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Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences RSS feed -- current issue1471-2946August, 2018Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences1364-5021<![CDATA[Interfacial load transfer mechanisms in carbon nanotube-polymer nanocomposites]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/474/2216/20170705?rss=1
Carbon nanotubes (CNTs) are highly promising for strength reinforcement in polymer nanocomposites, but conflicting interfacial properties have been reported by single nanotube pull-out experiments. Here, we report the interfacial load transfer mechanisms during pull-out of CNTs from PMMA matrices, using massively- parallel molecular dynamics simulations. We show that the pull-out forces associated with non-bonded interactions between CNT and PMMA are generally small, and are weakly-dependent on the embedment length of the nanotube. These pull-out forces do not significantly increase with the presence of Stone Wales or vacancy defects along the nanotube. In contrast, low-density distribution of cross-links along the CNT-PMMA interface increases the pull-out forces by an order of magnitude. At each cross-linked site, mechanical unfolding and pull-out of single or pair polymer chain(s) attached to the individual cross-link bonds result in substantial interfacial strengthening and toughening, while contributing to interfacial slip between CNT and PMMA. Our interfacial shear-slip model shows that the interfacial loads are evenly-distributed among the finite number of cross-link bonds at low cross-link densities or for nanotubes with short embedment lengths. At higher cross-link densities or for nanotubes with longer embedment lengths, a no-slip zone now develops where shear-lag effects become important. Implications of these results, in the context of recent nanotube pull-out experiments, are discussed.
]]>2018-08-08T00:05:15-07:00info:doi/10.1098/rspa.2017.0705hwp:master-id:royprsa;rspa.2017.07052018-08-08Research articles47422162017070520170705<![CDATA[Radon signals in geological (natural) geogas and in a simultaneous enhanced confined mode simulation experiment]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/474/2216/20170787?rss=1
An enhanced confined mode (ECM) radon simulation experiment, tested in the laboratory in Jerusalem, was relocated to a subsurface geophysical observatory located 400 km apart, at a depth of 150 m and with a stable temperature. Five gamma sensors are placed around the ECM canister and lead shielding minimizes the influence of natural local gamma radiation. Simultaneous measurement of the geological radon and from radon in the ECM system indicates that the temporal variation of gamma radiation from radon in the ECM system contains annual, multi-day and daily signals, that correspond to signals in the local geological radon. This implies that a common external driver influences the radiation pattern of the geological radon and from radon inside the ECM canister. Once activated at BGO the typical variation pattern of the experimental system occurring in the laboratory changed to that occurring at the observatory. This is interpreted to indicate that the overall style of the temporal patterns of radiation from radon is site dependent. The outcome of this investigation conforms and further substantiates the recent suggestion that a component in solar radiation is driving the annual and daily periodic components in the variation of radon. New geophysical research potential is indicated.
]]>2018-08-01T00:05:26-07:00info:doi/10.1098/rspa.2017.0787hwp:master-id:royprsa;rspa.2017.07872018-08-01Research articles47422162017078720170787<![CDATA[Analytical estimation of non-local deformation-mediated magneto-electric coupling in soft composites]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/474/2216/20170803?rss=1
For a long time, the search for magneto-electric materials concentrated on multi-ferroics and hard-matter composites. By contrast, rather recently the exploitation of strain-mediated magneto-electric (ME) coupling in soft composites was proposed. The basic idea behind this approach is to combine the magneto- and electro-mechanical responses of composites consisting of a soft matrix carrying magnetic inclusions. Despite that such composites are straightforward to manufacture and have cheap constituents, they did not gain much attention up to now. In this contribution, we demonstrate that ME coupling induced by finite deformations could be of significant magnitude. Our approach relies on shape effects as a special non-local phenomenon in magneto- and electro-elasticity. Based on that we characterize an up to now overlooked ME coupling mechanism which purely relies on these shape effects in soft-matter-based magnetic and electric media. While soft magnetic media are commonly realized as composites, the coupling effect to be highlighted exists independently of the origin of a body's magnetic and electric properties. We show that the magnitude of the effect is indeed significant and, among ellipsoidal bodies, most pronounced for those of spherical to moderately prolate shape. Finite-element simulations are performed to assess the quality of the analytical predictions.
