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IN THIS ISSUE

### Research Papers

J. Appl. Mech. 2016;83(5):051001-051001-13. doi:10.1115/1.4032572.

Kaleidocycles are continuously rotating n-jointed linkages. We consider a certain class of six-jointed kaleidocycles which have a spring at each joint. For this class of kaleidocycles, stored energy varies throughout the rotation process in a nonconstant, cyclic pattern. The purpose of this paper is to model and provide an analysis of the stored energy of a kaleidocycle throughout its motion. In particular, we will solve analytically for the number of stable equilibrium states for any kaleidocycle in this class.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2016;83(5):051002-051002-9. doi:10.1115/1.4032549.

Static and dynamic responses of a circular cylindrical shell made of hyperelastic arterial material are studied. The material is modeled as a combination of Neo-Hookean and Fung materials. Two types of pressure loads are studied—distributed radial forces and deformation-dependent pressure. The static responses of the shell under these two loads differ essentially at moderate strains, while the behavior is similar for small loads. The principal difference is that the axial displacements are much larger for the shell under distributed radial forces, while for actual pressure the shell is stretched both in circumferential and axial directions. Free and forced vibrations around preloaded configurations are analyzed. In both cases, the nonlinearity of the single-mode (driven mode) response of the preloaded shell is quite weak, but a resonant regime with both driven and companion modes active has been found with more complicated nonlinear dynamics.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2016;83(5):051003-051003-9. doi:10.1115/1.4032500.

We investigate continuous axial rotation as a mechanism for extending the reach of an elastic rod injected into a horizontal cylindrical constraint, prior to the onset of helical buckling. Our approach focuses on the development of precision desktop experiments to allow for a systematic investigation of three parameters that affect helical buckling: rod rotation speed, rod injection speed, and cylindrical constraint diameter. Within the parameter region explored, we found that the presence of axial rotation increases horizontal reach by as much as a factor of 5, when compared to the nonrotating case. In addition, we develop an experimentally validated theory that takes into account anisotropic friction and torsional effects. Our theoretical predictions are found to be in good agreement with experiments, and our results demonstrate the benefits of using axial rotation for extending reach of a rod injected into a constraining pipe.

Topics: Rotation , Friction , Buckling
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2016;83(5):051004-051004-5. doi:10.1115/1.4032691.

The diffraction of elastic harmonic waves by a finite plane tunnel crack is studied. A solution is derived from an analysis of the integral equations describing the problem, using the Wiener–Hopf technique and the method of compound asymptotic expansions. Taking into account the successive reflections of Rayleigh waves from crack tips, an approximate analytical solution is expressed in a closed-form that is computationally effective and yields accurate results in the resonance region of dimensionless wave numbers. Both direct and inverse scattering problems are considered.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2016;83(5):051005-051005-7. doi:10.1115/1.4032692.

This paper presents a new crack band model (CBM) for probabilistic analysis of quasibrittle fracture. The model is anchored by a probabilistic treatment of damage initiation, localization, and propagation. This model regularizes the energy dissipation of a single material element for the transition between damage initiation and localization. Meanwhile, the model also takes into account the probabilistic onset of damage localization inside the finite element (FE) for the case where the element size is larger than the crack band width. The random location of the localization band is related to the random material strength, whose statistics is described by a finite weakest link model. The present model is applied to simulate the probability distributions of the nominal strength of different quasibrittle structures. It is shown that for quasibrittle structures direct application of the conventional CBM for stochastic FE simulations would lead to mesh-sensitive results. To mitigate such mesh dependence, it is essential to incorporate the strain localization mechanism into the formulation of the sampling distribution functions of material constitutive parameters.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2016;83(5):051006-051006-9. doi:10.1115/1.4032690.

