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Research Papers

J. Appl. Mech. 2018;86(1):011001-011001-9. doi:10.1115/1.4041471.

Specific adhesion of soft elastic half spaces via molecular bond clusters has been extensively studied in the past ten years. In this study, the adhesion of a soft elastic solid with finite size is considered aiming to investigate how their size and shape may affect the adhesion strength. To model this problem, plane strain assumption is adopted to describe the deformation of the elastic solid. This deformation couples the stochastic behavior of adhesive bonds, for which we have considered the mean field treatment based on the classical Bell theory. Numerical solutions have revealed that, besides the elastic modulus, size of the elastic solid and spatial arrangement of the bond clusters are all crucial factors in mediating the adhesion strength. Most interestingly, there clearly exists an optimal size/shape of the elastic solid that corresponds to the largest adhesion strength. These findings provide new insights and inspirations in understanding various phenomena of cellular adhesion and designing advanced functional biomaterials.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2018;86(1):011002-011002-9. doi:10.1115/1.4041352.

The plastic properties that characterize the uniaxial stress–strain response of a plastically isotropic material are not uniquely related to the indentation force versus indentation depth response. We consider results for three sets of plastic material properties that give rise to essentially identical curves of indentation force versus indentation depth in conical indentation. The corresponding surface profiles after unloading are also calculated. These computed results are regarded as the “experimental” data. A simplified Bayesian-type statistical approach is used to identify the values of flow strength and strain hardening exponent for each of the three sets of material parameters. The effect of fluctuations (“noise”) superposed on the “experimental” data is also considered. We build the database for the Bayesian-type analysis using finite element calculations for a relatively coarse set of parameter values and use interpolation to refine the database. A good estimate of the uniaxial stress–strain response is obtained for each material both in the absence of fluctuations and in the presence of sufficiently small fluctuations. Since the indentation force versus indentation depth response for the three materials is nearly identical, the predicted uniaxial stress–strain response obtained using only surface profile data differs little from what is obtained using both indentation force versus indentation depth and surface profile data. The sensitivity of the representation of the predicted uniaxial stress–strain response to fluctuations increases with increasing strain hardening. We also explore the sensitivity of the predictions to the degree of database refinement.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2018;86(1):011003-011003-7. doi:10.1115/1.4041500.

A major contributor to rolling resistance is road roughness-induced energy dissipation in vehicle suspension systems. We identify the parameters driving this dissipation via a combination of dimensional analysis and asymptotic analysis. We begin with a mechanistic model and basic random vibration theory to relate the statistics of road roughness profile and the dynamic properties of the vehicle to dissipated energy. Asymptotic analysis is then used to unravel the dependence of the dissipation on key vehicle and road characteristics. Finally, closed form expressions and scaling relations are developed that permit a straightforward application of the proposed road-vehicle interaction model for evaluating network-level environmental footprint associated with roughness-induced energy dissipation.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2018;86(1):011004-011004-9. doi:10.1115/1.4041319.

In the present work, it is intended to discuss how to achieve real-time structural topology optimization (i.e., obtaining the optimized distribution of a certain amount of material in a prescribed design domain almost instantaneously once the objective/constraint functions and external stimuli/boundary conditions are specified), an ultimate dream pursued by engineers in various disciplines, using machine learning (ML) techniques. To this end, the so-called moving morphable component (MMC)-based explicit framework for topology optimization is adopted for generating training set and supported vector regression (SVR) as well as K-nearest-neighbors (KNN) ML models are employed to establish the mapping between the design parameters characterizing the layout/topology of an optimized structure and the external load. Compared with existing approaches, the proposed approach can not only reduce the training data and the dimension of parameter space substantially, but also has the potential of establishing engineering intuitions on optimized structures corresponding to various external loads through the learning process. Numerical examples provided demonstrate the effectiveness and advantages of the proposed approach.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2018;86(1):011005-011005-7. doi:10.1115/1.4041415.

Energy absorption structures are widely used in many scenarios. Thin-walled members have been heavily employed to absorb impact energy. This paper presents a novel, Ron Resch origami pattern inspired energy absorption structure. Experimental characterization and numerical simulations were conducted to study the energy absorption of this structure. The results show a new collapse mode in terms of energy absorption featuring multiple plastic hinge lines, which lead to the peak force reduction and larger effective stroke, as compared with the classical honeycomb structure. Overall, the Ron Resch origami-inspired structure and the classical honeycomb structure are quite complementary as energy absorption structures.

