Tensile fracture of an adhesive joint: the role of crack length and of material mismatch

The tensile strength of an adhesive joint is predicted for a centre-cracked elastic layer, sandwiched between elastic substrates, and subjected to remote tensile stress. A tensile cohesive plastic zone, of Dugdale type, is placed at each crack tip, and the cohesive zone is characterised by a finite strength and a finite toughness. An analytical theory of the fracture strength is developed (and validated by finite element simulations). The macroscopic strength of the adhesive joint is determined as a function of the relative magnitude of crack length, layer thickness, plastic zone size, specimen width and elastic modulus mismatch between layer and substrates. Fracture maps are constructed to reveal competing regimes of behaviour. The maps span the full range of behaviour from a perfectly brittle response (with no crack tip plasticity) to full plastic collapse. When the sum of crack length and cohesive zone length is less than 0.3 times the layer height, the effect of elastic mismatch between substrate and adhesive layer has only a minor influence upon the macroscopic fracture strength. For this case, the cracked adhesive layer behaves as a centre-crack in an infinite solid made from adhesive, and a transition from toughness control to strength control occurs when the crack length is comparable to that of the cohesive zone length. Alternatively, when the sum of crack length and cohesive zone length exceeds 0.3 times the layer height, the elastic mismatch plays a major role; again there is a transition from toughness control to strength control, but it occurs at a ratio of crack length to layer thickness that depends upon both the elastic mismatch and the ratio of cohesive zone length to layer height. The study also highlights the importance of a structural length scale in the form of layer height times modulus mismatch: this scale is on the order of 1 metre when the layer height equals one millimetre and the elastic modulus of the substrate is one thousand times that of the adhesive layer. The in-plane structural dimensions (including crack length) must exceed this structural dimension in order for a remote K-field to exist within the substrate. Experimental validation of the cohesive zone approach is achieved by measuring the sensitivity of fracture strength to crack length and layer height for a centre-cracked strip made from cellulose acetate layer, sandwiched between aluminium alloy substrates.Financial support from the Engineering and Physical Sciences Research Council (UK) award 1611305, the ERC MULTILAT grant 669764, and SABIC are gratefully acknowledged

Prospective Analysis Spin- and CP-sensitive Variables in H -> ZZ -> l_1 l_1 l_2 l_2 with Atlas

A possibility to prove spin and CP-eigenvalue of a Standard Model (SM) Higgs boson is presented. We exploit angular correlations in the subsequent decay H -> ZZ -> 4l (muons or electrons) for Higgs masses above 200 GeV. We compare the angular distributions of the leptons originating from the SM Higgs with those resulting from decays of hypothetical particles with differing quantum numbers. We restrict our analysis to the use of the Atlas-detector which is one of two multi-purpose detectors at the upcoming 14 TeV proton-proton-collider (LHC) at CERN. By applying a fast simulation of the Atlas detector it can be shown that these correlations will be measured sufficiently well that consistency with the spin-CP hypothesis 0+ of the Standard Model can be verified and the 0- and 1+- can be ruled out with an integrated luminosity of 100 fb^-1.Comment: 25 pages, 9 figures Version 2: Minor changes made as requested by Atlas referee and Springer editor. Added a chapter where background subtraction is detaile

Designing synthetic networks in silico : A generalised evolutionary algorithm approach

Background: Evolution has led to the development of biological networks that are shaped by environmental signals. Elucidating, understanding and then reconstructing important network motifs is one of the principal aims of Systems & Synthetic Biology. Consequently, previous research has focused on finding optimal network structures and reaction rates that respond to pulses or produce stable oscillations. In this work we present a generalised in silico evolutionary algorithm that simultaneously finds network structures and reaction rates (genotypes) that can satisfy multiple defined objectives (phenotypes). Results: The key step to our approach is to translate a schema/binary-based description of biological networks into systems of ordinary differential equations (ODEs). The ODEs can then be solved numerically to provide dynamic information about an evolved networks functionality. Initially we benchmark algorithm performance by finding optimal networks that can recapitulate concentration time-series data and perform parameter optimisation on oscillatory dynamics of the Repressilator. We go on to show the utility of our algorithm by finding new designs for robust synthetic oscillators, and by performing multi-objective optimisation to find a set of oscillators and feed-forward loops that are optimal at balancing different system properties. In sum, our results not only confirm and build on previous observations but we also provide new designs of synthetic oscillators for experimental construction. Conclusions: In this work we have presented and tested an evolutionary algorithm that can design a biological network to produce desired output. Given that previous designs of synthetic networks have been limited to subregions of network- and parameter-space, the use of our evolutionary optimisation algorithm will enable Synthetic Biologists to construct new systems with the potential to display a wider range of complex responses

Multi-field continuum theory for medium with microscopic rotations

We derive the multi-field, micropolar-type continuum theory for the two-dimensional model of crystal having finite-size particles. Continuum theories are usually valid for waves with wavelength much larger than the size of primitive cell of crystal. By comparison of the dispersion relations, it is demonstrated that in contrast to the single-field continuum theory constructed in our previous paper the multi-field generalization is valid not only for long but also for short waves. We show that the multi-field model can be used to describe spatially localized short- and long wavelength distortions. Short-wave external fields of forces and torques can be also naturally taken into account by the multi-field continuum theory.Comment: 14 pages, 4 figures, submitted to International Journal of Solids and Structure

The mechanics of solid-state nanofoaming.