Failure in elastic dual-phase materials under transverse tension is studied numerically. Cohesive zones represent failure along the interface and the augmented finite element method (A-FEM) is used for matrix cracking. Matrix cracks are formed at an angle of $55 deg−60 deg$ relative to the loading direction, which is in good agreement with experiments. Matrix cracks initiate at the tip of the debond, and for equi-biaxial loading cracks are formed at both tips. For elliptical reinforcement the matrix cracks initiate at the narrow end of the ellipse. The load carrying capacity is highest for ligaments in the loading direction greater than that of the transverse direction.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2016;83(5):051007-051007-7. doi:10.1115/1.4032795.

The Euler–Lagrange equations and the associated boundary conditions have been derived for an inextensible beam undergoing large deflections. The inextensibility constraint between axial and transverse deflection is considered via two alternative approaches based upon Hamilton's principle, which have been proved to yield equivalent results. In one approach, the constraint has been appended to the system Lagrangian via a Lagrange multiplier, while in the other approach the axial deflection has been expressed in terms of the transverse deflection, and the equation of motion for the transverse deflection has been determined directly. Boundary conditions for a cantilevered beam and a free–free beam have been considered and allow for explicit results for each system's equations of motion. Finally, the Lagrange multiplier approach has been extended to equations of motion of cantilevered and free–free plates.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2016;83(5):051008-051008-6. doi:10.1115/1.4032796.

Using the location-dependent growth strain, a chemomechanical model is developed for the analysis of the stress evolution and distribution in the viscoplastic oxide scale during high-temperature oxidation. The problem of oxidizing a semi-infinite substrate is formulated and solved. The numerical results reveal high compressive stress and significant stress gradient. The maximum stress is at the oxide/substrate interface and the minimum stress at the oxygen/oxide interface in short oxidation time, while the maximum stress is no longer at the oxide/substrate interface in long oxidation time. The stress evolutions at different locations are also presented. The predicted results agree well with the experimental data.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2016;83(5):051009-051009-9. doi:10.1115/1.4032861.

One of the most crucial functionalities of load-bearing biological materials such as shell and bone is to protect their interior organs from damage and fracture arising from external dynamic impacts. However, how this class of materials effectively damp stress waves traveling through their structure is still largely unknown. With a self-similar hierarchical model, a theoretical approach was established to investigate the damping properties of load-bearing biological materials in relation to the biopolymer viscous characteristics, the loading frequency, the geometrical parameters of reinforcements, as well as the hierarchy number. It was found that the damping behavior originates from the viscous characteristics of the organic (biopolymer) constituents and is greatly tuned and enhanced by the staggered and hierarchical organization of the organic and inorganic constituents. For verification purpose, numerical experiments via finite-element method (FEM) have also been conducted and shown results consistent with the theoretical predictions. Furthermore, the results suggest that for the self-similar hierarchical design, there is an optimal aspect ratio of reinforcements for a specific loading frequency and a peak loading frequency for a specific aspect ratio of reinforcements, at which the damping capacity of the composite is maximized. Our findings not only add valuable insights into the stress wave damping mechanisms of load-bearing biological materials, but also provide useful guidelines for designing bioinspired synthetic composites for protective applications.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2016;83(5):051010-051010-5. doi:10.1115/1.4032766.

A family of analytic solutions for the prediction of interlaminar stresses in angle-ply laminates has been developed and is presented in a unified form and as a unique set of solutions. The uniqueness of the formulation is demonstrated for the class of thermomechanical states of deformation for which the solutions are valid. These are shown to be limited to the specific cases wherein only two in-plane stress components and one interlaminar stress components are nonzero. Interlaminar shear stress in the angle-ply laminate subjected to thermomechanical loading conditions of uniaxial extension, uniform temperature change, and anticlastic bending is shown to make up the family of solutions in the unified formulation. Further, these are shown to comprise the complete set of the solutions and the conditions which control the limitations of this family of solutions are articulated.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2016;83(5):051011-051011-7. doi:10.1115/1.4032860.

