A New Finite Element Method for Strain Gradient Theories and Applications to Fracture Analyses

A new compatible finite element method for strain gradient theories is presented. In the new finite element method, pure displacement derivatives are taken as the fundamental variables. The new numerical method is successfully used to analyze the simple strain gradient problems – the fundamental fracture problems. Through comparing the numerical solutions with the existed exact solutions, the effectiveness of the new finite element method is tested and confirmed. Additionally, an application of the Zienkiewicz–Taylor C1 finite element method to the strain gradient problem is discussed. By using the new finite element method, plane-strain mode I and mode II crack tip fields are calculated based on a constitutive law which is a simple generalization of the conventional J2 deformation plasticity theory to include strain gradient effects. Three new constitutive parameters enter to characterize the scale over which strain gradient effects become important. During the analysis the general compressible version of Fleck–Hutchinson strain gradient plasticity is adopted. Crack tip solutions, the traction distributions along the plane ahead of the crack tip are calculated. The solutions display the considerable elevation of traction within the zone near the crack tip.

Fractals and Scaling in Fracture Induced by Microcrack Coalescence

A numerical model is proposed to simulate fracture induced by the coalescence of numerous microcracks, in which the condition for coalescence between two randomly nucleated microcracks is determined in terms of a load-sharing principle. The results of the simulation show that, as the number density of nucleated microcracks increases, stochastic coalescence first occurs followed by a small fluctuation, and finally a newly nucleated microcrack triggers a cascade coalescence of microcracks resulting in catastrophic failure. The fracture profiles exhibit self-affine fractal characteristics with a universal roughness exponent, but the critical damage threshold is sensitive to details of the model. The spatiotemporal distribution of nucleated microcracks in the vicinity of critical failure follows a power-law behaviour, which implies that the microcrack system may evolve to a critical state.

Effects of Nanostructures on the Fracture Strength of the Interfaces in Nacre

A strengthening mechanism arising from a type of inorganic nanostructure in the organic matrix layers is presented by studying the structural and mechanical properties of the interfaces in nacre. This nanostructural mechanism not only averagely increases the fracture strength of the organic matrix interfaces by about 5 times, but also effectively arrests the cracks in the organic matrix layers and causes the crack deflection in this biomaterial. The present investigation shows that the main mechanism governing the strength of the organic matrix interfaces relies on the inorganic nanostructures rather than the organic matrix. This study provides a guide to the interfacial design of synthetic materials.

Essential and Non-Essential Work of Fracture of PI/SiO2 Hybrid Thin Films

Essential work of fracture (EWF) analysis is used to study the effect of the silica doping level on fracture toughness of polyimide/silica (PI/SiO2) hybrid films. By using double-edge-notched-tension (DENT) specimens with different ligament lengths, it seems that the introduction of silica additive can improve the specific essential work of fracture (w (e) ) of PI thin films, but the specific non-essential work of fracture (beta w (p) ) will decease significantly as the silica doping level increasing from 1 to 5 wt.%, and even lower than that of neat PI. The failure process of the fracture is investigated with online scanning electron microscope (SEM) observation and the parameters of non-essential work of fracture, beta and w (p) , are calculated based on finite element (FE) method.

Signature-tagged transposon mutagenesis studies demonstrate the dynamic nature of cecal colonization of 2-week-old chickens by Campylobacter jejuni.

We have constructed plasmids to be used for in vitro signature-tagged mutagenesis (STM) of Campylobacter jejuni and used these to generate STM libraries in three different strains. Statistical analysis of the transposon insertion sites in the C. jejuni NCTC 11168 chromosome and the plasmids of strain 81-176 indicated that their distribution was not uniform. Visual inspection of the distribution suggested that deviation from uniformity was not due to preferential integration of the transposon into a limited number of hot spots but rather that there was a bias towards insertions around the origin. We screened pools of mutants from the STM libraries for their ability to colonize the ceca of 2-week-old chickens harboring a standardized gut flora. We observed high-frequency random loss of colonization proficient mutants. When cohoused birds were individually inoculated with different tagged mutants, random loss of colonization-proficient mutants was similarly observed, as was extensive bird-to-bird transmission of mutants. This indicates that the nature of campylobacter colonization in chickens is complex and dynamic, and we hypothesize that bottlenecks in the colonization process and between-bird transmission account for these observations.

A dynamic view of the spread and intracellular distribution of Salmonella enterica.

The events that determine the dynamics of proliferation, spread and distribution of microbial pathogens within their hosts are surprisingly heterogeneous and poorly understood. We contend that understanding these phenomena at a sophisticated level with the help of mathematical models is a prerequisite for the development of truly novel, targeted preventative measures and drug regimes. We describe here recent studies of Salmonella enterica infections in mice which suggest that bacteria resist the antimicrobial environment inside host cells and spread to new sites, where infection foci develop, and thus avoid local escalation of the adaptive immune response. We further describe implications for our understanding of the pathogenic mechanism inside the host.

