Finite element modeling of micropolar-based phononic crystals

The performance of a Cosserat/micropolar solid as a numerical vehicle to represent dispersive media is explored. The study is conducted using the finite element method with emphasis on Hermiticity, positive definiteness, principle of virtual work and Bloch–Floquet boundary conditions. The periodic boundary conditions are given for both translational and rotational degrees of freedom and for the associated force- and couple-traction vectors. Results in terms of band structures for different material cells and mechanical parameters are provided.     

Effects of thinner on RTV silicone rubber nanocomposites reinforced with GR and CNTs

The effects of thinner on rubber specimens with carbon nanotubes (CNTs) and graphitic nanofillers (GR) was studied for robotics applications. Rubber specimens were prepared by dispersing GR, CNTs and thinner in room temperature vulcanized (RTV) silicone rubber through solution mixing. Microscopic studies have confirmed occurrence of swelling in polymer chains due to migration of thinner. It results an increase in topological depth from 40 nm (no thinner) to 120 nm (40 phr of thinner). An elastic modulus of ~4.4 MPa (without thinner) was higher than 2.8 MPa (10 phr of thinner). At 100% strain, the lower dissipation losses of 110% (without thinner) and 70% (40 phr of thinner) were obtained. The resistance increases from 4.6 kΩ (without thinner) to 5.7 kΩ (10 phr of thinner). At 0.4‐mm‐thick elastomer slab, an actuation displacement of 0.81 mm (without thinner) was obtained which increased to 1.1 mm (60 phr of thinner). Thus, the thinner can be useful for easier processing, controlled stiffness, minimizing dissipation losses, increasing the actuation displacement and decreasing the cost of the device. Copyright © 2017 John Wiley & Sons, Ltd.     

On the efficient utilisation of duration

In this article we present a new approach to estimate the change of the present value of a given cashflow pattern caused by an interest rate shift. Our approximation is based on analysing the evolution of the present value function through a linear differential equation. The outcome is far more accurate than the standard approach achieved by a Taylor expansion. Furthermore, we derive an approximation formula of second order that produces nearly accurate results. In particular, we prove that our method is superior to any known alternative approximation formula based on duration. In order to demonstrate the power of this improved approximation we apply it to coupon bonds, level annuities, and level perpetuities. We finally generalise the approach to a non-flat term structure. As for applications in insurance, we estimate the change of the discounted value of future liabilities due to a proportional shift in the set of capital accumulation factors. These findings are of particular importance to capital adequacy calculations with respect to interest rate stress scenarios that are part of regulatory solvency requirements.     

Neutral nano-inhomogeneities in hyperelastic materials with a hyperelastic interface model

We examine the existence of neutral nano-inhomogeneities in a hyperelastic inhomogeneity-matrix system subjected to finite plane deformations when uniform (in-plane) external loading is imposed on the matrix. We incorporate nanoscale interface effects by representing the material interface as a separate hyperelastic membrane, perfectly bonded to the surrounding bulk material. We show that for any type of hyperelastic bulk material and practically any type of hyperelastic membrane representing the interface, neutral nano-inhomogeneities do exist but are necessarily circular in shape. We show further that the radius of the circular neutral nano-inhomogeneity is determined by the (uniform) external loading (which must be hydrostatic) and the respective strain energy density functions associated with the hyperelastic bulk and interface materials.     

Solution for Eshelby’s elliptic inclusion with polynomials distribution of the eigenstrains in plane elasticity

This paper provides a closed form solution for the Eshelby’s elliptic inclusion in plane elasticity with the polynomials distribution of the eigenstrains. The complex variable method and the conformal mapping technique are used. The continuity conditions for the traction and displacement along the interface in the physical plane are reduced to a similar condition along the unit circle of the mapping plane. From those continuity conditions, we can obtain two sets of the complex potentials for the region outside of the unit circle and for the ring region, respectively. Further, we can obtain the complex potentials in the physical plane, or z-plane (z = x + iy). The mapping function maps the ring region in the mapping plane into a finite elliptic region with a crack on the real axis in the physical plane. An exact form for the complex potentials defined in the ring region is studied and proposed. In addition, the stress distribution on the inclusion is evaluated. Those results are first obtained in the paper.     

Soliton-like solutions based on geometrically nonlinear Cosserat micropolar elasticity

The Cosserat model generalises an elastic material taking into account the possible microstructure of the elements of the material continuum. In particular, within the Cosserat model the structured material point is rigid and can only experience microrotations, which is also known as micropolar elasticity. We present the geometrically nonlinear theory taking into account all possible interaction terms between the elastic and microelastic structures. This is achieved by considering the irreducible pieces of the deformation gradient and of the dislocation curvature tensor. In addition we also consider the so-called Cosserat coupling term. In this setting we seek soliton type solutions assuming small elastic displacements, however, we allow the material points to experience full rotations which are not assumed to be small. By choosing a particular ansatz we are able to reduce the system of equations to a sine–Gordon type equation which is known to have soliton solutions.     

