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IN THIS ISSUE

### Research Papers

J. Appl. Mech. 2019;86(9):091001-091001-12. doi:10.1115/1.4043519.

This paper presents an analysis of void growth and coalescence in isotropic, elastoplastic materials exhibiting sigmoidal hardening using unit cell calculations and micromechanics-based damage modeling. Axisymmetric finite element unit cell calculations are carried out under tensile loading with constant nominal stress triaxiality conditions. These calculations reveal the characteristic role of material hardening in the evolution of the effective response of the porous solid. The local heterogeneous flow hardening around the void plays an important role, which manifests in the stress–strain response, porosity evolution, void aspect ratio evolution, and the coalescence characteristics that are qualitatively different from those of a conventional power-law hardening porous solid. A homogenization-based damage model based on the micromechanics of void growth and coalescence is presented with two simple, heuristic modifications that account for this effect. The model is calibrated to a small number of unit cell results with initially spherical voids, and its efficacy is demonstrated for a range of porosity fractions, hardening characteristics, and void aspect ratios.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2019;86(9):091002-091002-10. doi:10.1115/1.4043792.

This paper presents a new energy dissipation system composed of multistable cosine-curved domes (CCD) connected in series. The system exhibits multiple consecutive snap-through and snap-back buckling behavior with a hysteretic response. The response of the CCDs is within the elastic regime and hence the system's original configuration is fully recoverable. Numerical studies and experimental tests were conducted on the geometric properties of the individual CCD units and their number in the system to examine the force–displacement and energy dissipation characteristics. Finite element analysis (FEA) was performed to simulate the response of the system to develop a multilinear analytical model for the hysteretic response that considers the nonlinear behavior of the system. The model was used to study the energy dissipation characteristics of the system. Experimental tests on 3D printed specimens were conducted to analyze the system and validate numerical results. Results show that the energy dissipation mainly depends on the number and the apex height-to-thickness ratio of the CCD units. The developed multilinear analytical model yields conservative yet accurate values for the dissipated energy of the system. The proposed system offered reliable high energy dissipation with a maximum loss factor value of 0.14 for a monostable (self-recoverable) system and higher for a bistable system.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2019;86(9):091004-091004-6. doi:10.1115/1.4043890.

The interlayer attraction force between concentric carbon nanotubes (CNTs) plays an important role in CNT-based nanodevices. However, the precise measurement of the interlayer attraction force remains to date a challenge. Although theoretical investigations have identified the dependence of the interlayer attraction force on the tube radius, no explicit relation for such dependence has been established so far. Here, based on an analytical model, we find that the interlayer attraction force between two telescoping concentric CNTs is proportional to the mean (but not the inner nor the outer) radius of the contacting two tubes and consequently propose an explicit expression that relates the interlayer attraction force with the mean radius as well as the interlayer spacing. We also implement the effect of temperature in the present expression based on the linear dependence of the attraction force on temperature. The present expression can be compared with the existing theoretical and experimental results, offering an efficient way to evaluate the interlayer attraction force in the nanodevices composed of concentric CNTs.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2019;86(9):091005-091005-10. doi:10.1115/1.4043830.

In the past decades, various novel functions (i.e., negative Poisson's ratio, zero thermal expansion) have been obtained by tailoring the microstructures of the cellular structures. Among all the microstructures, the horseshoe topology shows a J-shaped stress–strain curve, which is quite different from the conventional materials. It can be inferred that the 2D lattice structure with horseshoe microstructure will also exhibit excellent out-of-plane impact resistance since the spider silk also exhibits the J-shaped stress–strain curve. In this paper, the out-of-plane sphere impact of 2D truss lattice structure is conducted using finite element method (FEM) simulation. The point has been made that, by replacing the direct-line beam to horseshoe curved beam, the out-of-plane impact resistance has been greatly improved. The most curved beam structure is found to have the best out-of-plane performs with the maximum energy absorption and the minimum passing through velocity.

Commentary by Dr. Valentin Fuster

### Technical Brief

J. Appl. Mech. 2019;86(9):094501-094501-6. doi:10.1115/1.4043886.

Protecting concrete structures from high energetic dynamic events such as blasts and impact is a major concern, in both civil- and military-related applications. Most conventional techniques fail to counter the unpredictable nature of dynamic loads, as well as the complex response of structures due to stress wave propagation. Hence, this paper explores the possibility of using a functionally graded—according to impedance—metallic composite system as a protective mechanism to a concrete structure. An analytical framework was developed using matlab, based on elastic and shock wave propagation theories, especially incorporating multiple interactions within the composite system, as well as reflections of free surfaces. A numerical analysis was carried out using the advanced finite element code LS-DYNA. The main objective of this paper was to compare the performance of the composite system against the conventional monolithic system.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2019;86(9):094502-094502-1. doi:10.1115/1.4043744.

Engineering students occasionally wonder: why not $12mc2$? While most have no need for Einstein’s special theory of relativity, this theory nevertheless offers them a shining example of the power of mathematical deduction and beautiful simplicity. At its 100th anniversary in 2005, I gave my students a one-page pencil note explaining this glorious gem of a theory. The note became popular, and here, upon invitation, I give a simplified derivation, trying to waste no word and achieve utmost brevity, a boost to clarity.

Commentary by Dr. Valentin Fuster