Topics: Absorption , Hinges
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2018;86(1):011006-011006-9. doi:10.1115/1.4041548.

Void coalescence is known to be the last microscopic event of ductile fracture in metal alloys and corresponds to the localization of plastic flow in between voids. Limit-analysis has been used to provide coalescence criteria that have been subsequently recast into effective macroscopic yield criteria, leading to models for porous materials valid for high porosities. Such coalescence models have remained up to now restricted to cubic or hexagonal lattices of spheroidal voids. Based on the limit-analysis kinematic approach, a methodology is first proposed to get upper-bound estimates of coalescence stress for arbitrary void shapes and lattices. Semi-analytical coalescence criteria are derived for elliptic cylinder voids in elliptic cylinder unit cells for an isotropic matrix material, and validated through comparisons to numerical limit-analysis simulations. The physical application of these criteria for realistic void shapes and lattices is finally assessed numerically.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2018;86(1):011007-011007-11. doi:10.1115/1.4041550.

Bio-inspired functional surfaces attract many research interests due to the promising applications. In this paper, tunable adhesion of a bio-inspired micropillar arrayed surface actuated by a magnetic field is investigated theoretically in order to disclose the mechanical mechanism of changeable adhesion and the influencing factors. Each polydimethylsiloxane (PDMS) micropillar reinforced by uniformly distributed magnetic particles is assumed to be a cantilever beam. The beam's large elastic deformation is obtained under an externally magnetic field. Specially, the rotation angle of the pillar's end is predicted, which shows an essential effect on the changeable adhesion of the micropillar arrayed surface. The larger the strength of the applied magnetic field, the larger the rotation angle of the pillar's end will be, yielding a decreasing adhesion force of the micropillar arrayed surface. The difference of adhesion force tuned by the applied magnetic field can be a few orders of magnitude, which leads to controllable adhesion of such a micropillar arrayed surface. Influences of each pillar's cross section shape, size, intervals between neighboring pillars, and the distribution pattern on the adhesion force are further analyzed. The theoretical predictions are qualitatively well consistent with the experimental measurements. The present theoretical results should be helpful not only for the understanding of mechanical mechanism of tunable adhesion of micropillar arrayed surface under a magnetic field but also for further precise and optimal design of such an adhesion-controllable bio-inspired surface in future practical applications.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2018;86(1):011008-011008-8. doi:10.1115/1.4041620.

Wrinkles in layered neo-Hookean structures were recently formulated as a Hamiltonian system by taking the thickness direction as a pseudo-time variable. This enabled an efficient and accurate numerical method to solve the eigenvalue problem for onset wrinkles. Here, we show that wrinkles in graded elastic layers can also be described as a time-varying Hamiltonian system. The connection between wrinkles and the Hamiltonian system is established through an energy method. Within the Hamiltonian framework, the eigenvalue problem of predicting wrinkles is defined by a series of ordinary differential equations with varying coefficients. By modifying the boundary conditions at the top surface, the eigenvalue problem can be efficiently and accurately solved with numerical solvers of boundary value problems. We demonstrated the accuracy of the symplectic analysis by comparing the theoretically predicted displacement eigenfunctions, critical strains, and wavelengths of wrinkles in two typical graded structures with finite element simulations.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2018;86(1):011009-011009-6. doi:10.1115/1.4041618.

We investigate the influence of material dissimilarity on the traction fields at the corners of a contact between an elastic right-angle wedge and an elastic half-plane. The local asymptotic fields are characterized in terms of the properties of the leading eigenvalue for cases of slip and stick as a function of the Dundurs bimaterial parameters α and β, and the coefficient of friction f. Permissible values of α and β are partitioned into two possible ranges, one where behavior is qualitatively similar to the case where the indenting wedge is rigid [α = 1] and the other where behavior is similar to the case where the materials are the same [α = β = 0]. The results give insight into the high local stresses at the edge of a contact between elastically dissimilar bodies and can also be used to evaluate the effectiveness of mesh refinement in corresponding finite element models.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2018;86(1):011010-011010-10. doi:10.1115/1.4041677.

