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Research Papers

J. Appl. Mech. 2019;86(7):071001-071001-10. doi:10.1115/1.4043144.

In this study, a new geometrically exact nonlinear model is developed for accurate analysis of buckling and postbuckling behavior of beams, for the first time. Three-dimensional nonlinear finite element analysis is conducted to verify the validity of the developed model even at very large postbuckling amplitudes. It is shown that the model commonly used in the literature for buckling analysis significantly underestimates the postbuckling amplitude. The proposed model is developed on the basis of the beam theory of Euler–Bernoulli, along with the assumption of centerline inextensibility, while taking into account the effect of initial imperfection. The Kelvin–Voigt model is utilized to model internal energy dissipation. To ensure accurate predictions in the postbuckling regime, the nonlinear terms in the equation of motion are kept exact with respect to the transverse motion, resulting in a geometrically exact model. It is shown that even a fifth-order truncated nonlinear model does not yield accurate results, highlighting the significant importance of keeping the terms exact with respect to the transverse motion. Using the verified geometrically exact model, the possibility of dynamic buckling is studied in detail. It is shown that dynamic buckling could occur at axial load variation amplitudes as small as 2.3% of the critical static buckling load.

Topics: Stress , Buckling
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2019;86(7):071002-071002-13. doi:10.1115/1.4043184.

This paper presents a conforming augmented finite element method (C-AFEM) that can account for arbitrary cracking in solids with similar accuracy of other conforming methods, but with a significantly improved numerical efficiency of about ten times. We show that the numerical gains are mainly due to our proposed new solving procedure, which involves solving a local problem for crack propagation and a global problem for structural equilibrium, through a tightly coupled two-step process. Through several numerical benchmarking examples, we further demonstrate that the C-AFEM is more accurate and mesh insensitive when compared with the original A-FEM, and both C-AFEM and A-FEM are much more robust and efficient than other parallel methods including the extended finite element method (XFEM)/generalized finite element (GFEM) and the conforming embedded discontinuity method.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2019;86(7):071003-071003-10. doi:10.1115/1.4043258.

Water-filled containers placed externally on an armored vehicle offer a potentially low cost, light-weight, and simple technique to mitigate near-field explosive blast, although the use of a gap or standoff between the container and target has not been studied. This paper uses experimental testing and numerical simulations to characterize the influence of this container standoff on the mitigation of near-field blast effects. The addition of the container standoff was not found to generally increase the blast mitigation effect provided by water-filled containers on the deformation caused to a steel target plate. While the container standoff was found to enhance the spreading and shadowing blast mitigation mechanisms provided by the water-filled container, this was offset by an increase in blast loading due to the container being closer to the explosive charge. A new mitigation mechanism was identified as the time delay between the initial loading of the steel plate by the blast wave and the subsequent impact of water ejected from the container. The results from this work provide engineers guidance into the design of water-filled containers for near-field blast protection of armored vehicles.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2019;86(7):071004-071004-8. doi:10.1115/1.4043354.

Microbond tests have been widely used for studying the interfacial mechanical properties of fiber-reinforced composites. However, experimental results reveal that the interfacial shear strength (IFSS) depends on the length of microdroplet-embedded fiber (le). Thus, it is essential to provide an insight into this size effect on IFSS. In this paper, microbond tests are conducted for two kinds of widely used composites, i.e., glass fiber/epoxy matrix and carbon fiber/epoxy matrix. The lengths of microdroplet-embedded glass fiber and carbon fiber are in the ranges from 114.29 µm to 557.14 µm and from 63.78 µm to 157.45 µm, respectively. We analyze the representative force–displacement curves, the processes of interfacial failure and frictional sliding, and the maximum force and the frictional force as functions of le. Experimental results show that IFSS of both material systems monotonically decreases with le and then approaches a constant value. The finite element model is used to analyze the size effect on IFSS and interfacial failure behaviors. For both material systems, IFSS predicted from simulations is consistent with that obtained from experiments. Moreover, by analyzing the shear stress distribution, a transition of interface debonding is found from more or less uniform separation to crack propagation when le increases. This study reveals the mechanism of size effect in microbond tests, serving as an effective method to evaluate the experimental results and is critical to guidelines for the design and optimization of advanced composites.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2019;86(7):071005-071005-8. doi:10.1115/1.4043286.

Peeling of thin films is a problem of great interest to scientists and engineers. Here, we study the peeling response of thin films with nonuniform thickness profile attached to a rigid substrate through a planar homogeneous interface. We show both analytically and using finite element analysis that patterning the film thickness may lead to direction-dependent adhesion such that the force required to peel the film in one direction is different from the force required in the other direction, without any change to the film material, the substrate interfacial geometry, or the adhesive material properties. Furthermore, we show that this asymmetry is tunable through modifying the geometric characteristics of the thin film to obtain higher asymmetry ratios than reported previously in the literature. We discuss our findings in the broader context of enhancing interfacial response by modulating the bulk geometric or compositional properties.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2019;86(7):071006-071006-9. doi:10.1115/1.4043285.

Of the many valid configurations that a curved fold may assume, it is of particular interest to identify natural—or lowest energy—configurations that physical models will preferentially assume. We present normalized coordinate equations—equations that relate fold surface properties to their edge of regression—to simplify curved-fold relationships. An energy method based on these normalized coordinate equations is developed to identify natural configurations of general curved folds. While it has been noted that natural configurations have nearly planar creases for curved folds, we show that nonplanar behavior near the crease ends substantially reduces the energy of a fold.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2019;86(7):071007-071007-10. doi:10.1115/1.4043283.