]]>2018-08-01T00:05:26-07:00info:doi/10.1098/rspa.2017.0803hwp:master-id:royprsa;rspa.2017.08032018-08-01Research articles47422162017080320170803<![CDATA[Small-amplitude static periodic patterns at a fluid-ferrofluid interface]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/474/2216/20180038?rss=1
We establish the existence of static doubly periodic patterns (in particular rolls, squares and hexagons) on the free surface of a ferrofluid near onset of the Rosensweig instability, assuming a general (nonlinear) magnetization law. A novel formulation of the ferrohydrostatic equations in terms of Dirichlet–Neumann operators for nonlinear elliptic boundary-value problems is presented. We demonstrate the analyticity of these operators in suitable function spaces and solve the ferrohydrostatic problem using an analytic version of Crandall–Rabinowitz local bifurcation theory. Criteria are derived for the bifurcations to be sub-, super- or transcritical with respect to a dimensionless physical parameter.
]]>2018-08-01T00:05:26-07:00info:doi/10.1098/rspa.2018.0038hwp:master-id:royprsa;rspa.2018.00382018-08-01Research articles47422162018003820180038<![CDATA[Wrinkling in engineering fabrics: a comparison between two different comprehensive modelling approaches]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/474/2216/20180063?rss=1
We consider two ‘comprehensive’ modelling approaches for engineering fabrics. We distinguish the two approaches using the terms ‘semi-discrete’ and ‘continuum’, reflecting their natures. We demonstrate a fitting procedure, used to identify the constitutive parameters of the continuum model from predictions of the semi-discrete model, the parameters of which are in turn fitted to experimental data. We, then, check the effectiveness of the continuum model by verifying the correspondence between semi-discrete and continuum model predictions using test cases not previously used in the identification process. Predictions of both modelling approaches are compared against full-field experimental kinematic data, obtained using stereoscopic digital image correlation techniques, and also with measured force data. Being a reduced order model and being implemented in an implicit rather than an explicit finite-element code, the continuum model requires significantly less computational power than the semi-discrete model and could therefore be used to more efficiently explore the mechanical response of engineering fabrics.
]]>2018-08-08T00:05:15-07:00info:doi/10.1098/rspa.2018.0063hwp:master-id:royprsa;rspa.2018.00632018-08-08Research articles47422162018006320180063<![CDATA[Comment on 'The cutting of metals by plastic buckling by Udupa et al.]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/474/2216/20180170?rss=1
In a recent paper on machining annealed copper at a low cutting speed, and at an uncut chip thickness one-tenth of the mean grain size of the copper, Udupa et al. (Proc. R. Soc A473, 20160863, doi:10.1098/rspa.2016.0863) report chip thicknesses larger than 10 times the uncut thickness and then a new mode of chip formation. Plastic bulging occurs in the surface of the copper ahead of the tool, leading to chip formation by a series of folds. The strain in the chip is less than that expected in a chip formed by shear according to long-standing classical theory. The authors suggest that the foundations of that theory need to be re-examined. In response, continuum mechanics numerical simulations presented here show a continuous transition from the classical condition towards that observed by Udupa et al. as the ratio of chip thickness to uncut thickness increases above approximately 7. Bulging is obtained by introducing (approximately) material heterogeneity to the simulations at a grain size scale but whether such heterogeneity is essential for the bulging flows remains an open question.
