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### Research Papers

J. Appl. Mech. 2018;85(4):041001-041001-15. doi:10.1115/1.4039039.

In order to design phononic crystals whose band-gaps are located in low-frequency ranges, researchers commonly adopt low stiffness polymeric materials as key constituents and exploit the high impedance mismatch between metals and polymers. However, there has been very little research on wave propagation at arbitrary angles in the sagittal plane of viscoelastic-elastic multilayered composites because there exist the intricate wave attenuation characteristics at the layer interfaces. The objective of our investigation is to obtain analytical dispersion relation for oblique wave motion in the sagittal plane of infinitely periodic multilayered composite composed of alternating viscoelastic and elastic solids, where the attenuation of harmonic plane waves is found to occur only in the direction perpendicular to the layers. By using this wave propagation characteristic, we directly apply the semi-analytical approach employed in elastic multilayered composites to calculate the dispersion relation of sagittal plane waves in alternating viscoelastic-elastic multilayered composites. Specifically, we consider a bilayered composite composed of alternating aluminum and polyurethane elastomer, whose complex-valued viscoelastic moduli are experimentally determined by performing dynamic mechanical analysis (DMA). The analysis shows that the alternating viscoelastic-elastic layered composite does not possess a phononic band-gap regardless of incident angles. In addition, wave motions at oblique angles are found to travel with a wide range of frequency contents compared to wave motions perpendicular to the layers. The presented analysis demonstrates that wave dispersion relation in viscoelastic-elastic layered composites is distinctly different from the corresponding elastic counterpart, and highlights the importance of the viscoelastic modeling of polymeric materials in wave dispersion analysis.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2018;85(4):041002-041002-10. doi:10.1115/1.4039040.

A systematic study is performed on the plane contact and adhesion of two elastic solids with an interface groove. The nonadhesion and Johnson–Kendall–Roberts (JKR) adhesion solutions for a typical groove shape are obtained in closed form by solving singular integral equations and using energy release rate approaches. It is found that the JKR adhesion solution depends solely on a dimensionless parameter $α$ and the groove is predicted to be unstably flattened with no applied load when $α≥0.535$. Furthermore, the corresponding Maugis–Dugdale adhesion model has been revisited with three possible equilibrium states. By introducing the classical Tabor parameter $μ$, a complete transition between the nonadhesion and the JKR adhesion contact models is captured, which can be recovered as two limiting cases of the Maugis–Dugdale model. Depending on two nondimensional parameters $α$ and $μ$, where $α2$ represents the ratio of the surface energy in the groove to the elastic strain energy when the grooved surface is flattened, different transition processes among three equilibrium states are characterized by one or more jumps between partial and full contact. Larger values of $α$ and $μ$ tend to induce more energy loss due to adhesion hysteresis. Combination values of $α$ and $μ$ are also suggested to design self-healing interface grooves due to adhesion.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2018;85(4):041003-041003-11. doi:10.1115/1.4038966.

We present a nondestructive approach to map the heterogeneous viscoelastic moduli from time harmonic motion via a constrained optimization strategy under the framework of finite element techniques. The adjoint equations are carefully derived to determine the gradient of the objective function with respect to the viscoelastic moduli. The feasibility of this inverse scheme is tested with simulated experiments under various driving frequencies. We observe that the overall strategy results in well-reconstructed moduli. For low frequencies, however, the mapped loss modulus is of inferior quality. To explain this observation, we analyze two simple one-dimensional (1D) models theoretically. The analysis reveals that the known displacement amplitude is less sensitive to the loss modulus value at low frequencies. Thus, we conclude that the inverse method is incapable of finding a well-reconstructed loss modulus distribution for low driving frequencies in the presence of noisy data. Overall, the inverse algorithms presented in this work are highly robust to map the storage and loss modulus with high accuracy given that a proper range of frequencies are utilized.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2018;85(4):041004-041004-10. doi:10.1115/1.4039048.

