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Research Papers

J. Appl. Mech. 2015;82(9):091001-091001-9. doi:10.1115/1.4030739.

This paper presents the nonlinear large deflection of the thin film and the effect of substrate deformation on the thin film deflection through the shaft-loaded blister test. The blister of thin film can be divided into two parts, namely, the annular contact brim and the central noncontact bulge. A two-coupled line spring model is developed to describe the deformation of the contact part, and Föppl–Hencky equations are employed to study the constitutive relation between the applied load and the central deflection. The analytical and numerical solutions for the constitutive relation between the applied load and the deflection of thin film with considering the deformation of substrate are derived.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2015;82(9):091002-091002-8. doi:10.1115/1.4030626.

Pure bending experiments on prismatic bars of square cross section composed of reticulated polymer foam exhibit deformation behavior not captured by classical elasticity theory. Perhaps the clearest example of this is the observed sigmoidal deformation of the bars' lateral surfaces, which are predicted by classical elasticity theory to tilt but remain planar upon pure moment application. Such foams have a non-negligible length scale compared to the bars' cross-sectional dimensions, whereas classical elasticity theory contains no inherent length scale. All these facts raise the intriguing question: is there a richer, physically sensible, yet still continuum and relatively simple elasticity theory capable of modeling the observed phenomenon in these materials? This paper reports our exploration of the hypothesis that Cosserat elasticity can. We employ the principle of minimum potential energy for homogeneous isotropic Cosserat linear elastic material in which the microrotation vector is taken to be independent of the macrorotation vector (as prior experiments indicate that it should be in general to model such materials) to obtain an approximate three-dimensional solution to pure bending of a prismatic bar having a square cross section. We show that this solution, and hence Cosserat elasticity, captures the experimentally observed nonclassical deformation feature, both qualitatively and quantitatively, for reasonable values of the Cosserat moduli. A further interesting conclusion is that a single experiment—the pure bending one—suffices to reveal directly, via the observation of surface deformation, the presence of nonclassical elastic effects describable by Cosserat elasticity.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2015;82(9):091003-091003-8. doi:10.1115/1.4030647.

In this paper, we investigate the asymmetric bifurcation behavior of an initially curved nanobeam accounting for Lorentz and electrostatic forces. The beam model was developed in the framework of Euler–Bernoulli beam theory, and the surface effects at the nanoscale were taken into account in the model by including the surface elasticity and the residual surface tension. Based on the Galerkin decomposition method, the model was simplified as two degrees of freedom reduced order model, from which the symmetry breaking criterion was derived. The results of our work reveal the significant surface effects on the symmetry breaking criterion for the considered nanobeam.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2015;82(9):091004-091004-10. doi:10.1115/1.4030666.

The dependence of the fracture toughness of two-dimensional (2D) elastoplastic lattices upon relative density and ductility of cell wall material is obtained for four topologies: the triangular lattice, kagome lattice, diamond lattice, and the hexagonal lattice. Crack-tip fields are explored, including the plastic zone size and crack opening displacement. The cell walls are treated as beams, with a material response given by the Ramberg–Osgood law. There is choice in the criterion for crack advance, and two extremes are considered: (i) the maximum local tensile strain (LTS) anywhere in the lattice attains the failure strain or (ii) the average tensile strain (ATS) across the cell wall attains the failure strain (which can be identified with the necking strain). The dependence of macroscopic fracture toughness upon failure strain, strain hardening exponent, and relative density is obtained for each lattice, and scaling laws are derived. The role of imperfections in degrading the fracture toughness is assessed by random movement of the nodes. The paper provides a strategy for obtaining lattices of high toughness at low density, thereby filling gaps in material property space.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2015;82(9):091005-091005-7. doi:10.1115/1.4030740.

