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IN THIS ISSUE

### Research Papers

J. Appl. Mech. 2019;86(8):081001-081001-11. doi:10.1115/1.4043094.

The size and distribution of particles suspended within a fluid influence the rheology of the suspension, as well as strength and other mechanical properties if the fluid eventually solidifies. An important motivating example of current interest is foamed cements used for carbon storage and oil and gas wellbore completion. In these applications, it is desired that the suspended particles maintain dispersion during flow and do not coalesce or cluster. This paper compares the role of mono- against polydispersity in the particle clustering process. The propensity of hard spherical particles in a suspension to transition from a random configuration to an ordered configuration, or to form localized structures of particles, due to flow is investigated by comparing simulations of monodisperse and polydisperse suspensions using Stokesian dynamics. The calculations examine the role of the polydispersity on particles rearrangements and structuring of particles due to flow and the effects of the particle size distribution on the suspension viscosity. A key finding of this work is that a small level of polydispersity in the particle sizes helps to reduce localized structuring of the particles in the suspension. A suspension of monodisperse hard spheres forms structures at a particle volume fraction of approximately $47%$ under shear, but a $47%$ volume fraction of polydisperse particles in suspension does not form these structures.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2019;86(8):081002-081002-8. doi:10.1115/1.4043439.

We propose a modeling strategy to predict the mechanical response of porous solids to imposed multiaxial strain histories. A coarse representation of the microstructure of a porous material is obtained by subdividing a volume element into cubic cells by a regular tessellation; some of these cells are modeled as a plastically incompressible elastic-plastic solid, representing the parent material, while the remaining cells, representing the pores, are treated as a weak and soft compressible solid displaying densification behavior at large compressive strains. The evolution of homogenized deviatoric and hydrostatic stress is explored for different porosities by finite element simulations. The predictions are found in good agreement with previously published numerical studies in which the microstructural geometry was explicitly modeled.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2019;86(8):081003-081003-10. doi:10.1115/1.4043473.

The measurement results of various nitrile butadiene rubber (NBR) O-Ring sizes are presented, and reduced-order models are developed in order to predict the stiffness and damping coefficient as a function of O-Ring geometry, Shore hardness, squeeze, and excitation frequency. The results show that the curvature ratio d/D needs to be considered in the reduced-order models. The assessment of the model suggests a maximum deviation of 30% in predicted stiffness compared to the measurement data. However, taking into account the typical Shore hardness tolerance given by O-Ring manufacturers and other measurement uncertainties, the proposed model enables the prediction of various O-Rings with a good accuracy in the frequency range of 1.5–3.75 kHz, which corresponds to typical gas bearing supported rotor applications.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2019;86(8):081004-081004-13. doi:10.1115/1.4043616.

Conventional energy absorber usually employs stubby thin-walled structures. Compared with the limited number of stubby thin-walled structures, an equipment has a large number of slender thin-walled structures that has the potential to be used for energy absorption purpose as well. Therefore, improving the energy absorption capacity of these slender thin-walled structures can significantly benefit the crashworthiness of the equipment. However, these slender structures are inclined to deform in Euler buckling mode, which greatly limits their application for energy absorption. In this paper, kirigami approach combined with welding technology is adopted to avoid the Euler buckling mode of a slender cruciform. Both finite element simulations and experiments demonstrated that the proposed approach can trigger a desirable progressive collapse mode and thus improve the energy absorption by around 155.22%, compared with the conventional cruciform. Furthermore, parametric studies related to the kirigami pattern and global slenderness ratio (GSR) are conducted to investigate the improvement of this proposed approach on the energy absorption and the maximum critical value of GSR.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2019;86(8):081005-081005-10. doi:10.1115/1.4043440.

