Research Papers

J. Appl. Mech. 2018;85(5):051001-051001-8. doi:10.1115/1.4039289.

Dielectric elastomer actuators (DEAs) exhibit interesting muscle-like attributes including large voltage-induced deformation and high energy density, thus can function as artificial muscles for soft robots/devices. This paper focuses on soft planar DEAs, which have extensive applications such as artificial muscles for jaw movement, stretchers for cell mechanotransduction, and vibration shakers for tactile feedback, etc. Specifically, we develop a soft planar DEA, in which compression springs are employed to make the entire structure freestanding. This soft freestanding actuator can achieve both linear actuation and turning without increasing the size, weight, or structural complexity, which makes the actuator suitable for driving a soft crawling robot. Furthermore, its simple structure and homogeneous deformation allow for analytic modeling, which can be used to interpret the large voltage-induced deformation and interesting mechanics phenomenon (i.e., wrinkling and electromechanical instability). A preliminary demonstration showcases that this soft planar actuator can be employed as an artificial muscle to drive a soft crawling robot.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2018;85(5):051002-051002-7. doi:10.1115/1.4039336.

This work presents a theoretical method for surface love waves in poroelastic media loaded with a viscous fluid. A complex analytic form of the dispersion equation of surface love waves has been developed using an original resolution based on pressure–displacement formulation. The obtained complex dispersion equation was separated in real and imaginary parts. mathematica software was used to solve the resulting nonlinear system of equations. The effects of surface layer porosity and fluid viscosity on the phase velocity and the wave attenuation dispersion curves are inspected. The numerical solutions show that the wave attenuation and phase velocity variation strongly depend on the fluid viscosity, surface layer porosity, and wave frequency. To validate the original theoretical resolution, the results in literature in the case of an homogeneous isotropic surface layer are used. The results of various investigations on love wave propagation can serve as benchmark solutions in design of fluid viscosity sensors, in nondestructive testing (NDT) and geophysics.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2018;85(5):051003-051003-17. doi:10.1115/1.4039374.

Soft network materials that incorporate wavy filamentary microstructures have appealing applications in bio-integrated devices and tissue engineering, in part due to their bio-mimetic mechanical properties, such as “J-shaped” stress–strain curves and negative Poisson's ratios. The diversity of the microstructure geometry as well as the network topology provides access to a broad range of tunable mechanical properties, suggesting a high degree of design flexibility. The understanding of the underlying microstructure-property relationship requires the development of a general mechanics theory. Here, we introduce a theoretical model of infinitesimal deformations for the soft network materials constructed with periodic lattices of arbitrarily shaped microstructures. Taking three representative lattice topologies (triangular, honeycomb, and square) as examples, we obtain analytic solutions of Poisson's ratio and elastic modulus based on the mechanics model. These analytic solutions, as validated by systematic finite element analyses (FEA), elucidated different roles of lattice topology and microstructure geometry on Poisson's ratio of network materials with engineered zigzag microstructures. With the aid of the theoretical model, a crescent-shaped microstructure was devised to expand the accessible strain range of network materials with relative constant Poisson's ratio under large levels of stretching. This study provides theoretical guidelines for the soft network material designs to achieve desired Poisson's ratio and elastic modulus.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2018;85(5):051004-051004-13. doi:10.1115/1.4038967.

The application of explicit dynamics to simulate quasi-static events often becomes impractical in terms of computational cost. Different solutions have been investigated in the literature to decrease the simulation time and a family of interesting, increasingly adopted approaches are the ones based on the proper orthogonal decomposition (POD) as a model reduction technique. In this study, the algorithmic framework for the integration of the equation of motions through POD is proposed for discrete linear and nonlinear systems: a low dimensional approximation of the full order system is generated by the so-called proper orthogonal modes (POMs), computed with snapshots from the full order simulation. Aiming to a predictive tool, the POMs are updated in itinere alternating the integration in the complete system, for the snapshots collection, with the integration in the reduced system. The paper discusses details of the transition between the two systems and issues related to the application of essential and natural boundary conditions (BCs). Results show that, for one-dimensional (1D) cases, just few modes are capable of excellent approximation of the solution, even in the case of stress–strain softening behavior, allowing to conveniently increase the critical time-step of the simulation without significant loss in accuracy. For more general three-dimensional (3D) situations, the paper discusses the application of the developed algorithm to a discrete model called lattice discrete particle model (LDPM) formulated to simulate quasi-brittle materials characterized by a softening response. Efficiency and accuracy of the reduced order LDPM response are discussed with reference to both tensile and compressive loading conditions.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2018;85(5):051005-051005-8. doi:10.1115/1.4039373.

Thermal inclusion in an elastic half-space is a classical micromechanical model for describing localized heating near a surface. This paper presents explicit analytical solutions for the complete elastic fields, including displacements, strains, and stresses, produced by an ellipsoidal thermal inclusion in a three-dimensional semi-infinite space. Unlike the famous Eshelby solution corresponding to the infinite space case, the present work demonstrates that the interior strain and stress components are no longer uniform and appear to be much more complex. Nevertheless, the results can be represented in a more compact and geometrically meaningful form by constructing auxiliary confocal ellipsoids. The derived explicit solution indicates that the shear components of the stress and strain may be represented in closed-form. The jump conditions are examined and proven to be exactly identical to the infinite space case. A purposely selected benchmark example is studied to illustrate the free boundary surface effects. The degenerate case of a spherical thermal inclusion may be derived in a closed form, and is verified by the well-known Mindlin solution.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2018;85(5):051006-051006-13. doi:10.1115/1.4039170.