An asymptotic theory of composite plates is constructed using the variational asymptotic method. To maximize simplicity and promote efficiency of the developed model, a transformation procedure is required to establish a mathematical link between an asymptotically correct energy functional derived herein and a simpler engineering model, such as a generalized Reissner–Mindlin model. Without relaxing the warping constraints and performing “smart minimization” or optimization procedures introduced in previous work, a different approach is suggested in this paper. To eliminate all partial derivatives of the 2D generalized strains in the asymptotically correct energy functional, a hybrid transformation procedure is systematically carried out by involving modified equilibrium and compatibility equations, and solving a system of linear algebraic equations via the pseudo-inverse method. Equivalent constitutive laws for the generalized Reissner–Mindlin plate model are then estimated. Several examples as a preliminary validation are used to demonstrate the capability and accuracy of this new model.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2015;82(9):091006-091006-7. doi:10.1115/1.4030742.

A plane contact and partial slip model of an elastic layer with randomly rough surface were established by combining the Greenwood–Williamson (GW) rough contact model and the Cattaneo–Mindlin partial slip model. The rough surface of the elastic layer bonded to a rigid base is modeled as an ensemble of noninteracting asperities with identical radius of curvature and Gaussian-distributed heights. By employing the Hertzian solution and the Cattaneo–Mindlin solution to each individual asperity of the rough surface, we derive the total normal force, the real contact area, and the total tangential force for the rough surface, respectively, and then examine the normal contact and partial slip behaviors of the layer. An effective Coulomb coefficient is defined to account for interfacial friction properties. Furthermore, a typical stick–slip transition for the rough surface was also captured by distinguishing the stick and slip contacting asperities according to their respective indentation depths. Our analysis results show that an increasing layer thickness may result in a larger real contact area, a lower mean contact pressure, and a higher effective Coulomb coefficient.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2015;82(9):091007-091007-7. doi:10.1115/1.4030820.
OPEN ACCESS

The Young's modulus of human skin is of great interests to dermatology, cutaneous pathology, and cosmetic industry. A wearable, ultrathin, and stretchable device provides a noninvasive approach to measure the Young's modulus of human skin at any location, and in a way that is mechanically invisible to the subject. A mechanics model is developed in this paper to establish the relation between the sensor voltage and the skin modulus, which, together with the experiments, provides a robust way to determine the Young's modulus of the human skin.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2015;82(9):091008-091008-12. doi:10.1115/1.4030795.

In this paper, we combine recent developments in modeling of fatigue-damage, isogeometric analysis (IGA) of thin-shell structures, and structural health monitoring (SHM) to develop a computational steering framework for fatigue-damage prediction in full-scale laminated composite structures. The main constituents of the proposed framework are described in detail, and the framework is deployed in the context of an actual fatigue test of a full-scale wind-turbine blade structure. The results indicate that using an advanced computational model informed by in situ SHM data leads to accurate prediction of the damage zone formation, damage progression, and eventual failure of the structure. Although the blade fatigue simulation was driven by test data obtained prior to the computation, the proposed computational steering framework may be deployed concurrently with structures undergoing fatigue loading.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2015;82(9):091009-091009-9. doi:10.1115/1.4030850.

In this paper, we investigated the temperature-dependent viscoelastic behavior of dielectric elastomers (DEs) and the effects of viscoelasticity on the electro-actuation behavior. We performed dynamic thermomechanical analysis to measure the master curve of the stress relaxation function and the temperature dependence of the relaxation time of VHB 4905, a commonly used DE. The master curve was applied to calculate the viscoelastic spectrum for a discrete multiprocess finite deformation viscoelastic model. In addition, we performed uniaxial creep and stress relaxation experiments and electrical actuation experiments under different prestretch conditions. The measured spectrum was applied to predict the experimental results. Generally, the model produced good quantitative agreement with both the viscoelastic and electro-actuation experiments, which shows the necessity of using a multiprocess relaxation model to accurately capture the viscoelastic response for VHB. However, the model underpredicted the electro-actuated creep strain for high voltages near the pull-in instability. We attributed the discrepancies to the complex boundary conditions that were not taken into account in the simulation. We also investigated the failure of VHB membrane caused by viscoelastic creep when prestretched and subjected to constant voltage loading. The experimental time to failure for the specimens decreased exponentially with voltage, which agreed well with the predictions of the model.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2015;82(9):091010-091010-8. doi:10.1115/1.4030796.

