Research Papers

J. Appl. Mech. 2018;85(12):121001-121001-7. doi:10.1115/1.4041162.

This study addresses the dynamic behaviors of a bearing supporting structure composed of rubber O-rings. To develop an analytical method to predict the dynamic properties of the O-rings without using any dimension-dependent experimental data, the viscoelastic behaviors of the material were modeled with Maxwell-hyperelasticity proposed by the authors. The viscoelastic model was implemented using the finite element method (FEM), and a dynamic analysis was performed, the results of which were compared with the experimental data. The influences of the dimensions, frequency, squeeze, and surface condition on the dynamic properties of the O-rings were clarified, and independent design parameters were determined. The values and distributions of hydrostatic pressure, principal strain, and viscous dissipation energy were also discussed.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2018;85(12):121002-121002-10. doi:10.1115/1.4041163.

Vibrational microplatforms that exploit complex three-dimensional (3D) architectures assembled via the controlled compressive buckling technique represent promising candidates in 3D micro-electromechanical systems (MEMS), with a wide range of applications such as oscillators, actuators, energy harvesters, etc. However, the accuracy and efficiency of such 3D MEMS might be significantly reduced by the viscoelastic damping effect that arises from material viscosity. Therefore, a clear understanding and characterization of such effects are essential to progress in this area. Here, we present a study on the viscoelastic damping effect in complex 3D structures via an analytical model and finite element analysis (FEA). By adopting the Kelvin–Voigt model to characterize the material viscoelasticity, an analytical solution is derived for the vibration of a buckled ribbon. This solution then yields a scaling law for the half-band width or the quality factor of vibration that can be extended to other classes of complex 3D structures, as validated by FEA. The scaling law reveals the dependence of the half-band width on the geometries of 3D structures and the compressive strain. The results could serve as guidelines to design novel 3D vibrational microplatforms for applications in MEMS and other areas of technology.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2018;85(12):121003-121003-11. doi:10.1115/1.4041223.

Mussel adhesion is a problem of great interest to scientists and engineers. Recent microscopic imaging suggests that the mussel material is porous with patterned void distributions. In this paper, we study the effect of the pore distribution on the interfacial-to-the overall response of an elastic porous plate, inspired from mussel plaque, glued to a rigid substrate by a cohesive interface. We show using a semi-analytical approach that the existence of pores in the vicinity of the crack reduces the driving force for crack growth and increases the effective ductility and fracture toughness of the system. We also demonstrate how the failure mode may switch between edge crack propagation and inner crack nucleation depending on the geometric characteristics of the bulk in the vicinity of the interface. Numerically, we investigate using the finite element method two different void patterns; uniform and graded. Each case is analyzed under displacement-controlled loading. We show that by changing the void size, gradation, or volume fraction, we may control the peak pulling force, maximum elongation at failure, as well as the total energy dissipated at complete separation. We discuss the implications of our results on design of bulk heterogeneities for enhanced interfacial behavior.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2018;85(12):121004-121004-11. doi:10.1115/1.4041041.

It is crucial to investigate the dynamic mechanical behavior of materials at the nanoscale to create nanostructured protective systems that have superior ballistic impact resistance. Inspired from recent experimental advances that enable ballistic materials testing at small scales, here we report a comparative analysis of the dynamic behavior of nanoscale thin films made from multilayer graphene (MLG), polymer, gold, and aluminum under high-speed projectile impact. We employ atomistic and coarse-grained (CG) molecular dynamics (MD) simulations to measure the ballistic limit velocity (V50) and penetration energy (Ep) of these nanoscale films and investigate their distinctive failure mechanisms over a wide range of impact velocities (Vi). For the local penetration failure mechanism observed in polymer and metal films, we find that the intrinsic mechanical properties influence Ep at low Vi, while material density tends to govern Ep at high Vi. MLG films uniquely show a large impact propagation zone (IPZ), which transfers the highly localized impact energy into elastic deformation energy in a much larger area through cone wave propagation. We present theoretical analyses that corroborate that the size of IPZ should depend not only on material properties but also on a geometrical factor, specifically, the ratio between the projectile radius and film thickness. This study clearly illustrates how material properties and geometrical factors relate to the ballistic penetration energy, thereby allowing a quantitative comparison of the nanoscale ballistic response of different materials.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2018;85(12):121005-121005-7. doi:10.1115/1.4041224.