The dynamic tensile response of additively manufactured (AM) dense and porous Ti6Al4V specimens was investigated under quasi-static and dynamic tension. The porous specimens contained single embedded spherical pores of different diameters. Such artificial spherical pores can mimic the behavior of realistic flaws in the material. It was found that beyond a certain pore diameter (Ø600 μm), the failure is determined according to the pore location, characterized by an abrupt failure and a significant decrease of ductility, while below that diameter, necking and fracture do not occur at the pore. The dynamic tensile mechanical behavior of the additively manufactured dense material was found to be similar to that of the conventional equivalent material, but the ductility to failure of the latter is observed to be higher.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2018;85(4):041005-041005-9. doi:10.1115/1.4039042.

Elastic metamaterials utilize locally resonant mechanical elements to onset band gap characteristics that are typically exploited in vibration suppression and isolation applications. The present work employs a comprehensive structural intensity analysis (SIA) to depict the structural power distribution and variations associated with band gap frequency ranges, as well as outside them along both dimensions of a two-dimensional (2D) metamaterial. Following a brief theoretical dispersion analysis, the actual mechanics of a finite metamaterial plate undergoing flexural loading and consisting of a square array of 100 cells is examined experimentally using a fabricated prototype. Scanning laser Doppler vibrometer (SLDV) tests are carried out to experimentally measure the deformations of the metamaterial in response to base excitations within a broad frequency range. In addition to confirming the attenuation and blocked propagation of elastic waves throughout the elastic medium via graphical visualizations of power flow maps, the SIA reveals interesting observations, which give additional insights into energy flow and transmission in elastic metamaterials as a result of the local resonance effects. A drastic reduction in power flow magnitudes to the bulk regions of the plate within a band gap is noticeably met with a large amplification of structural intensity around and in the neighborhood of the excitation source as a compensatory effect. Finally, the theoretical and experimentally measured streamlines of power flow are presented as an alternative tool to predict the structural power patterns and track vortices as well as confined regions of energy concentrations.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2018;85(4):041006-041006-10. doi:10.1115/1.4038920.

Coefficients of restitution (CoR) is used to scale the kinetic energy dissipation, which is a necessary parameter for discrete element modeling simulations of granular flow. Differences from the collision of spherical particles, CoRs of spheroid particle are affected not only by materials, particle size, and impacting velocity, but also by the contact inclination angle of the particle. This article presents our experimental investigation to measure the velocities of translation and rotation using high-speed camera and calculate the CoR in normal direction of prolate spheroid particles impacting flat targets. The results show that this CoR of a prolate spheroid particle is composed of two parts, translation and rotation. The effect from the contact inclination angle is not obvious for a given velocity. When the contact point is close to a pole, the first part plays a major role. On the contrary, the second part dominates the CoR, when the contact point is close to the equator. A dimensionless number, e*, is defined to scale the proportion of velocity due to rotation in the total rebound velocity at the contact point. The relationship between the contact inclination angle, ϕ, and e* for 25 deg < ϕ < 90 deg is given in this article.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2018;85(4):041007-041007-12. doi:10.1115/1.4039046.

The mechanical behavior of knitted textiles is simulated using finite element analysis (FEA). Given the strong coupling between geometrical and physical aspects that affect the behavior of this type of engineering materials, there are several challenges associated with the development of computational tools capable of enabling physics-based predictions, while keeping the associated computational cost appropriate for use within design optimization processes. In this context, this paper investigates the relative contribution of a number of computational factors to both local and global mechanical behavior of knitted textiles. Specifically, different yarn-to-yarn interaction definitions in three-dimensional (3D) finite element models are compared to explore their relative influence on kinematic features of knitted textiles' mechanical behavior. The relative motion between yarns identified by direct numerical simulations (DNS) is then used to construct reduced order models (ROMs), which are shown to be computationally more efficient and providing comparable predictions of the mechanical performance of knitted textiles that include interfacial effects between yarns.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2018;85(4):041008-041008-10. doi:10.1115/1.4039047.