The electrospinning process enables the fabrication of randomly distributed nonwoven polymer fiber networks with high surface area and high porosity, making them ideal candidates for multifunctional materials. The mechanics of nonwoven networks has been well established for elastic deformations. However, the mechanical properties of the polymer fibrous networks with large deformation are largely unexplored, while understanding their elastic and plastic mechanical properties at different fiber volume fractions, fiber aspect ratio, and constituent material properties is essential in the design of various polymer fibrous networks. In this paper, a representative volume element (RVE) based finite element model with long fibers is developed to emulate the randomly distributed nonwoven fibrous network microstructure, enabling us to systematically investigate the mechanics and large deformation behavior of random nonwoven networks. The results show that the network volume fraction, the fiber aspect ratio, and the fiber curliness have significant influences on the effective stiffness, effective yield strength, and the postyield behavior of the resulting fiber mats under both tension and shear loads. This study reveals the relation between the macroscopic mechanical behavior and the local randomly distributed network microstructure deformation mechanism of the nonwoven fiber network. The model presented here can also be applied to capture the mechanical behavior of other complex nonwoven network systems, like carbon nanotube networks, biological tissues, and artificial engineering networks.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2018;86(1):011011-011011-10. doi:10.1115/1.4041678.

Flexible elastic beams can function as dexterous manipulators at multiple length-scales and in various niche applications. As a step toward achieving controlled manipulation with flexible structures, we introduce the problem of approximating desired quasi-static deformations of a flexible beam, modeled as an elastica, by optimizing the loads applied. We presume the loads to be concentrated, with the number and nature of their application prescribed based on design considerations and operational constraints. For each desired deformation, we pose the problem of computing the requisite set of loads to mimic the target shape as one of optimal approximations. In the process, we introduce a novel generalization of the forward problem by considering the inclinations of the loads applied to be functionals of the solution. This turns out to be especially beneficial when analyzing tendon-driven manipulators. We demonstrate the shape control realizable through load optimization using a diverse set of experiments.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2018;86(1):011012-011012-6. doi:10.1115/1.4041679.

Polydimethylsiloxane (PDMS) has a good elasticity but with a pretty low fracture toughness, which limits its use in practical applications. This paper presents a simple and low-cost approach to manufacture a PDMS/fabric composite through incorporating the commercially available stretchy plain weft-knitted nylon fabric into the PDMS matrix. The fracture toughness of the composite is much higher than that of pure PDMS with an increase up to 700%. The toughening mechanism, which can be attributed to the deformation localization induced fiber stretch and damage propagation in the PDMS matrix, is fully investigated. During cyclic loadings, the composite may exhibit a linear elastic response or a significant hysteresis depending on the stretch level. These results provide physical insights into the deformation mechanism of a soft fabric-reinforced composite and may offer practical routes to realize robust crack-insensitive PDMS.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2018;86(1):011013-011013-10. doi:10.1115/1.4041826.

The competition between the structural rigidity and the van der Waals interactions may lead to collapsing of aligned nanotubes, and the resulting changes of both configurations and properties promise the applications of nanotubes in nano-composites and nano-electronics. In this paper, a finite-deformation model is applied to study the adhesion of parallel multiwall nanotubes with both partial and full collapsing, in which the noncontact adhesion energy is analytically determined. The analytical solutions of both configurations and energies of collapsed nanotubes are consistent with the molecular dynamics (MD) results, demonstrating the effectiveness of the finite-deformation model. To study the critical conditions of generating the partially and fully collapsed multiwall nanotubes, our analytical model gives the predictions for both the geometry- and energy-related critical diameters, which are helpful for the stability analysis and design of nanotube-based nano-devices.

Topics: Adhesion , Nanotubes
Commentary by Dr. Valentin Fuster

Technical Brief

J. Appl. Mech. 2018;86(1):014501-014501-3. doi:10.1115/1.4041549.

The introduction of a dislocation from the free-surface of a grain A of a polycrystal has been investigated from the theoretical point of view. Assuming two disclination dipoles are lying in a high angle boundary separating the corresponding grain A and a neighbor grain B, the equilibrium position of the dislocation has been determined in the grain A versus the separation distance between the two dipoles, the length and strength of each dipole.

Commentary by Dr. Valentin Fuster

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