An innovative bistable energy-absorbing cylindrical shell structure composed of multiple unit cells is presented in this paper. The structural parameters of the single-layer cylindrical shell structure that produces bistable characteristics are expounded both analytically and numerically. The influence of the number of circumferential cells and the size parameters of the cell ligament on the structure’s macroscopic mechanical response was analyzed. A series of cylindrical shell structures with various size parameters were fabricated using a stereolithography apparatus (SLA). Uniaxial loading and unloading experiments were conducted to achieve force–displacement relationships. Deformation of the structural multistable phase transition response was discussed based on experimental and finite element simulation results. The results show that the proposed innovative single-layer cylindrical shell structure will stabilize at two different positions under certain parameters. The multilayer cylindrical shell exhibits different force–displacement response curves under loading and unloading, and these curves enclose a closed area. In addition, this structure can be cyclically loaded and unloaded, thanks to its good stability and reproducibility, making it attractive in applications requiring repetitive energy absorption.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2019;86(7):071008-071008-11. doi:10.1115/1.4043145.
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In the previous studies by the authors and others, it was demonstrated that there are two possible defect growth modes and a characteristic material length for any soft material. For a pre-existing defect smaller than the material characteristic length, the energy is dissipated all around the defect as it grows and the critical load for the growth is independent of the defect size. For defects larger than the characteristic length, the growth is by cracking and the energy is dissipated along a plane. Thus, the critical load for the growth is size dependent and can be predicted by fracture mechanics. In this study, we apply the same energy-based argument to the failure of thin membranes, with the focus on the first growth mode that gives the maximum critical load. We assume that strain localization due to damage is the precursor to rupture, and hence, we model the corresponding zone as a through-thickness hole, with its size smaller than the material characteristic length. The defect grows when the elastic energy relaxed by the growth is enough to provide the energy needed for internal microstructure changes. This leads us to the size-independent failure conditions for membranes under the biaxial load. The conditions are expressed in terms of either two principal stretches or two principal stresses for two different types of materials. For verification, we test the theory using the published experimental data on natural and styrene-butadiene rubber. By using the experimental data from equal biaxial loading, we predict the critical principal stretch ratios and critical stresses for different biaxialities. The predictions agree well with the experimental results.

Topics: Stress , Failure , Membranes
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2019;86(7):071009-071009-8. doi:10.1115/1.4043143.

In this paper, we studied planar collisions of balls and cylinders with an emphasis on the coefficient of restitution (COR). We conducted a set of experiments using three types of materials: steel, wood, and rubber. Then, we estimated the kinematic COR for all collision pairs. We discovered unusual variations among the ball–ball (B–B) and ball–cylinder (B–C) CORs. We proposed a discretization method to investigate the cause of the variations in the COR. Three types of local contact models were used for the simulation: rigid body, bimodal linear, and bimodal Hertz models.

Based on simulation results, we discovered that the bimodal Hertz model produced collision outcomes that had the greatest agreement with the experimental results. In addition, our simulations showed that softer materials need to be segmented more than harder ones. Softer materials are materials with smaller collision stiffness values than harder ones. Moreover, we obtained a relationship between the collision stiffness ratio and the number of segments of softer materials to produce physically accurate simulations of B–C CORs. We validated this relationship and the proposed method by conducting two additional sets of experiments.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2019;86(7):071010-071010-13. doi:10.1115/1.4043284.

Curved shell structures are known for their excellent load-carrying capability and are commonly used in thin-walled constructions. Although theoretically able to withstand greater buckling loads than flat structures, shell structures are notoriously sensitive to imperfections owing to their postbuckling behavior often being governed by subcritical bifurcations. Thus, shell structures often buckle at significantly lower loads than those predicted numerically and the ensuing dynamic snap to another equilibrium can lead to permanent damage. Furthermore, the strong sensitivity to initial imperfections, as well as their stochastic nature, limits the predictive capability of current stability analyses. Our objective here is to convert the subcritical nature of the buckling event to a supercritical one, thereby improving the reliability of numerical predictions and mitigating the possibility of catastrophic failure. We explore the elastically nonlinear postbuckling response of axially compressed cylindrical panels using numerical continuation techniques. These analyses show that axially compressed panels exhibit a highly nonlinear and complex postbuckling behavior with many entangled postbuckled equilibrium curves. We unveil isolated regions of stable equilibria in otherwise unstable postbuckled regimes, which often possess greater load-carrying capacity. By modifying the initial geometry of the panel in a targeted—rather than stochastic—and imperceptible manner, the postbuckling behavior of these shells can be tailored without a significant increase in mass. These findings provide new insight into the buckling and postbuckling behavior of shell structures and opportunities for modifying and controlling their postbuckling response for enhanced efficiency and functionality.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2019;86(7):071011-071011-7. doi:10.1115/1.4043287.

The adherens junction (AJ) plays an important role in many collective mechanobiological processes, such as gastrulation, embryonic morphogenesis, and tissue homeostasis. In this study, we construct a coarse-grained Monte Carlo simulation model to probe the mechanical properties of AJs. We confirm that cadherin cluster induced by cooperative trans and cis bindings is responsible for AJ’s strength. Systematic simulations reveal that depending on the AJ’s size, the separation force scales with or decouples with the adhesion area, which can explain the conflicting force–area relations in experiments. Moreover, we find that the separation force can be enhanced not only by inter-membrane trans binding but also by intra-membrane cis binding. This cis strengthening effect can indeed boost AJ’s adhesion strength up to the level of focal adhesions, although cadherin’s affinity is three orders of magnitude lower than that of integrin. This work deepens the current understanding of AJ’s mechanics and may help study its functioning in tissue development and tumor progression.

Commentary by Dr. Valentin Fuster

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