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Research Papers

J. Appl. Mech. 2018;85(11):111001-111001-11. doi:10.1115/1.4040646.

Nature has a proven track record of advanced materials with outstanding mechanical properties, which has been the focus of recent research. A well-known trade-off between ultimate strength and toughness is one of the main challenges in materials design. Progress has been made by mimicking tough biological fibers by applying the concepts of (1) sacrificial bond and (2) hidden length, providing a so-called “safety-belt” for biological materials. Prior studies indicate a relatively common behavior across scales, from nano- to macro-, suggesting the potential of a generalized theoretical mechanistic framework. Here, we undertake molecular dynamics (MD) based simulation to investigate the mechanical properties of model nanoscale fibers. We explore representative models of serial looped or coiled fibers with different parameters—specifically number of loops, loop radii, cross-link strength, and fiber stiffness—to objectively compare strength, extensibility, and fiber toughness gain. Observing consistent saw-tooth like behavior, and adapting worm-like chain (WLC) mechanics (i.e., pseudo-entropic elasticity), a theoretical scaling relation which can describe the fiber toughness gain as a function of the structural factors is developed and validated by simulation. The theoretical model fits well with the simulation results, indicating that engineering the mechanical response based on controlled structure is possible. The work lays the foundation for the design of uniaxial metamaterials with tunable and predictable tensile behavior and superior toughness.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2018;85(11):111002-111002-6. doi:10.1115/1.4040696.

The sensitivity of crack growth resistance to the choice of isotropic or kinematic hardening is investigated. Monotonic mode I crack advance under small scale yielding conditions is modeled via a cohesive zone formulation endowed with a traction–separation law. R-curves are computed for materials that exhibit linear or power law hardening. Kinematic hardening leads to an enhanced crack growth resistance relative to isotropic hardening. Moreover, kinematic hardening requires greater crack extension to achieve the steady-state. These differences are traced to the nonproportional loading of material elements near the crack tip as the crack advances. The sensitivity of the R-curve to the cohesive zone properties and to the level of material strain hardening is explored for both isotropic and kinematic hardening.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2018;85(11):111003-111003-9. doi:10.1115/1.4040694.

This paper presents a detailed study on the fracture behaviors of soft materials with hard inclusion. Stress concentrations on the interfaces of hard and soft materials are considered as the key factor for structure fracture. Based on linear fracture theory, the fracture behaviors of soft materials with elliptical hard inclusion are investigated. Stress concentrations, consisting of tensile, hoop, and compressive stress, are observed with changes of inclusion geometries and the modulus ratio of hard and soft materials. And their influences on the categories of principal stress concentration are shown in a phase diagram in the current paper. Finite element analysis is carried out with consideration of the large deformation of soft material, which demonstrates the effectiveness of the theoretical predictions in a great scope of applied loading. Finally, the predictions based on theoretical and simulation results are validated by experiments. This work points out that the hard line inclusion is the source of danger in soft materials just like the crack in brittle materials.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2018;85(11):111004-111004-7. doi:10.1115/1.4040693.

Nonlinear dynamics and mode aberration of rotating plates and shells are discussed in this work. The mathematical formalism is based on the one-dimensional (1D) Carrera unified formulation (CUF), which enables to express the governing equations and related finite element arrays as independent of the theory approximation order. As a consequence, three-dimensional (3D) solutions accounting for couplings due to geometry, material, and inertia can be included with ease and with low computational costs. Geometric nonlinearities are incorporated in a total Lagrangian scenario and the full Green-Lagrange strains are employed to outline accurately the equilibrium path of structures subjected to inertia, centrifugal forces, and Coriolis effect. A number of representative numerical examples are discussed, including multisection blades and shells with different radii of curvature. Particular attention is focused on the capabilities of the present formulation to deal with nonlinear effects, and comparison with s simpler linearized approach shows evident differences, particularly in the case of deep shells.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2018;85(11):111005-111005-6. doi:10.1115/1.4040777.