This paper studies a new comprehensive model for toppling dynamics of regularly spaced dominoes in an array. The model has unlocked the hypotheses introduced by Stronge and Shu (Stronge, W. J., and Shu, D., 1988, “The Domino Effect: Successive Destabilization by Cooperative Neighbours,” Proc. R. Soc. A, 418(1854), pp. 155–163), which can provide us some essential insights into the mechanism of domino wave. Extensive comparisons are made between the proposed model and the experimental results studied in the existing literature. Our numerical studies show that the existing theoretical models are special cases of the proposed model, and the fluctuation in the waveform of propagation speed observed from experiments was caused by the irregular multiple impacts between colliding dominoes. The influence of physical parameters of domino on the natural speed of toppling dominoes is also considered, and it is found that the coefficients of friction and restitution between colliding dominoes have more effects due to the energy dissipation during impact.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2018;85(4):041009-041009-5. doi:10.1115/1.4039041.

Polydimethylsiloxane (PDMS) is extensively used in clinical flexible electronics, due to its biocompatibility and stability. When it is employed in a stretchable epidermal sensor for long-term monitoring, PDMS must have open pores within it to assure the sweat penetration. In the present paper, we focus on the mechanical properties of porous PDMS with different volume porosities at different temperatures. The emulsion polymerization technique is applied to fabricate porous PDMS. By controlling the ratio of water to PDMS prepolymer, different porosities of PDMS were obtained, and elastic moduli of such porous PDMS were measured in experiment. Results indicate that the elastic modulus increases nonlinearly as its temperature rises from 0 °C to 40 °C (a temperature range frequently encountered in clinical applications). Meanwhile, an asymptotic homogenization method (AHM) is employed to theoretically predict the elastic modulus and Poisson's ratio of porous PDMS, whose reliability is testified by comparing the results with experimentally measured data. Further theoretical discussions on mechanical properties are carried out, and results show that the pore size of porous PDMS has almost no effect on the elastic modulus and Poisson's ratio for certain porosities. Porosity of porous PDMS, however, has significant effect on both of these two mechanical parameters. Two fitted nonlinear formulas are then proposed to estimate the elastic modulus and Poisson's ratio of porous PDMS for any volume porosity less than 50%. All the results in the present paper are essential for mechanical design and optimization of clinical flexible electronics based on porous PDMS.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2018;85(4):041010-041010-11. doi:10.1115/1.4039044.

This paper investigates the tip region of a hydraulic fracture propagating near a free-surface via the related problem of the steady fluid-driven peeling of a thin elastic layer from a rigid substrate. The solution of this problem requires accounting for the existence of a fluid lag, as the pressure singularity that would otherwise exist at the crack tip is incompatible with the underlying linear beam theory governing the deflection of the thin layer. These considerations lead to the formulation of a nonlinear traveling wave problem with a free boundary, which is solved numerically. The scaled solution depends only on one number $K$, which has the meaning of a dimensionless toughness. The asymptotic viscosity- and toughness-dominated regimes, respectively, corresponding to small and large $K$, represent the end members of a family of solutions. It is shown that the far-field curvature can be interpreted as an apparent toughness, which is a universal function of $K$. In the viscosity regime, the apparent toughness does not depend on $K$, while in the toughness regime, it is equal to $K$. By noting that the apparent toughness represents an intermediate asymptote for the layer curvature under certain conditions, the obtention of time-dependent solutions for propagating near-surface hydraulic fractures can be greatly simplified. Indeed, any such solutions can be constructed by a matched asymptotics approach, with the outer solution corresponding to a uniformly pressurized fracture and the inner solution to the tip solution derived in this paper.

Commentary by Dr. Valentin Fuster

### Technical Brief

J. Appl. Mech. 2018;85(4):044501-044501-6. doi:10.1115/1.4038965.

The idealized inverse-opal lattice is a network of slender struts that has cubic symmetry. We analytically investigate the elastoplastic properties of the idealized inverse-opal lattice. The analysis reveals that the inverse-opal lattice is bending-dominated under all loadings, except under pure hydrostatic compression or tension. Under hydrostatic loading, the lattice exhibits a stretching dominated behavior. Interestingly, for this lattice, Young's modulus and shear modulus are equal in magnitude. The analytical estimates for the elastic constants and yield behavior are validated by performing unit-cell finite element (FE) simulations. The hydrostatic buckling response of the idealized inverse-opal lattice is also investigated using the Floquet–Bloch wave method.

Commentary by Dr. Valentin Fuster