Solid-state nanofoaming experiments are conducted on two polymethyl methacrylate (PMMA) grades of markedly different molecular weight using CO2 as the blowing agent. The sensitivity of porosity to foaming time and foaming temperature is measured. Also, the microstructure of the PMMA nanofoams is characterized in terms of cell size and cell nucleation density. A one-dimensional numerical model is developed to predict the growth of spherical, gas-filled voids during the solid-state foaming process. Diffusion of CO2 within the PMMA matrix is sufficiently rapid for the concentration of CO2 to remain almost uniform spatially. The foaming model makes use of experimentally calibrated constitutive laws for the uniaxial stress versus strain response of the PMMA grades as a function of strain rate and temperature, and the effect of dissolved CO2 is accounted for by a shift in the glass transition temperature of the PMMA. The maximum achievable porosity is interpreted in terms of cell wall tearing and comparisons are made between the predictions of the model and nanofoaming measurements; it is deduced that the failure strain of the cell walls is sensitive to cell wall thickness

Can overturning motions in penumbral filaments be detected?

Numerical simulations indicate that the filamentation of sunspot penumbrae and the associated systematic outflow (the Evershed effect) are due to convectively driven fluid motions constrained by the inclined magnetic field. We investigate whether these motions, in particular the upflows in the bright filaments and the downflows at their edges can be reliably observed with existing instrumentation. We use a snapshot from a sunspot simulation to calculate 2D maps of synthetic line profiles for the spectral lines Fe\sci 7090.4 \AA ~ and C\sci 5380.34 \AA. The maps are spatially and spectrally degraded according to typical instrument properties. Line-of-sight velocities are determined from line bisector shifts. We find that the detectability of the convective flows is strongly affected by spatial smearing, particularly so for the downflows. Furthermore, the line-of-sight velocities are dominated by the Evershed flow unless the observation is made very near to disk center. These problems may have compromised recent attempts to detect overturning penumbral convection. Lines with a low formation height are best suited to detect the convective flows.Comment: 8 pages, 12 figures, accepted for publication in ApJ on 28th Ju

The influence of cell size on the mechanical properties of nanocellular PMMA

Solid-state foaming experiments are conducted on three grades of polymethyl methacrylate (PMMA). Nanocellular PMMA foams are manufactured with an average cell size ranging from 20 nm to 84 nm and a relative density between 0.37 and 0.5. For benchmarking purposes, additional microcellular PMMA foams with an average cell size close to 1 µm and relative density close to that of the nanocellular foams are manufactured. Uniaxial compression tests and single edge notch bend tests are conducted on the PMMA foams. The measured Young’s modulus and yield strength of the PMMA foams are independent of cell size whereas the fracture toughness of the PMMA foam increases with decreasing average cell size from the micron range to the nanometer range.Financial assistance from MINECO, FEDER, UE (MAT2015-69234-R), the Junta of Castile and Leon (VA275P18) and Spanish Ministry of Science, Innovation and Universities (RTI2018-098749-B-I00) are gratefully acknowledged. Financial support from FPU grant FPU14/02050 (V. Bernardo) from the Spanish Ministry of Education and Junta of Castile and Leon grant (J. Martín-de León) are gratefully acknowledged. Financial support from SABIC and the EPSRC award 1611305 (F. Van Loock), and the ERC project MULTILAT (N. A. Fleck) are acknowledged too

Quiet-Sun imaging asymmetries in NaI D1 compared with other strong Fraunhofer lines

Imaging spectroscopy of the solar atmosphere using the NaI D1 line yields marked asymmetry between the blue and red line wings: sampling a quiet-Sun area in the blue wing displays reversed granulation, whereas sampling in the red wing displays normal granulation. The MgI b2 line of comparable strength does not show this asymmetry, nor does the stronger CaII 8542 line. We demonstrate the phenomenon with near-simultaneous spectral images in NaI D1, MgI b2, and CaII 8542 from the Swedish 1-m Solar Telescope. We then explain it with line-formation insights from classical 1D modeling and with a 3D magnetohydrodynamical simulation combined with NLTE spectral line synthesis that permits detailed comparison with the observations in a common format. The cause of the imaging asymmetry is the combination of correlations between intensity and Dopplershift modulation in granular overshoot and the sensitivity to these of the steep profile flanks of the NaI D1 line. The MgI b2 line has similar core formation but much wider wings due to larger opacity buildup and damping in the photosphere. Both lines obtain marked core asymmetry from photospheric shocks in or near strong magnetic concentrations, less from higher-up internetwork shocks that produce similar asymmetry in the spatially averaged CaII 8542 profile.Comment: Accepted by Astron & Astrophys. In each in-text citation the year links to the corresponding ADS abstract pag