of MWNTs, and numerical results are worked out for MWNTs with different aspect ratios under fixed and simply supported boundary conditions. It is shown that the critical buckling load of MWNTs is insensitive to boundary conditions, except for nanotubes with smaller radii and very small aspect ratio. The associated buckling modes for different layers of MWNTs are in-phase, and the buckling displacement ratios for different layers are independent of the boundary conditions and the length of MWNTs. Moreover, for simply supported boundary conditions, the critical buckling load is compared with the corresponding one for axial compressive buckling, which indicates that the critical buckling load for axial compressive buckling can be well approximated by the corresponding one for axisymmetric compressive buckling. In particular, for axial compressive buckling of double-walled carbon nanotubes, an analytical expression is given for approximating the critical buckling load. The present investigation may be of some help in further understanding the mechanical properties of MWNTs.     

A 3-phase model for the numerical analysis of semi-crystalline polymer films in finite elastoplastic strains

In this paper, the mechanical behavior of semi-crystalline polymer films in finite elastoplastic strains is investigated. A 3-phase constitutive model has been specially developed in a previous paper and validated for various materials in both uniaxial and biaxial uniform hot drawing. In the present study, the numerical implementation of this 3-phase model in a finite element software is outlined in the perspective of using this model in more general non-uniform cases of complex geometries and/or loadings. In the present case, only polyethylene films at room temperature are considered. First, uniaxial tensile experimental tests are performed so as to calibrate the model parameters. Then, for validation purposes, two series of experimental tests are conducted on tensile specimens with central holes and double edge notched tensile (DENT) specimens. During these tests, digital image correlation is used to analyze the strain (or displacement) field history during loading. Finally, numerical computations are performed with the help of the finite element software including the 3-phase model previously implemented (cohesive elements are also needed for the simulation of the crack propagation in DENT specimens). In both cases, the comparison between the experimental and numerical force–displacement curves, together with the comparisons between the experimental and numerical strain fields at different times, give very satisfactory results.     

Local buckling and debonding problem of a bonded two-layer plate

The problem of local buckling, debonding initiation and growth process of the debonding of a bonded two-layer plate is treated. In the weaker layer of the plate, compression appears due to the external compressive axial force and bending moment. The conditions for local buckling of the weaker layer have been studied where the possibility that the stress state in the layers could be in elasto-plastic domain has been considered.A mathematical model is developed to determine the bending displacements of laminate layers after the weaker layer buckles locally, and in the state after the plate has been unloaded. The third-order theory introduced by Chwalla has been implemented. Mechanical properties of the layers and adhesive used in the numerical model were measured with experiments. Experimental work comprised the determination of mechanical properties of the chosen materials and experimental verification of the presented mathematical model. Numerically obtained results are compared with those obtained by an experimental approach, and are found to be in good agreement.     

Full-Field Strain Measurement and Identification of Composites Moduli at High Strain Rate with the Virtual Fields Method

The present paper deals with full-field strain measurement on glass/epoxy composite tensile specimens submitted to high strain rate loading through a split Hopkinson pressure bar (SHPB) device and with the identification of their mechanical properties. First, the adopted methodology is presented: the device, including an Ultra-High Speed camera, and the experimental procedure to obtain relevant displacement maps are described. The different full-field results including displacement, strain and acceleration maps for two mechanical tests are then addressed. The last part of the paper deals with an original procedure to identify stiffnesses on this dynamic case only using the actual strain and acceleration maps (without the applied force) by using the Virtual Fields Method. The results provide very promising values of Young’s modulus and Poisson’s ratio on a quasi-isotropic glass-epoxy laminate. The load reconstructed from the moduli and strains compares favourably with that from the readings.     

冲击载荷下猪后腿肌肉的横向同性本构模型

基于纤维增强复合材料连续介质力学理论及粘弹性理论,提出了猪后腿肌肉的率相关本构模型。 通过拟合以往研究中猪后腿肌肉的SHPB和SHTB实验应力应变曲线,确定了本构模型的相关参数。结果 表明:提出的本构模型既能描述猪后腿肌肉沿纤维方向的动态压缩力学性能又能描述其动态拉伸性能,理论 模型与实验模型有较好的一致性。该结果可为安全防护数值模拟提供一定的理论依据。