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Mystical materials in indentation

As an indenter penetrates an elastoplastic material, the indentation load P can be measured as a continuous function of the indentation displacement δ, to obtain the so-called P-δ curve. A primary goal of the indentation analysis is to relate the material elastoplastic properties (such as the Young's modulus, yield stress, and work-hardening exponent) with the indentation response (i.e. the shape factors of the P-δ curve, including its curvature, unloading stiffness, loading work, unloading work, maximum penetration, residual penetration, maximum load, etc.). The sharp indenters (e.g.

Indentation: A widely used technique for measuring mechanical properties

Indentation is one of the most widely used techniques of measuring mechanical properties of materials, especially for materials of small volume. In micro- or nano- scales, performing traditional tests such as the tension test and bending test becomes less feasible because of the nontrivial task of sample preparation. In contrast, by using the indentation technique, the difficulty of sample preparation may be dramatically reduced. On the other hand, indentation test is not a direct measurement and advanced mechanics analysis is needed to correlate the material properties with the indentation response. 

In an indentation test, a hard tip is pressed into a sample. The tip can be sharp or spherical. After the tip is removed, an impression is left. The hardness is defined as the indentation load divided by the projected area of impression. Moreover, by means of instrumental indentation testers, the indentation load and indentation depth can be continuously and simultaneously measured. Many models have been developed to extract the material properties from the recorded indentation load-depth curve, including the elastic modulus, yield stress, strain hardening coefficient, residual stress, fracture toughness, etc. 

the FFT based algorithm to solve the continuum electrostatic field

In the paper[1], the continuum electrostatic simulation in the ion transport through membrane-spanning nanopores is realized by the implicit-solvent method. To solve the problem, the governing equation (Poisson equation for systems with heterogeneous permittivity) is expressed and the electric field is calculated in its reciprocal space by applying 3D-FFT[2]. The system is considered periodic, and a modified vacuum field outside is defined. The rectangular unit cell is discredited into grid points. By iteratively revise this modified vacuum field, the residual of the electric field at the grid points reach its minimum in the real space. After getting the predefined threshold, the iteration is terminated and the reaction potential is calculated. The potential at any point in the domain is interpolate by its eight surrounding grid points. The accuracy and convergence properties of this proposed algorithm are very well, with an overall speed comparable to a typical finite-difference solver.

Carbon nanotubes

Carbon nanotube has been widely investigated and perceived as having great potential in nanomechanical and nanoelectronic devices due to uniqe combination of mechanical, electrical and chemical properties. The carbon nanotubes may be applied (a) as light-weight structural materials with extraordinary mechanical properties such as stiffness and strength; (b) in nano-electronic components as the next-generation of semi-conductors and nanowires; (c) as probes in scanning probe microscopy and atomic force microscopy with the added advantage of a chemically-functionalized tip; (d) as high-sensitivity microbalances; (e) as gas and molecule sensors; (f) in hydrogen storage devices thanks to its high surface-volume ratio; (g) as field-emission type displays; (h) as electrodes in organic light-emitting diodes and (i) as tiny tweezers for nanoscale manipulation, to name a few.

As a postdoc in Xi Chen's group, my current research in the mechanics of carbon nanotubes concentrates in the following areas: a) thermal vibration and application as strain/mass/specie sensors; b) buckling of nanotubes caused by compression, bending, torsion, and indentation; c) mechanical properties of carbon nanotubes in axial and radial directions, and effective continuum modeling; d) fluid conduction in nanotubes. I have published 14 journal papers since 2005 in these areas. I will introduce more details in my blog later.

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Why is molecular mechanics simulation at 0K useful?

Although it is more realistic to study the mechanical properties of nanostructures such as the carbon nanotubes (CNTs) at room temperature, atomistic simulations at finite temperature (such as molecular dynamics, MD) may cause the following problems: (1) Due to the limitation of the time scale achievable in MD (typically at the nanosecond scale), the loading rate in MD simulation at any finite temperature is not realistic. Very often, the loading rate used in MD simulations may well exceed 10m/s at 300K and thus many orders of magnitude higher than the real loading rate used in experiments. (2) A great advantage of simulation is to be able to turn on and turn off certain features and explore their effects, which is otherwise impossible in experiments. For example, the buckling behavior of CNTs is very sensitive to geometrical perturbations, which is prominent at room temperature and such perturbations causes severe uncertainties and makes it difficult to explore the intrinsic buckling behaviors. Therefore, by removing the temperature effect, we could better evaluate other key factors affecting the intrinsic buckling behavior, such as tube chirality, radius, and length, which could be otherwise covered by the thermal fluctuation effect. (3) Due to both time and length scale limitations, the MD simulations of large system are not yet possible, and thus the effective continuum models must be developed which need to be calibrated by atomistic simulations. At present, the temperature factor is still absent in most continuum models. Therefore, atomistic simulations at 0K or near 0K may provide a useful benchmark for the development of parallel continuum models, focusing on the most intrinsic and basic mechanical properties of nanostructures. Based on the above analysis, atomistic simulations at 0K by using the molecular mechanics (MM) method are still very useful, especially to us as mechanicians.