The interaction between the cohesive zone and the elastic stiffness heterogeneity in the peeling of an adhesive tape from a rigid substrate is examined experimentally and with finite element simulations. It is established in the literature that elastic stiffness heterogeneities can greatly enhance the force required to peel a tape without changing the properties of the interface. However, much of these concern brittle materials where the cohesive zone is limited in size. This paper reports the results of peeling experiments performed on pressure-sensitive adhesive tapes with both an elastic stiffness heterogeneity and a substantial cohesive zone. These experiments show muted enhancement in the peeling force and suggest that the cohesive zone acts to smooth out the effect of the discontinuity at the edge of the elastic stiffness heterogeneities, suppressing their effect on peel force enhancement. This mechanism is examined through numerical simulation which confirms that the peel force enhancement depends on the strength of the adhesive and the size of the cohesive zone.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2018;85(12):121006-121006-13. doi:10.1115/1.4041225.

This paper seeks to determine the relationship between the parameters that define microstructures composed of a matrix with periodic elliptical inclusions and the effectiveness of structural optimization through the application of existing methods. Stiffness properties for a range of microstructures were obtained computationally through homogenization, and these properties were used to conduct separate homogeneous topology optimization and heterogeneous microstructural optimization on two canonical structural problems. Effectiveness was evaluated on the basis of final total strain energy when compared to a reference configuration. Local minima were found for the two structural problems and various microstructure configurations, indicating that the microstructure of composites with elliptical inclusions can be fine-tuned for optimization. For example, when applying topology optimization to a cantilever beam made from a material with soft, horizontal inclusions, ensuring that the aspect ratio of the inclusions is 2.25 will yield the stiffest structure. In the case of heterogeneous microstructural optimization, one of the results obtained from this analysis was that optimizing the aspect ratio of the inclusion is much more impactful in terms of increasing the stiffness than optimizing the inclusion orientation. The existence of these optimal designs have important implications in composite component design.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2018;85(12):121007-121007-8. doi:10.1115/1.4041318.

A new type of all-solid metamaterial model with anisotropic density and fluid-like elasticity is proposed for controlling acoustic propagation in an underwater environment. The model consists of a regular hexagonal lattice as the host that defines the overall isotropic stiffness, in which all lattice beams have been sharpened at both ends to significantly diminish the shear resistance. The inclusion structure, which involves epoxy, rubber, and lead material constituents, is designed to attain a large density–anisotropy ratio in the broad frequency range. The wave-control capability of metamaterials is evaluated in terms of underwater acoustic stretching, shifting, and ground cloaking, which are generated by the transformation acoustic method. The decoupling design method was developed for the metamaterial microstructure using band-structure, effective-medium, and modal-field analyses. The acoustic performance of these metamaterial devices was finally verified with full-wave numerical simulations. Our study provides new insight into broadband underwater acoustic manipulation by all-solid anisotropic-density metamaterials.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2018;85(12):121008-121008-14. doi:10.1115/1.4041317.

The cruciforms are widely employed as energy absorbers in ships and offshore structures, or basic components in sandwich panel and multicell structure. The kirigami approach is adopted in the design of cruciform in this paper for the following reasons. First, the manufacture process is simplified. Second, it can alter the stiffness distribution of a structure to trigger desirable progressive collapse modes (PCMs). Third, the kirigami pattern can be referred as a type of geometric imperfection to lower the initial peak force during impact. Experiments and numerical simulations were carried out to validate the effectiveness of kirigami approach for cruciform designs. Numerical simulations were carried out to perform comparative and parametric analyses. The comparative studies among single plate (SP), single plate with kirigami pattern (SPKP), and kirigami cruciform (KC) show that the normalized mean crushing force of KC is nearly two times higher than those of SP and SPKP, whereas the normalized initial peak force of KC reduces by about 20%. In addition, the parametric analyses suggest that both the parameters controlling the overall size (i.e., the global slenderness and local slenderness) and those related to the kirigami pattern (i.e., the length ratio and the relative position ratio) could significantly affect the collapse behavior of the cruciforms.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2018;85(12):121009-121009-10. doi:10.1115/1.4041499.