In this paper, an acoustomechanical constitutive model is developed to describe the heating effect of a tissue-mimicking gel by cavitation in exposure to high-intensity focused ultrasound (HIFU). An internal variable, representing the evolution of cavitation process, is introduced into the Helmholtz free energy under the framework of thermodynamics that combines the acoustic radiation stress theory and the nonlinear elasticity theory together. Thus, the internal variable is related to the cavitation process and the mechanical energy dissipation of a tissue-mimicking gel from a macroscopic viewpoint. Since the temperature rise of cavitation phenomenon is more remarkable than that of heating waves, the temperature inside the tissue-mimicking gel rises rapidly mainly due to large amounts of cavitation bubbles. This phenomenon can be quantitatively described by the present model, which fits the existing experimental data well.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2018;85(11):111006-111006-13. doi:10.1115/1.4040890.

The linear theory of dual-porosity and dual-permeability poro-chemo-electro-elasticity is presented. The theory outlines the dual-continuum formulation of multiple coupled processes involving solid deformation, pore fluid flow, and electrically charged species transport, within and in between two coexisting porosity systems of a fluid-saturated, poro-elastic medium. The described formulation is used to derive the analytical solutions to the inclined wellbore problem and axisymmetric Mandel-Type problem of dual-porosity, dual-permeability poro-chemo-electro-elasticity. The effects of chemical and electrical potentials on the distributions of stress and pore pressure are demonstrated by numerical examples pertaining to the considered problems. It is shown that the fully coupled nature of the solutions rigorously captures the seemingly anomalous time variations of the effective stress as driven by the pore fluid pressure disturbances, as well as the distribution and movement of anions/cations within the dual-porosity porous medium. The existing subset of published solutions on the subject is successfully reproduced as special cases of the solutions presented in this paper.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2018;85(11):111007-111007-11. doi:10.1115/1.4040948.

This study investigates the significance of fluid–structure interaction (FSI) effects on structural response to pressure wave and shock wave loading. Finite element (FE) simulations and one-dimensional (1D) analytical models are used to compare the responses of simple structures in presence and absence of FSI. Results are provided in nondimensional form and allow rapid estimation of the significance of FSI. The cases of a square elastic plate in bending and a square rigid-perfectly plastic plate undergoing membrane stretching are discussed in detail. We deduce simple formulae to identify scenarios in which effects of FSI can be neglected.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2018;85(11):111008-111008-13. doi:10.1115/1.4040949.

Two novel nonparametric identification approaches are proposed for piezoelectric mechanical systems. The novelty of the approaches is using not only mechanical signals but also electric signals. The expressions for unknown mechanical and electric terms are given based on the Hilbert transform. The signals are decomposed and re-assembled to obtain smooth stiffness and damping curves. The current mapping approach is developed to identify accurately a piezoelectric mechanical system with strongly nonlinear electric terms. The developed identification approaches are successfully implemented to simulate signals obtained from different nonlinear piezoelectric mechanical systems, including Duffing nonlinearity, softening and hardening nonlinearity, and Duffing nonlinearity with strong nonlinear electric terms. The proposed approaches are successfully applied to experimental signals of a circular laminated plate device in order to identify the nonlinear stiffness functions, damping functions, electromechanical coupling functions, and equivalent capacitance functions. The results show both softening and hardening nonlinearity in the stiffness characteristic and weak nonlinearity in electric characteristics. The results of the Hilbert transform based approach and the current mapping approach are compared, and the outcomes show good agreements.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2018;85(11):111009-111009-8. doi:10.1115/1.4041039.

This paper presents a method to achieve high deformability levels in dielectric elastomer actuators (DEAs) by applying a modulated voltage waveform. The method relies on supplying the electrostatic energy during the specific phase of the oscillation cycle, resulting in the enhanced travel range at a relatively low driving voltage. We consider a standard sandwich configuration of the DE actuator with neo-Hookean material model and outline an energy-based approach for delineating the underlying principles of the proposed method. A comparison of the deformability levels achieved using the quasi-static, Heaviside step, and the modulated input waveforms is presented. Significant reduction in instability voltages together with a considerable increase in the stable actuation limit is observed in the case of the modulated voltage input. The estimates of the stability thresholds are validated by integrating the equation of motion obtained using Hamilton's principle. The effect of energy dissipation is assessed by considering variations in the quality factor. Further, a qualitative comparison with experimental observations is presented highlighting the practical feasibility of the method. This investigation can find its potential use in the design and development of DEAs subjected to a time-dependent motion.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2018;85(11):111010-111010-10. doi:10.1115/1.4040405.

