Research Papers

J. Appl. Mech. 2017;84(11):111001-111001-13. doi:10.1115/1.4037739.

Exact solutions to the three-dimensional (3D) contact problem of a rigid flat-ended circular cylindrical indenter punching onto a transversely isotropic thermoporoelastic half-space are presented. The couplings among the elastic, hydrostatic, and thermal fields are considered, and two different sets of boundary conditions are formulated for two different cases. We use a concise general solution to represent all the field variables in terms of potential functions and transform the original problem to the one that is mathematically expressed by integral (or integro-differential) equations. The potential theory method is extended and applied to exactly solve these integral equations. As a consequence, all the physical quantities of the coupling fields are derived analytically. To validate the analytical solutions, we also simulate the contact behavior by using the finite element method (FEM). An excellent agreement between the analytical predictions and the numerical simulations is obtained. Further attention is also paid to the discussion on the obtained results. The present solutions can be used as a theoretical reference when practically applying microscale image formation techniques such as thermal scanning probe microscopy (SPM) and electrochemical strain microscopy (ESM).

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2017;84(11):111002-111002-8. doi:10.1115/1.4037683.

Massively parallel molecular dynamics (MD) simulations have been performed to understand the plastic deformation of metals. However, the intricate interplay between the deformation mechanisms and the various material properties is largely unknown in alloy systems for the limited available interatomic potentials. We adopt the meta-atom method proposed by Wang et al., which unifies MD simulations of both pure metals and alloys in the framework of the embedded atom method (EAM). Owing to the universality of EAM for metallic systems, meta-atom potentials can fit properties of different classes of alloys. Meta-atom potentials for both aluminum bronzes and hypothetic face-centered-cubic (FCC) metals have been formulated to study the parametric dependence of deformation mechanisms, which captures the essence of competitions between dislocation motion and twinning or cleavage. Moreover, the solid-solution strengthening effect can be simply accounted by introducing a scaling factor in the meta-atom method. As the computational power enlarges, this method can extend the capability of massively parallel MD simulations in understanding the mechanical behaviors of alloys. The calculation of macroscopic measurable quantities for engineering oriented alloys is expected to be possible in this way, shedding light on constructing materials with specific mechanical properties.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2017;84(11):111003-111003-9. doi:10.1115/1.4037740.

Conformability of bio-integrated electronics to soft and microscopically rough biotissues can enhance effective electronics–tissue interface adhesion and can facilitate signal/heat/mass transfer across the interface. When biotissues deform, for example, when skin stretches or heart beats, the deformation may lead to changes in conformability. Although a theory concerning just full conformability (FC) under deformation has been developed (i.e., the FC theory), there is no available theory for partially conformable (PC) systems subjected to deformation. Taking advantage of the path-independent feature of elastic deformation, we find that the total energy of a PC system subjected to stretching or compression can be analytically expressed and minimized. We discover that the FC theory is not sufficient in predicting FC and a full energy landscape obtained by our PC theory is needed for searching for the equilibrium. Our results reveal that stretching enhances conformability while compression degrades it. In addition to predicting the critical parameters to maintain FC under deformation, our PC theory can also be applied to predict the critical compressive strain beyond which FC is lost. Our theory has been validated by laminating poly(methyl methacrylate) (PMMA) membranes of different thicknesses on human skin and inducing skin deformation.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2017;84(11):111004-111004-7. doi:10.1115/1.4037704.

Epidermal electronic devices (EEDs) are very attractive in applications of monitoring human vital signs for diagnostic, therapeutic, or surgical functions due to their ability for integration with human skin. Thermomechanical analysis is critical for EEDs in these applications since excessive heating-induced temperature increase and stress may cause discomfort. An axisymmetric analytical thermomechanical model based on the transfer matrix method, accounting for the coupling between the Fourier heat conduction in the EED and the bio-heat transfer in human skin, the multilayer feature of human skin and the size effect of the heating component in EEDs, is established to study the thermomechanical behavior of the EED/skin system. The predictions of the temperature increase and principle stress from the analytical model agree well with those from finite element analysis (FEA). The influences of various geometric parameters and material properties of the substrate on the maximum principle stress are fully investigated to provide design guidelines for avoiding the adverse thermal effects. The thermal and mechanical comfort analyses are then performed based on the analytical model. These results establish the theoretical foundation for thermomechanical analysis of the EED/skin system.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2017;84(11):111005-111005-6. doi:10.1115/1.4037833.

Wrinkles widely existing in sheets and membranes have attracted a lot of attention in the fields of material science and engineering applications. In this paper, we present a new method to generate ordered (striplike) and steady wrinkles of a constrained dielectric elastomer (DE) sheet coated with soft electrodes on both sides subjected to high voltage. When the voltage reaches a certain value, wrinkles will nucleate and grow. We conduct both experimental and theoretical studies to investigate the wavelength and amplitude of the wrinkle. The results show a good agreement between theory and experiment. Moreover, the amplitude and wavelength of ordered wrinkles can be tuned by varying the prestretch and geometry of the DE sheet, as well as the applying voltage. This study can help future design of DE transducers such as diffraction grating and optical sensor.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2017;84(11):111006-111006-11. doi:10.1115/1.4037883.