Peroxide‐initiated chemical modification of poly(isobutylene‐co‐isoprene): H‐atom transfer yields and regioselectivity

The yield and regioselectivity of H‐atom abstraction by cumyloxy radicals from poly(isobutylene‐co‐isoprene) (IIR) are quantified and discussed in the context of cross‐linking/degradation outcomes and vinyltriethoxysilane (VTEOS) graft yields. Studies of IIR materials with different isoprene contents show that H‐atom abstraction from the allylic functionality provided by isoprene mers is responsible for the heightened H‐atom transfer reactivity of IIR relative to poly(isobutylene). Differences in the reactivity of allylic and alkyl macroradical intermediates makes high isoprene IIR materials less prone to peroxide‐initiated chain scission, but less responsive to VTEOS grafting formulations. Improved knowledge of H‐atom transfer reactivity is extended to a new approach for IIR cross‐linking involving acrylate‐functionalized nitroxyl chemistry. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2016 , 54, 3102–3109     

Decay rates in nano tubes with consideration of surface elasticity

In the present paper we examine the Saint-Venant end effect in the nano tubes via a continuum mechanics with consideration of surface elasticity. The Saint-Venant end effect is quantitatively described by the decay rate. By analytically solving an axial-symmetric torsion in a circular cross-section tube configuration, we demonstrate that the decay rate decreases as the radius of the nano wire/tube decreases with consideration of the surface effect.     

Influences of different dimensional carbon-based nanofillers on fracture and fatigue resistance of natural rubber composites

The dimensions of reinforcing filler is a key factor in influencing the fracture and fatigue of rubbers. Here, the fracture and fatigue resistance of natural rubber (NR) filled with different dimensional carbon-based fillers including zero-dimensional spherical carbon black (CB), one-dimensional fibrous carbon nanotubes (CNTs) and two-dimensional planar graphene oxide (GO) were explored. To obtain equal hardness, a control indicator in the rubber industry, the amounts of CB, CNTs, and GO were 10.7 vol%, 1.2 vol%, and 1.6 vol%, respectively. J-integral and dynamic fatigue tests revealed that NR filled with CB exhibited the best quasi-static fracture resistance and dynamic crack growth resistance. The much higher hysteresis loss of NR filled with CNTs weakened its fatigue resistance. The planar GO played a limited role in preventing crack growth. Furthermore, digital image correlation revealed that NR filled with CB had the highest strain amplification level and area at the crack tip, which dissipated the most local input energy and then improved the fracture and fatigue performance.     

On Bifurcations of Equilibria of Intrinsically Curved, Electrically Charged, Rod-like Structures that Model DNA Molecules in Solution

DNA molecules in the familiar Watson–Crick double helical B form can be treated as though they have rod-like structures obtained by stacking dominoes one on top of another with each rotated by approximately one-tenth of a full turn with respect to its immediate predecessor in the stack. These “dominoes” are called base pairs. A recently developed theory of sequence-dependent DNA elasticity (Coleman, Olson, & Swigon, J. Chem. Phys. 118:7127–7140, 2003) takes into account the observation that the step from one base pair to the next can be one of several distinct types, each having its own mechanical properties that depend on the nucleotide composition of the step. In the present paper, which is based on that theory, emphasis is placed on the fact that, as each base in a base pair is attached to the sugar-phosphate backbone chain of one of the two DNA strands that have come together to form the Watson–Crick structure, and each phosphate group in a backbone chain bears one electronic charge, two such charges are associated with each base pair, which implies that each base pair is subject to not only the elastic forces and moments exerted on it by its neighboring base pairs but also to long range electrostatic forces that, because they are only partially screened out by positively charged counter ions, can render the molecule’s equilibrium configurations sensitive to changes in the concentration c of salt in the medium. When these electrostatic forces are taken into account, the equations of mechanical equilibrium for a DNA molecule with N + 1 base pairs are a system of μN non-linear equations, where μ, the number of kinematical variables describing the relative displacement and orientation of adjacent pairs is in general 6; it reduces to 3 when base-pair steps are assumed to be inextensible and non-shearable. As a consequence of the long-range electrostatic interactions of base pairs, the μN × μN Jacobian matrix of the equations of equilibrium is full. An efficient numerically stable computational scheme is here presented for solving those equations and determining the mechanical stability of the calculated equilibrium configurations. That scheme is employed to compute and analyze bifurcation diagrams in which c is the bifurcation parameter and to show that, for an intrinsically curved molecule, small changes in c can have a strong effect on stable equilibrium configurations. Cases are presented in which several stable configurations occur at a single value of c.