On some intriguing problems in Hamiltonian graph theory -- A survey

We survey results and open problems in Hamiltonian graph theory centred around three themes: regular graphs, $t$-tough graphs, and claw-free graphs

Hamilton cycles in graphs and hypergraphs: an extremal perspective

As one of the most fundamental and well-known NP-complete problems, the Hamilton cycle problem has been the subject of intensive research. Recent developments in the area have highlighted the crucial role played by the notions of expansion and quasi-randomness. These concepts and other recent techniques have led to the solution of several long-standing problems in the area. New aspects have also emerged, such as resilience, robustness and the study of Hamilton cycles in hypergraphs. We survey these developments and highlight open problems, with an emphasis on extremal and probabilistic approaches.Comment: to appear in the Proceedings of the ICM 2014; due to given page limits, this final version is slightly shorter than the previous arxiv versio

Measuring the notched compressive strength of composite laminates: Specimen size effects

Large fibre reinforced composite structures can give much lower strengths than small test specimens, so a proper understanding of scaling is vital for their safe and efficient use. Small size (scale) specimens are commonly tested to justify allowable stresses, but could be dangerous if results are extrapolated without accounting for scaling effects. On the other hand large factors are sometimes applied to compensate for uncertainties, resulting in overweight designs. The most important variables of scaling effects on the strength of composites with open holes have been identified from experimental tests as notch size, ply and laminate thickness. In this study, these have been scaled both independently and simultaneously over a large range of combinations. The specimens are fabricated from commercially available (Hexcel Composites Ltd.) carbon/epoxy pre-impregnated tapes 0.125 mm thick (IM7/8552). The material is laid up by hand in unidirectional [04]ns with n = 2, 3, 4, and 8 (i.e., 2, 3, 4 and 8 mm thick) and multidirectional laminates; two generic quasi-isotropic lay-ups, one fabricated with blocked plies [45n/90n/−45n/0n]s and the other with distributed layers [45/90/−45/0]ns with n = 2, 4 and 8 are examined. It is shown that the critical failure mechanism in these laminates is in the form of fibre microbuckling or kinking. The unnotched compressive strength in unidirectional specimens thicker than 2 mm is found to be limited by the stress concentration developed at the end tabs and manufacturing induced defects in the form of ply waviness, fibre misalignment and voids rather than specimen size (scaling). In the open hole specimens, for both lay-ups, the strength reduction observed is due to hole size effect rather than specimen thickness or volume increase. The open hole (notched) compressive strength results obtained compare favourably to predictions by a linear softening cohesive zone fracture model developed in earlier work by the second author

The Effect of Thin Film Adhesives on Mode I Interlaminar Fracture Toughness in Carbon Fiber Composites with Shape Memory Alloy Inserts

Shape Memory Alloy (SMA) was placed within Polymer Matrix Composite (PMC) panels alongside film adhesives to examine bonding. Double cantilever beam (DCB) testing was performed using ASTM D5528. C-scanning was performed before testing, modal acoustic emissions (MAE) were monitored during testing, and microscopy performed post-test. Data was analyzed using modified beam theory (MBT), compliance calibration (CC) and modified compliance calibration (MCC) methods. Fracture toughness for control specimens was higher than previously reported due to fiber-bridging. Specimens with SMAs and adhesives stabilized crack propagation. Results revealed SMA-bridging; a phenomenon mimicking fiber-bridging which increased the load and fracture toughness of SMA specimens

A new test methodology based on structural resonance for mode I fatigue delamination growth in an unidirectional composite

A specific device has been set up to test by vibration resonance the mode I fatigue delamination growth onset of composite laminates. This test system, based on the DCB test specimen, is a mass-spring-specimen dynamic system designed to resonate. The defined operating conditions allow performing delamination propagation tests under imposed load and stopping the test under reproducible conditions, identical to the ones recommended in the ASTM-D6115 standard. This system allows fatigue tests to be driven up to 100Hz, reducing the time taken by a factor of ten without detrimental heat being generated in the material. The effect of frequency on the fatigue delamination growth on mode I has been investigated through a comparison with standard tests performed at 10Hz. A decrease in resistance to the propagation of delamination is observed with the increase in frequency for the composite studied. This frequency effect seems to be a strain rate effect and was taken in consideration by using dynamical critical energy restitution rate for the G-N curve plotting