Quantifying interactions between motors and filaments is important for the understanding of intriguing emergent behaviors of motor–filament systems, which play critical roles in various biological processes. Recently, unusually high detachment rates of a myosin from actin were obtained with a force spectroscopy technique of an unprecedented spatial–temporal resolution. Here, we suggest that these high apparent detachment rates may be due to the inherent coupling between bond breaking and state transition, which can be common in protein–protein interactions. Based on a kinetic model for the chemomechanical cycle of single myosin, rates of bond breaking between myosin and actin at different nucleotide states are systematically calculated. These quantitative results indicate that myosins may adopt much higher transition rates than bond breaking rates at different nucleotide states under physiological conditions when applied forces are relatively low. This work also indicates that accurate biophysical models considering both protein unbinding dynamics and protein state transitions are required in order to properly interpret the experimental data when the ultrafast force-clamp spectroscopy technique is employed to study, for example, the DNA–protein interactions.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2016;83(5):051012-051012-7. doi:10.1115/1.4032857.

Curvature is simply expressed as the second derivative of the plate deflection in prior studies of post-buckling of plates. It is shown in this paper that the higher-order terms in curvature should be retained, consistent with Koiter's post-buckling theory. This paper also solves the dilemma whether the increase of post-buckling load is proportional to the square of the ratio of the post-buckling deflection w to the plate thickness t, $(w/t)2$, as in most prior studies, or to the characteristic in-plane length L of the plate, $(w/L)2$, as discovered in some recent studies.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2016;83(5):051013-051013-7. doi:10.1115/1.4032858.

Tensile stability of healthy medial arterial tissue and its constituents, subject to initial geometrical and/or material imperfections, is investigated based on the long wavelength approximation. The study employs existing constitutive models for elastin, collagen, and vascular smooth muscle which comprise the medial layer of large elastic (conducting) arteries. A composite constitutive model is presented based on the concept of the musculoelastic fascicle (MEF) which is taken to be the essential building block of medial arterial tissue. Nonlinear equations governing axial stretch and areal stretch imperfection growth quantities are obtained and solved numerically. Exact, closed-form results are presented for both initial and terminal rates of imperfection growth with nominal load. The results reveal that geometrical imperfections, in the form of area nonuniformities, and material imperfections, in the form of constitutive parameter nonuniformities, either decrease or increase only slightly with increasing nominal load; a result which is to be expected for healthy tissue. By way of contrast, an examination of a simple model for elastin with a degrading stiffness gives rise to unbounded imperfection growth rates at finite values of nominal load. The latter result indicates how initial geometrical and material imperfections in diseased tissues might behave, a topic of future study by the authors.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2016;83(5):051014-051014-8. doi:10.1115/1.4032907.

It has been recognized that cells are able to actively sense and respond to the mechanical signals through an orchestration of many subcellular processes, such as cytoskeleton remodeling, nucleus reorientation, and polarization. However, the underlying mechanisms that regulate these behaviors are largely elusive; in particular, the quantitative understanding of these mechanical responses is lacking. In this study, combining experimental measurement and theoretical modeling, we studied the effects of rigidity and pattern geometry of substrate on collective cell behaviors. We showed that the mechanical force took pivotal roles in regulating the alignment and polarization of cells and subcellular structures. The cell, cytoskeleton, and nucleus preferred to align and polarize along the direction of maximum principal stress in cell monolayer, and the driving force is the in-plane maximum shear stress. The higher the maximum shear stress, the more the cells and their subcellular structures preferred to align and polarize along the direction of maximum principal stress. In addition, we proved that in response to the change of in-plane shear stresses, the actin cytoskeleton is more sensitive than the nucleus. This work provides important insights into the mechanisms of cellular and subcellular responses to mechanical signals. And it also suggests that the mechanical force does matter in cell behaviors, and quantitative studies through mechanical modeling are indispensable in biomedical and tissue engineering applications.

Commentary by Dr. Valentin Fuster

### Technical Brief

J. Appl. Mech. 2016;83(5):054501-054501-4. doi:10.1115/1.4032856.

A variationally consistent approach to constrained rigid-body motion is presented that extends D'Alembert's principle in a way that has a form similar to Kane's equations. The method results in minimal equations of motion for both holonomic and nonholonomic systems without a priori consideration of preferential coordinates.

Commentary by Dr. Valentin Fuster