The response of low-dimensional solid objects combines geometry and physics in unusual ways, exemplified in structures of great utility such as a thin-walled tube that is ubiquitous in nature and technology.
I was a little bit surprised in the introduction of this new forum to see mention of elastic and plastic contacts but no specific mention of viscoelastic contacts.
In the era of commercially-available instruments for indentation testing, the examination of viscoelastic contact mechanics, both in the context of polymers and biological tissues, seems to have taken on new life. To a first approximation, for indentation testing in the time domain, the fundamental mechanics has not much advanced beyond a few classic papers of the 1960s: Lee and Radok, J. Appl. Mech. 27 (1960) 438 and Ting TCT, J. Appl. Mech. 88 (1966) 845. However, the implementation of techniques for analysis of experimental data has progressed substantially. With spherical indenters the use of linearly viscoelastic models for characterization of a material creep or relaxation function is straightforward. Recent experimental studies have confirmed this, while more lingering questions remain for sharp contacts including Berkovich pyramidal indenters (most commonly shipped with commercial indenters). Sharp contacts seem to give rise to nonlinearly viscoelastic responses. Other topics of recent interest include frequency-domain measurements and examination of oscillating contacts and adhesion. (Although not mentioned in the listing of KLJ's most-loved topics in contact mechanics, viscoelastic contact has been the subject of several recent KLJ publications!) Although research in viscoelastic contact mechanics has been strong in recent years, perhaps a challenge remains in the dissemination of information and the establishment of approachable experimental techniques for use by non-experts.
When I was a graduate student, I spent several months to measure interfacial toughness between metalic (Cu and Au) films and thick substrates(Si and Polycarbonate). My methods were bulge test (blistering test) and 4-point bending test. I had many problems such as making an initial crack(pre-cracking), changing load phase angle applied to specimens, preparing/patterning thin films, constructing my own test apparatus, etc. The biggest problem was to measure the interfacial toughness over a wide range of loading phase angle. For a bimaterial with a non-zero oscillatory index(epsilon), we don't know the phase angle for a minimum interfacial toughness beforehand. Therefore, we need to measure the interfacial toughness over a wide range of phage angle. For engineering purpose, we need a minimum interfacial toughness value for reliability design because this value will lead to a conservative design of systems.
Given link is for a stochastic micromechanical model developed for predicting probabilistic characteristics of elastic mechanical properties of an isotropic functionally graded material (FGM) subject to statistical uncertainties in material properties of constituents and their respective volume fractions.
Last year I spent three months modeling the compressive behavior of aluminum alloy foams. I had hoped to find some evidence of the banding instability that is often observed in elastomeric foams [1]. Lakes writes that this sort of banding instability provides indirect experimental evidence for negative shear modulus [2].
I wanted to share some our work on the deformation behavior of metal nanowires that was recently published in Advanced Functional Materials. In this work, we considered the tensile deformation of three experimentally observed silver nanowire geometries, including five-fold twinned, pentagonal nanowires. The manuscript abstract and urls to videos of the tensile deformation of the three nanowire geometries are below. A copy of the manuscript is attached.
Abstract. This letter addresses the dependence of homogeneous dislocation nucleation on the crystallographic orientation of pure copper under uniaxial tension and compression. Molecular dynamics simulation results with an embedded-atom method potential show that the stress required for homogeneous dislocation nucleation is highly dependent on the crystallographic orientation and the uniaxial loading conditions; certain orientations require a higher stress in compression (e.g., <110> and <111>) and other orientations require a higher stress in tension (<100>). Furthermore, the resolved shear stress in the slip direction is unable to completely capture the dependence of homogeneous dislocation nucleation on crystal orientation and uniaxial loading conditions.
In this short note we remark that, at least for the theory of Fuller & Tabor for the adhesive contact of rough random surfaces, fractal surfaces have a limiting zero pull-off force, for all fractal dimensions or amplitudes of roughness. This paradoxical result raises some questions. I ask the iMechanica community for opinions, comparisons of experiments, etc.
If we read Ken Johnson’s Timoshenko medal 2006 speech also posted in iMechanica, the subjects Ken mentions in his brief and humorous speech are:-
These are probably the subjects Ken is most attached to. Some are older (but perhaps not solved, lke corrugation, for which the “short-pitch” fixed wavelength mechanism is still unclear despite Ken’s 40 years of efforts (!), and some are certainly fashionable today (like adhesion and friction at atomic scale). In starting this forum, why not start from here? Should we prepare a 1 page summary on each of these topics? Since I start this, I will do the effort on corrugation I promise in the next week or so!
Regards, Mike
Might also be useful for simulating dislocation motion in a finite body.
Several sets of boundary integral equations for two dimensional elasticity are derived from Cauchy integral theorem.These equations reveal the relations between displacements and resultant forces, between displacements and tractions, and between the tangential derivatives of displacements and tractions on solid boundary.Special attention is given to the formulation that is based on tractions and the tangential derivatives of displacements on boundary, because its integral kernels have the weakest singularities.The formulation is further extended to include singular points, such as dislocations and line forces, in a finite body, so that the singular stress field can be directly obtained from solving the integral equations on the external boundary without involving the linear superposition technique often used in the literature. Body forces and thermal effect are subsequently included. The general framework of setting up a boundary value problem is discussed and continuity conditions at a non-singular corner are derived. The general procedure in obtaining the elastic field around a circular hole is described, and the stress fields with first and second order singularities are obtained. Some other analytical solutions are also derived by using the formulation.