]]>2018-08-01T00:05:26-07:00info:doi/10.1098/rspa.2018.0170hwp:master-id:royprsa;rspa.2018.01702018-08-01Comment47422162018017020180170<![CDATA[Dispersive shock waves governed by the Whitham equation and their stability]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/474/2216/20180278?rss=1
Dispersive shock waves (DSWs), also termed undular bores in fluid mechanics, governed by the non-local Whitham equation are studied in order to investigate short wavelength effects that lead to peaked and cusped waves within the DSW. This is done by combining the weak nonlinearity of the Korteweg–de Vries equation with full linear dispersion relations. The dispersion relations considered are those for surface gravity waves, the intermediate long wave equation and a model dispersion relation introduced by Whitham to investigate the 120° peaked Stokes wave of highest amplitude. A dispersive shock fitting method is used to find the leading (solitary wave) and trailing (linear wave) edges of the DSW. This method is found to produce results in excellent agreement with numerical solutions up until the lead solitary wave of the DSW reaches its highest amplitude. Numerical solutions show that the DSWs for the water wave and Whitham peaking kernels become modulationally unstable and evolve into multi-phase wavetrains after a critical amplitude which is just below the DSW of maximum amplitude.
]]>2018-08-01T00:05:26-07:00info:doi/10.1098/rspa.2018.0278hwp:master-id:royprsa;rspa.2018.02782018-08-01Research articles47422162018027820180278<![CDATA[From arteries to boreholes: transient response of a poroelastic cylinder to fluid injection]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/474/2216/20180284?rss=1
The radially outward flow of fluid through a porous medium occurs in many practical problems, from transport across vascular walls to the pressurization of boreholes in the subsurface. When the driving pressure is non-negligible relative to the stiffness of the solid structure, the poromechanical coupling between the fluid and the solid can control both the steady state and the transient mechanics of the system. Very large pressures or very soft materials lead to large deformations of the solid skeleton, which introduce kinematic and constitutive nonlinearity that can have a non-trivial impact on these mechanics. Here, we study the transient response of a poroelastic cylinder to sudden fluid injection. We consider the impacts of kinematic and constitutive nonlinearity, both separately and in combination, and we highlight the central role of driving method in the evolution of the response. We show that the various facets of nonlinearity may either accelerate or decelerate the transient response relative to linear poroelasticity, depending on the boundary conditions and the initial geometry, and that an imposed fluid pressure leads to a much faster response than an imposed fluid flux.
]]>2018-08-01T00:05:26-07:00info:doi/10.1098/rspa.2018.0284hwp:master-id:royprsa;rspa.2018.02842018-08-01Research articles47422162018028420180284<![CDATA[On the geometrically exact low-order modelling of a flexible beam: formulation and numerical tests]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/474/2216/20180423?rss=1
This paper proposes a low-order geometrically exact flexible beam formulation based on the utilization of generic beam shape functions to approximate distributed kinematic properties of the deformed structure. The proposed nonlinear beam shapes approach is in contrast to the majority of geometrically nonlinear treatments in the literature in which element-based—and hence high-order—discretizations are adopted. The kinematic quantities approximated specifically pertain to shear and extensional gradients as well as local orientation parameters based on an arbitrary set of globally referenced attitude parameters. In developing the dynamic equations of motion, an Euler angle parametrization is selected as it is found to yield fast computational performance. The resulting dynamic formulation is closed using an example shape function set satisfying the single generic kinematic constraint. The formulation is demonstrated via its application to the modelling of a series of static and dynamic test cases of both simple and non-prismatic structures; the simulated results are verified using MSC Nastran and an element-based intrinsic beam formulation. Through these examples, it is shown that the nonlinear beam shapes approach is able to accurately capture the beam behaviour with a very minimal number of system states.
]]>2018-08-08T00:05:15-07:00info:doi/10.1098/rspa.2018.0423hwp:master-id:royprsa;rspa.2018.04232018-08-08Research articles47422162018042320180423<![CDATA[Designing heterogeneous catalysts]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/474/2216/20180514?rss=1
2018-08-15T00:05:20-07:00info:doi/10.1098/rspa.2018.0514hwp:master-id:royprsa;rspa.2018.05142018-08-15Special feature47422162018051420180514