Dielectric elastomer (DE) is a promising electroactive polymer. As DE material, rubbers are often filled with functional particles to improve their electromechanical performance. However, the filled particles also bring stress softening, which is known as Mullins effect. In this paper, we prepared the carbon nanotube filled silicone elastomer (SE) as DE composite and modeled its Mullins effect using the pseudo-elastic theory. Then, the thermodynamics of DE was combined to predict the idealized electromechanical softening behavior. Two cases are considered: linear dielectric and saturated dielectric. For linear dielectric with an initial force, “residual strain” will appear after every voltage-controlled cycle, and instability may be eliminated in reloading. For saturated dielectric, the material response changes a lot after saturation, which also affects the subsequent softening behavior. At last, viscoelasticity was further incorporated to account for rate-dependent softening deformation, and we also carried out some simple electromechanical experiments on VHB 4910 to explore its softening behavior. This work may lead to a better understanding of the softening behavior in DEs undergoing electromechanical coupling situations.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2018;85(11):111011-111011-15. doi:10.1115/1.4041040.

Based on a linear poroelastic formulation, we present an asymptotic analysis of the transient crack-tip fields for stationary cracks in polymer gels under plane-strain conditions. A center crack model is studied in detail, comparing numerical results by a finite element method to the asymptotic analysis. The time evolution of the crack-tip parameters is determined as a result of solvent diffusion coupled with elastic deformation of the gel. The short-time and long-time limits are obtained for the stress intensity factor and the crack-tip energy release rate under different chemo-mechanical boundary conditions (immersed versus not-immersed, displacement versus load controlled). It is found that, under displacement-controlled loading, the crack-tip energy release rate increases monotonically over time for the not-immersed case, but for the immersed case, it increases first and then decreases, with a long-time limit lower than the short-time limit. Under load control, the energy release rate increases over time for both immersed and not-immersed cases, with different short-time limits but the same long-time limit. These results suggest that onset of crack growth may be delayed until the crack-tip energy release rate reaches a critical value if the applied displacement or traction is subcritical but greater than a threshold.

Commentary by Dr. Valentin Fuster

Technical Brief

J. Appl. Mech. 2018;85(11):114501-114501-5. doi:10.1115/1.4040695.

An analytical model is derived for the delamination of a thin film from a rigid substrate by a cylindrical shaft with a flat end and finite radius. We show that, within certain limitations, a point-load model can be applied to the system, to give simple relations between the film-substrate energy of adhesion and the measured variables of applied shaft force, blister height, and blister radius. The results are applicable to systems where a finite size cylindrical shaft or disk generates delamination of the film from the substrate.

Commentary by Dr. Valentin Fuster

Discussion

J. Appl. Mech. 2018;85(11):115501-115501-1. doi:10.1115/1.4040950.

The authors have dealt with a problem that is quite common when nonconformal rough surfaces come into contact [1]. They state “To our best knowledge, however, no attempt has been reported to solve the contact problem with positive overlap between two rough particles.” This discussion is aimed at highlighting that such work does exist and provide additional insight. Specifically, Ref. [2] deals with two contacting rough surfaces, one flat and the other hemispherical (similar to the case herein). But the work in Ref. [2] deals with real surfaces having the complication that both contain nonhomogeneous and anisotropic roughness properties. A procedure is given [2] where these properties had been reduced to parameters (spectral moments) that the GW model needs. It should be noted that what the authors call “GW, E-GW, and EP-GW” cases, are seamlessly handled in Ref. [2] without resorting to labeling, because the three regimes of elastic, elastic–plastic, and fully plastic are inherently imbedded in the JG model [32,43]. Because Ref. [2] uses the commonly known models of GW and JG, no new numerical procedures (such as “DEM”) are needed. It just takes a thought process to fuse the said models for nonconformal rough surfaces, combining them in straightforward procedure outlined in Ref. [2]. Two cases are examined in Ref. [2]: a small load (0.1 N), and a high load (8 N) that puts the two cases in the elastic–plastic, and fully plastic regimes, respectively. The results are qualitatively similar to what appears herein but unfortunately, this paper does not provide sufficient information on the surface roughness properties (asperity density, radius of asperities, etc.) or spectral moments for quantitative comparisons to be made.

Commentary by Dr. Valentin Fuster

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