The nonlinear response of a flexible structure, subjected to generally supported conditions with nonlinearities, is investigated for the first time. An analytical procedure is proposed first. Moreover, a simulation technique usually employed in static analysis is developed for confirmation. Generally, ordinary perturbation methods could analyze dynamics of flexible structures with linear boundary conditions. As nonlinear boundaries are taken into account, they are out of operation for the modal shape that is hardly to be obtained, which is the key to the analysis. In order to overcome this, nonlinear boundary conditions are rescaled and the technique of modal revision is employed. Consequently, each governing equation with different time-scales could be analyzed exactly according to corresponding rescaled boundary conditions. The total response of any point at the flexible structure will be composed by harmonic responses yielded by the analytical method. Furthermore, the differential quadrature element method (DQEM), a numerical simulation technique could satisfy boundary conditions strictly, is introduced to certify analytical results. The comparison shows a reasonable agreement between these two methods. In fact, the accuracy of the analytical method for nonlinear boundaries could be explained in theory. Based on the certification, boundary nonlinearities are discussed in detail analytically and found to play an important role in responses. Because of the important role played by the nonlinear factors in the vibration and control of the flexible structure, this paper will open the vibration analysis and numerical study of the flexible structure with nonlinear constraints.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2017;84(11):111007-111007-7. doi:10.1115/1.4037884.

The immobilization of receptor–ligand molecules in dynamic force spectroscopy (DFS) often relies on an extra noncovalent linkage to solid surfaces, resulting in two barrier-crossing diffusion processes in series and concurrent bond dissociations. One outstanding theoretical issue is whether the linkage between the immobilizer and biomolecule is sufficiently strong during repeated force ramping in the measurements and how it might influence the interpretation on receptor–ligand kinetics. Following the classical framework by Kramers, we regard each dissociation process as a flux of probabilistic bond configuration outward over an energy barrier in the coordinated energy landscape, and solve the two coupled boundary value problems in the form of Smoluchowski equation. Strong kinetic and mechanical coupling is observed between the two molecular bonds in series, with the results showing that involving a noncovalent linkage in DFS can obscure the unbinding characteristics of the receptor–ligand bond. Our approach provides a quantitative assessment to the hidden effects of having a fragile molecular anchorage in DFS and allows the corrected interpretation on receptor–ligand dissociation kinetics in the case.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2017;84(11):111008-111008-17. doi:10.1115/1.4037880.

Rocks underground often have pores and bedding planes, which are appropriate to be described by the transversely isotropic poroelastic constitutive model. Drilling boreholes in these rocks must be careful, since stresses and pore pressure would change with time, because of the inherent time dependent property of poroelasticity as well as pore fluid diffusion. In order to correlate the behavior of transversely isotropic poroelastic model of borehole in plane strain with the behavior of isotropic poroelastic model, an equivalent isotropic material is built with carefully chosen material constants, and correlation rules are successfully developed. With the solutions for the borehole problem in an isotropic model obtained previously, the solutions to transversely isotropic model can be obtained. Two cases of tensile failure and six cases of shear failure for the borehole are considered. As a result, the allowable borehole working pressure range is formulated by explicit expressions. The failure case, time, and location could also be obtained for any given drilling pressure. Results obtained from the Hooke’s traditional elastic model are compared, and it is found that poroelastic model is necessary in borehole safety check, while Hooke’s model is not on the safe side.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2017;84(11):111009-111009-7. doi:10.1115/1.4037882.

Volume conservation during plastic deformation is the most important feature and should be realized in elastoplastic theories. However, it is found in this paper that an elastoplastic theory is not volume conserved if it improperly sets an arbitrary plastic strain rate tensor to be deviatoric. We discuss how to rigorously realize volume conservation in finite strain regime, especially when the unloading stress free configuration is not adopted in the elastoplastic theories. An accurate condition of volume conservation is first clarified and used in this paper that the density of a volume element after the applied loads are completely removed should be identical to that of the initial stress free states. For the elastoplastic theories that adopt the unloading stress free configuration (i.e., the intermediate configuration), the accurate condition of volume conservation is satisfied only if specific definitions of the plastic strain rate are used among many other different definitions. For the elastoplastic theories that do not adopt the unloading stress free configuration, it is even more difficult to realize volume conservation as the information of the stress free configuration lacks. To find a universal approach of realizing volume conservation for elastoplastic theories whether or not adopt the unloading stress free configuration, we propose a single assumption that the density of material only depends on the trace of the Cauchy stress by using their objectivities. Two strategies are further discussed to satisfy the accurate condition of volume conservation: directly and slightly revising the tangential stiffness tensor or using a properly chosen stress/strain measure and elastic compliance tensor. They are implemented into existing elastoplastic theories, and the volume conservation is demonstrated by both theoretical proof and numerical examples. The potential application of the proposed theories is a better simulation of manufacture process such as metal forming.

Topics: Deformation , Stress , Tensors
Commentary by Dr. Valentin Fuster

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