Experimental data have made it abundantly clear that the strength of polycrystalline silicon (poly-Si) microelectromechanical systems (MEMS) structures exhibits significant variability, which arises from the random distribution of the size and shape of sidewall defects created by the manufacturing process. Test data also indicated that the strength statistics of MEMS structures depends strongly on the structure size. Understanding the size effect on the strength distribution is of paramount importance if experimental data obtained using specimens of one size are to be used with confidence to predict the strength statistics of MEMS devices of other sizes. In this paper, we present a renewal weakest-link statistical model for the failure strength of poly-Si MEMS structures. The model takes into account the detailed statistical information of randomly distributed sidewall defects, including their geometry and spacing, in addition to the local random material strength. The large-size asymptotic behavior of the model is derived based on the stability postulate. Through the comparison with the measured strength distributions of MEMS specimens of different sizes, we show that the model is capable of capturing the size dependence of strength distribution. Based on the properties of simulated random stress field and random number of sidewall defects, a simplified method is developed for efficient computation of strength distribution of MEMS structures.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2019;86(8):081006-081006-10. doi:10.1115/1.4043663.

The statistical size effect has generally been explained by the weakest-link model, which is valid if the failure of one representative volume element (RVE) of material, corresponding to one link, suffices to cause failure of the whole structure under the controlled load. As shown by the recent formulation of fishnet statistics, this is not the case for some architectured materials, such as nacre, for which one or several microstructural links must fail before reaching the maximum load or the structure strength limit. Such behavior was shown to bring about major safety advantages. Here, we show that it also alters the size effect on the median nominal strength of geometrically scaled rectangular specimens of a diagonally pulled fishnet. To derive the size effect relation, the geometric scaling of a rectangular fishnet is split into separate transverse and longitudinal scalings, for each of which a simple scaling rule for the median strength is established. Proportional combination of both then yields the two-dimensional geometric scaling and its size effect. Furthermore, a method to infer the material failure probability (or strength) distribution from the median size effect obtained from experiments or Monte Carlo simulations is formulated. Compared to the direct estimation of the histogram, which would require more than ten million test repetitions, the size effect method requires only a few (typically about six) tests for each of three or four structure sizes to obtain a tight upper bound on the failure probability distribution. Finally, comparisons of the model predictions and actual histograms are presented.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2019;86(8):081007-081007-7. doi:10.1115/1.4043720.

We find that the ratio of dielectric permittivity to shear modulus is linearly related to the number of polar groups per polymer chain in polar dielectric elastomers (PDEs). Our discovery is verified via computational modeling and validated by experimental evidences. Based on the finding, we introduce the new concept of dielectric imperfection (DI) and provide some physical insights into understanding it through demonstrating the large nonlinear deformation of PDEs with DIs under electric fields. The results show remarkable DI-induced inhomogeneous deformation and indicate that the size and dielectric permittivity of DIs have a significant impact on the deformation stability of PDEs under electric fields. With this concept, we propose some potential applications of PDEs with DIs.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2019;86(8):081008-081008-17. doi:10.1115/1.4043721.

This paper introduces a method for calculating the deformation displacement of the origami mechanism. The bearing capacity of each face can be analyzed by the relationship between the stress and displacement, which can provide a reference for the origami design. The Miura origami mechanism unit is considered. First, the folding angle of each crease is solved based on the geometric characteristics. The deforming form of the creases is then analyzed, and the bending moment acting on the paper surface is solved. Based on the geometric characteristics and stress forms, the paper surface is modeled as a sheet. Based on the bending theory of a thin plate with small deflection, the complex external load forms are decomposed by Levy's method and the superposition principle, and the expression of the deflection curve during the folding process is obtained. According to the stress and bending moment equations, the relationship between the bending moment and displacement is obtained. Finally, through an application example, the maximum deflection of the paper surface is calculated by matlab, and the deflection diagram of the deformed paper surface is drawn, which verifies the expression of the deflection curve.

Commentary by Dr. Valentin Fuster

### Discussion

J. Appl. Mech. 2019;86(8):085501-085501-3. doi:10.1115/1.4043547.

In this discussion, we provide corrections to the second-order kinematic equations describing contact between three-dimensional rigid bodies, originally published in Sarkar et al. (1996) [“Velocity and Acceleration Analysis of Contact Between Three-Dimensional Rigid Bodies,” ASME J. Appl. Mech., 63(4), pp. 974–984].

Topics: Kinematics
Commentary by Dr. Valentin Fuster