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A molecular dynamics-decorated finite element framework for simulating the mechanical behaviors of biomolecules

Cover of Biophysical JournalOur first paper in biomechanics is featured as the cover of the Biophysical Journal. The paper is attached. Several freelance writers in biophysics have reported this paper in magazines and websites/blogs. This framework is very versatile and powerful, and we are now implementing more details/atomistic features into this phenomenological approach, and the follow-up paper will be submitted soon.

Abstract: The gating pathways of mechanosensitive channels of large conductance (MscL) in two bacteria (Mycobacterium tuberculosis and Escherichia coli) are studied using the finite element method. The phenomenological model treats transmembrane helices as elastic rods and the lipid membrane as an elastic sheet of finite thickness; the model is inspired by the crystal structure of MscL. The interactions between various continuum components are derived from molecular-mechanics energy calculations using the CHARMM all-atom force field. Both bacterial MscLs open fully upon in-plane tension in the membrane and the variation of pore diameter with membrane tension is found to be essentially linear. The estimated gating tension is close to the experimental value. The structural variations along the gating pathway are consistent with previous analyses based on structural models with experimental constraints and biased atomistic molecular-dynamics simulations. Upon membrane bending, neither MscL opens substantially, although there is notable and nonmonotonic variation in the pore radius. This emphasizes that the gating behavior of MscL depends critically on the form of the mechanical perturbation and reinforces the idea that the crucial gating parameter is lateral tension in the membrane rather than the curvature of the

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Appropriate range of materials used in indentation analysis

The conventional indentation analysis uses finite element simulations on a wide range of materials and studies their indentation responses, which is known as the forward analysis; then, from the reverse analysis it may be possible to extract material properties from the indentation responses on a particular specimen. In doing so, it is important to selecte a wide yet appropriate range of materials during the forward analysis. Often times when I read or review papers, I found some authors "randomly" select a large range of materials without really knowing what does that mean and whether it is practical; in many cases the materials employed in their forward/reverse analyses do not exist in reality or are actually not suitable for conventional indentation analysis.

In indentation analysis the constitutive elastoplastic properties of the specimen is often expressed by the power-law form. It is important to note that most brittle ceramic or glass materials crack upon indentation, and polymers creep during indentation experiment, moreover the tension and compression behaviors of polymers are often very different; thus, they typically cannot be well-described by the power-law form and their mechanical properties cannot be obtained from the conventional indentation analysis. Thus, ceramics and polymers should be excluded from the present analysis, as well as the highly anisotropic woods. In addition, composite materials, nanocomposites and other nano-structured materials, as well as thin films also need to be excluded from the continuum analysis because the underlying micro/nanostructures play a key role in their mechanical responses. Therefore, only the more ductile and "plastic" polycrystalline bulk metals and alloys are suitable for conventional indentation analysis at room temperature since large strain will occur beneath the indenter during indentation, and also because the conventional plasticity theory is developed for metals which is the foundation of the elastoplastic finite element analysis. The indentation depth also has to be sufficient large on the bulk specimen so as to overcome the strain gradient effect.

The material selection chart taken from page 425 of the famous handbook"Materials selection in mechanical design" by Mike Ashby can be used as a guide. In general, for most engineering metals and alloys suitable for conventional indentation study, the Young's modulus is from about 10 to 600GPa, and the yield strength is from roughly 10MPa to 2GPa, and the inverse of yield strain is in the range roughly from 100 to about 5000 (some pure metals may have even higher inverse yield strain, but should not far exceed such bound). Note that since the specimen must undergo relatively large strain during indentation without cracking, thus the material must be sufficiently ductile (i.e. plastic or soft).

In forward analysis, however, the material range chosen in finite element simulation needs to be moderately larger than the aforementioned bound, so as to avoid possible numerical ill conditions at the boundaries. The reverse analysis, however, should focus on the more practical materials, i.e. the range of metals and alloys listed above.

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use NMA to get the elastic properties of loop

(originally written by Yuye Tang) A key procedure of the molecular-dynamics decorated finite element method (MDeFEM) is to determine the effective properties of components of a macromolecule. Here I illustrate how could one use the NMA computed from MD to estimate the elastic properties of loops in mechanosensitive channels, which is related with my research.

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