Identification of material properties of hyper-elastic materials such as soft tissues of the human body or rubber-like materials has been the subject of many works in recent decades. Boundary conditions generally play an important role in solving an inverse problem for material identification, while their knowledge has been taken for granted. In reality, however, boundary conditions may not be available on parts of the problem domain such as for an engineering part, e.g., a polymer that could be modeled as a hyper-elastic material, mounted on a system or an in vivo soft tissue. In these cases, using hypothetical boundary conditions will yield misleading results. In this paper, an inverse algorithm for the characterization of hyper-elastic material properties is developed, which takes into consideration unknown conditions on a part of the boundary. A cost function based on measured and calculated displacements is defined and is minimized using the Gauss–Newton method. A sensitivity analysis is carried out by employing analytic differentiation and using the finite element method (FEM). The effectiveness of the proposed method is demonstrated through numerical and experimental examples. The novel method is tested with a neo–Hookean and a Mooney–Rivlin hyper-elastic material model. In the experimental example, the material parameters of a silicone based specimen with unknown boundary condition are evaluated. In all the examples, the obtained results are verified and it is observed that the results are satisfactory and reliable.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2018;85(5):051007-051007-8. doi:10.1115/1.4039172.

Void growth in an anisotropic ductile solid is studied by numerical analyses for three-dimensional (3D) unit cells initially containing a void. The effect of plastic anisotropy on void growth is the main focus, but the studies include the effects of different void shapes, including oblate, prolate, or general ellipsoidal voids. Also, other 3D effects such as those of different spacings of voids in different material directions and the effects of different macroscopic principal stresses in three directions are accounted for. It is found that the presence of plastic anisotropy amplifies the differences between predictions obtained for different initial void shapes. Also, differences between principal transverse stresses show a strong interaction with the plastic anisotropy, such that the response is very different for different anisotropies. The studies are carried out for one particular choice of void volume fraction and stress triaxiality.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2018;85(5):051008-051008-8. doi:10.1115/1.4039478.

A theoretical and computational model has been developed for the nonlinear motion of an inextensible beam undergoing large deflections for cantilevered and free–free boundary conditions. The inextensibility condition was enforced through a Lagrange multiplier which acted as a constraint force. The Rayleigh–Ritz method was used by expanding the deflections and the constraint force in modal series. Lagrange's equations were used to derive the equations of motion of the system, and a fourth-order Runge–Kutta solver was used to solve them. Comparisons for the cantilevered beam were drawn to experimental and computational results previously published and show good agreement for responses to both static and dynamic point forces. Some physical insights into the cantilevered beam response at the first and second resonant modes were obtained. The free–free beam condition was investigated at the first and third resonant modes, and the nonlinearity (primarily inertia) was shown to shift the resonant frequency significantly from the linear natural frequency and lead to hysteresis in both modes.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2018;85(5):051009-051009-8. doi:10.1115/1.4039479.

The use of chopped fibers in the manufacturing of carbon fiber composite parts is becoming more popular in order to reduce production costs, especially in the automotive, wind, and gas storage industries. The orientation of the fibers in a chopped fiber part is important because the material properties of the part depend upon it. Phenomena such as shear alignment can result in undesired material properties, and therefore, a method for detecting the presence of undesired fiber orientations is needed. In this paper, a metric based on a part's curvature mode shapes is developed to identify the presence and location of fibers whose orientation is different from that of a desired alignment. A proof-of-concept experimental analysis shows the effectiveness of the metric at locating a region in a carbon fiber laminate plate that has been modified by rotating the fibers 90 deg. A finite element model is also developed to validate the experimental results and explore other modification scenarios. In each case, the metric is effective in identifying areas in which fiber alignment changed relative to a baseline model. In one case, a change as small as 3 deg was identified.

Topics: Fibers , Mode shapes
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2018;85(5):051010-051010-11. doi:10.1115/1.4039480.

Through the analysis of a model problem, a thin elastic plate bonded to an elastic foundation, we address several issues related to the miniature bulge test for measuring the energy-release rate associated with the interfacial fracture of a bimaterial system, where one of the constituents is a thin foil. These issues include the effect of the substrate compliance on the interpretation of the energy release rate, interfacial strength, and the identification of the boundary of the deforming bulge or the location of the interfacial crack front. The analysis also suggests a way for measuring the so-called foundation modulus, which characterizes the property of the substrate. An experimental example, a stainless steel thin foil bonded to an aluminum substrate through hot-isostatic-pressing (HIP), is used to illustrate and highlight some of the conclusions of the model analysis.

Commentary by Dr. Valentin Fuster

Technical Brief

J. Appl. Mech. 2018;85(5):054501-054501-3. doi:10.1115/1.4039171.

A rectangular film is clamped at the opposite ends before being inflated into a blister by an external pressure, p. The bulging film adheres to a constraining plate with distance, w0, above. Increasing pressure expands the contact area of length, 2c. Depressurization shrinks the contact area and ultimate detaches the film. The relation of (p, w0, c) is established for a fixed interfacial adhesion energy.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2018;85(5):054502-054502-4. doi:10.1115/1.4039436.

In this paper, a new strategy based on generalized cell mapping (GCM) method will be introduced to investigate the stochastic response of a class of impact systems. Significant difference of the proposed procedure lies in the choice of a novel impact-to-impact mapping, which is built to calculate the one-step transition probability matrix, and then, the probability density functions (PDFs) of the stochastic response can be obtained. The present strategy retains the characteristics of the impact systems, and is applicable to almost all types of impact systems indiscriminately. Further discussion proves that our strategy is reliable for different white noise excitations. Numerical simulations verify the efficiency and accuracy of the suggested strategy.

Commentary by Dr. Valentin Fuster

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