For convenient characterization of the roughness of the interface between two different piezoelectric/piezomagnetic materials (PPMs), a wavy contact model is developed. Eight potential functions are proposed, which makes the considered mixed boundary values problems mathematically tractable. Important physical objectives, such as the unknown contact region and surface normal stress, are presented explicitly. Results in a special case, full contact, are offered. Figures are plotted to show the effects of the piezoelectric phase volume fraction and the external loading on the interactions between two different PPMs. Numerical test reveals that enhancing the piezoelectric phase volume fraction produces a wider contact region.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2015;82(9):091011-091011-11. doi:10.1115/1.4030853.

In this research, we have employed molecular dynamics (MD) simulations to computationally explore the effects of hydrostatic stress on the shear deformation behavior of nanocrystalline (NC) Cu, over a range of grain size (5–20 nm) and temperature (10–500 K). Simulated nanocrystals were deformed under shear with superimposed isotropic tensile/compressive hydrostatic stress $σ∧$ of magnitude up to 5 GPa. The results suggest that the shear strength increases under imposed compressive $σ∧$, and decreases under imposed tensile $σ∧$, by around 0.05–0.09 GPa for every GPa of imposed hydrostatic pressure. At 300 K, we computed activation volumes (3.5–9 b3) and activation energies (0.2–0.3 eV), with values agreeing with those reported in previous experimental and theoretical work, notwithstanding the extreme deformation rates imposed in MD simulations. Additionally, we observed that shear deformation under an imposed compressive hydrostatic stress tends to slightly increase both the activation volumes and the energy activation barrier. Finally, no discernible pressure effect could be observed on the distribution of inelastic shear strain.

Commentary by Dr. Valentin Fuster

Technical Brief

J. Appl. Mech. 2015;82(9):094501-094501-5. doi:10.1115/1.4030502.

Graphynes, a new family of carbon allotropes, exhibit superior mechanical properties depending on their atomic structures and have been proposed as a promising building materials for nanodevices. Accurate modeling and clearer understanding of their mechanical properties are essential to the future applications of graphynes. In this paper, an analytical molecular mechanics model is proposed for relating the elastic properties of graphynes to their atomic structures directly. The closed-form expressions for the in-plane stiffness and Poisson's ratio of graphyne-n are obtained for small strains. It is shown that the in-plane stiffness is a decreasing function whereas Poisson's ratio is an increasing function of the number of acetylenic linkages between two adjacent hexagons in graphyne-n. The present analytical results enable direct linkages between mechanical properties and lattice structures of graphynes; thereby, providing useful guidelines in designing graphyne configurations to suit their potential applications. Based on an effective bond density analysis, a scaling law is also established for the in-plane stiffness of graphyne-n which may have implications for their other mechanical properties.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2015;82(9):094502-094502-2. doi:10.1115/1.4030743.

The equilibrium equations and boundary conditions in terms of the second Piola–Kirchhoff membrane stress and moment are given in this note, which are necessary for the finite deformation analysis of shells.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2015;82(9):094503-094503-2. doi:10.1115/1.4030741.

Critical displacements are determined for snap-through of shallow, extensible, and elastic arches that are pushed downward quasi-statically at any point along the span. The initial arch is circular and unstrained, and the ends of the arch are pinned and immovable. When the vertical position at the push-down location reaches a critical value, the arch jumps into an inverted shape (unless the arch is extremely shallow). The critical displacement is given or approximated by an unstable equilibrium configuration of the unloaded arch, for which an analyical formula is derived.

Commentary by Dr. Valentin Fuster