The problem of an infinite isotropic elastic space subjected to uniform far-field load and containing an isotropic elastic spherical inhomogeneity with Steigmann–Ogden interface is considered. The interface is treated as a shell of vanishing thickness possessing surface tension as well as membrane and bending stiffnesses. The constitutive and equilibrium equations of the Steigmann–Ogden theory for a spherical surface are written in explicit forms. Closed-form analytical solutions are derived for two cases of loading conditions—the hydrostatic loading and deviatoric loading with vanishing surface tension. The single inhomogeneity-based estimates of the effective properties of macroscopically isotropic materials containing spherical inhomogeneities with Steigmann–Ogden interfaces are presented. It is demonstrated that, in the case of vanishing surface tension, the Steigmann–Ogden model describes a special case of thin and stiff uniform interphase layer.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2018;85(12):121010-121010-5. doi:10.1115/1.4041469.

We consider the plane deformations of an infinite elastic solid containing an arbitrarily shaped compressible liquid inhomogeneity in the presence of uniform remote in-plane loading. The effects of residual interface tension and interface elasticity are incorporated into the model of deformation via the complete Gurtin–Murdoch (G–M) interface model. The corresponding boundary value problem is reformulated and analyzed in the complex plane. A concise analytical solution describing the entire stress field in the surrounding solid is found in the particular case involving a circular inhomogeneity. Numerical examples are presented to illustrate the analytic solution when the uniform remote loading takes the form of a uniaxial compression. It is shown that using the simplified G–M interface model instead of the complete version may lead to significant errors in predicting the external loading-induced stress concentration in gel-like soft solids containing submicro- (or smaller) liquid inhomogeneities.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2018;85(12):121011-121011-9. doi:10.1115/1.4041470.

Considerable effort has been made to model, predict, and mitigate wear as it has significant global impact on the environment, economy, and energy consumption. This work proposes generalized foundation-based wear models and a simulation procedure for single material and multimaterial composites subject to rotary or linear abrasive sliding wear. For the first time, experimental calibration of foundation parameters and asymmetry effects are included. An iterative wear simulation procedure is outlined that considers implicit boundary conditions to better reflect the response of the whole sample and counter-body system compared to existing models. Key features such as surface profile, corresponding contact pressure evolution, and material loss can be predicted. For calibration and validation, both rotary and linear wear tests are conducted on purpose-built tribometers. In particular, an experimental calibration procedure for foundation parameters is developed based on a Levenberg–Marquardt optimization algorithm. This procedure is valid for specific counter-body and wear systems using experimentally measured steady-state worn surface profiles. The calibrated foundation model is validated by a set of rotary wear tests on different bimaterial composite samples. The established efficient and accurate wear simulation framework is well suited for future design and optimization purposes.

Commentary by Dr. Valentin Fuster

Technical Brief

J. Appl. Mech. 2018;85(12):124501-124501-5. doi:10.1115/1.4041320.

The shear stress–strain response of an aluminum alloy is measured to a shear strain of the order of one using a pure torsion experiment on a thin-walled tube. The material exhibits plastic anisotropy that is established through a separate set of biaxial experiments on the same tube stock. The results are used to calibrate Hill's quadratic anisotropic yield function. It is shown that because in simple shear the material axes rotate during deformation, this anisotropy progressively reduces the material tangent modulus. A parametric study demonstrates that the stress–strain response extracted from a simple shear test can be influenced significantly by the anisotropy parameters. It is thus concluded that the material axes rotation inherent to simple shear tests must be included in the analysis of such experiments when the material exhibits anisotropy.

Commentary by Dr. Valentin Fuster

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