Wave dynamic processes induced by a supersonic projectile discharging from a shock tube

A numerical study on wave dynamic processes occurring in muzzle blast flows, which are created by a supersonic projectile released from the open-end of a shock tube into ambient air, is described in this paper. The Euler equations, assuming axisymmetric flows, are solved by using a dispersion-controlled scheme implemented with moving boundary conditions. Three test cases are simulated for examining friction effects on the muzzle flow. From numerical simulations, the wave dynamic processes, including two blast waves, two jet flows, the bow shock wave and their interactions in the muzzle blasts, are demonstrated and discussed in detail. The study shows that the major wave dynamic processes developing in the muzzle flow remain similar when the friction varies, but some wave processes, such as shock-shock interactions, shock-jet interactions and the contact surface instability, get more intensive, which result in more complex muzzle blast flows.

Dynamic SIF of interface crack between two dissimilar viscoelastic bodies under impact loading

In this paper, the transient dynamic stress intensity factor (SIF) is determined for an interface crack between two dissimilar half-infinite isotropic viscoelastic bodies under impact loading. An anti-plane step loading is assumed to act suddenly on the surface of interface crack of finite length. The stress field incurred near the crack tip is analyzed. The integral transformation method and singular integral equation approach are used to get the solution. By virtue of the integral transformation method, the viscoelastic mixed boundary problem is reduced to a set of dual integral equations of crack open displacement function in the transformation domain. The dual integral equations can be further transformed into the first kind of Cauchy-type singular integral equation (SIE) by introduction of crack dislocation density function. A piecewise continuous function approach is adopted to get the numerical solution of SIE. Finally, numerical inverse integral transformation is performed and the dynamic SIF in transformation domain is recovered to that in time domain. The dynamic SIF during a small time-interval is evaluated, and the effects of the viscoelastic material parameters on dynamic SIF are analyzed.

Thermoplastic shear localisation in titanium alloys during dynamic deformation

Cylindrical specimens (4 mm diameter and 4 mm height) of titanium alloy bar were given various heat treatments to provide a wide range of microstructures and mechanical parameters. These specimens were then subjected to high plastic strain at a large strain rate (103 s-1 ) during dynamic compression by a split Hopkinson bar at ambient temperature. The microstructures of the localised shear bands were examined by optical and transmission electron microscopy. The results show that there are two types of localised shear bands: deformed and white shear bands. A detailed observation reveals that there is no difference in the nature of the deformed and white shear bands, but they occur at different stages of localised deformation. It is found that there is a burst of strain, corresponding to a critical strain rate at which the white shear band occurs and no phase transformation occurs in the shear bands.

The relationship of SIF between plate and plane fracture problems and the effect of the plate thickness on SIF

In the present paper, it is shown that the zero series eigenfunctions of Reissner plate cracks/notches fracture problems are analogous to the eigenfunctions of anti-plane and in-plane. The singularity in the double series expression of plate problems only arises in zero series parts. In view of the relationship with eigen-values of anti-plane and in-plane problem, the solution of eigen-values for Reissner plates consists of two parts: anti-plane problem and in-plane problem. As a result the corresponding eigen-values or the corresponding eigen-value solving programs with respect to the anti-plane and in-plane problems can be employed and many aggressive SIF computed methods of plane problems can be employed in the plate. Based on those, the approximate relationship of SIFs between the plate and the plane fracture problems is figured out, and the effect relationship of the plate thickness on SIF is given.

Wave Dynamic Processes in Cellular Detonation Reflection from Wedges

When the cell width of the incident detonation wave (IDW) is comparable to or larger than the Mach stem height, self-similarity will fail during IDW reflection from a wedge surface. In this paper, the detonation reflection from wedges is investigated for the wave dynamic processes occurring in the wave front, including transverse shock motion and detonation cell variations behind the Mach stem. A detailed reaction model is implemented to simulate two-dimensional cellular detonations in stoichiometric mixtures of H (2)/O (2) diluted by Argon. The numerical results show that the transverse waves, which cross the triple point trajectory of Mach reflection, travel along the Mach stem and reflect back from the wedge surface, control the size of the cells in the region swept by the Mach stem. It is the energy carried by these transverse waves that sustains the triple-wave-collision with a higher frequency within the over-driven Mach stem. In some cases, local wave dynamic processes and wave structures play a dominant role in determining the pattern of cellular record, leading to the fact that the cellular patterns after the Mach stem exhibit some peculiar modes.