Dynamic fracture of a dissimilar chain

International audienceIn this paper, we study the dynamic fracture of a dissimilar chain composed of two different mass-spring chains and connected with other springs. The propagation of the fault (crack) is realized under externally applied moving forces. In comparison with a homogeneous double chain, the considered structure displays some new essential features of steady-state crack propagation. Specifically, the externally applied forces are of a different strength, unlike a static case, and should be appropriately chosen to satisfy the equilibrium of the structure. Moreover, there exists a gap in the range of crack speeds where the steady-state fracture cannot occur. We analyse the admissibility of solutions for different model parameters and crack speeds. We complement analytical findings with numerical simulations to validate our results

Dynamic fracture of a discrete media under moving load

Most of the research concerting crack propagation in discrete media is concerned with specific types of external loading: displacements on the boundaries, or constant energy fluxes or feeding waves originating from infinity. In this paper the action of a moving load is analysed on the simplest lattice model: a thin strip, where the fault propagating in its middle portion as the result of the moving force acting on the destroyed part of the structure. We study both analytically and numerically how the load amplitude and its velocity influence the possible solution, and specifically the way the fracture process reaches its steady-state regime. We present the relation between the possible steady-state crack speed and the loading parameters, as well as the energy release rate. In particular, we show that there exists a class of loading regime corresponding to each point on the energy-speed diagram (and thus determine the same limiting steady-state regime). The phenomenon of the forbidden regimes is discussed in detail, from both the points of view of force and energy. For a sufficiently anisotropic structure, we find a stable steady-state propagation corresponding to the slow crack. Numerical simulations reveal various ways by which the process approaches - or fails to approach - the steady-state regime. The results extend our understanding of fracture processes in discrete structures, and reveal some new questions that should be addressed

Universality classes of transition fronts in the FPU model

Steady transition fronts in nonlinear lattices are among the most important dynamic coherent structures. We use the Fermi-Pasta-Ulam model with piecewise linear nonlinearity to show that there are exactly three distinct classes of such fronts which differ fundamentally in how (and whether) they produce and transport oscillations. To make this Hamiltonian problem analytically transparent, we construct a quasicontinuum approximation generating all three types of fronts and then show that the interconnection between different classes of fronts in the original discrete model is the same as in the quasicontinuum model. The proposed framework unifies previous attempts to classify the transition fronts as radiative, dispersive, topological or compressive and categorizes them instead as different types of dynamic defects

On stress singularity near the tip of a crack with surface stresses

In the framework of the simplified linear Gurtin–Murdoch surface elasticity we discuss a singularity of stresses and displacements in the vicinity of a mode III crack. We show that inhomogeneity in surface elastic properties may significantly affect the solution and to change the order of singularity. We also demonstrate that implicitly or explicitly assumed symmetry of the problem may also lead to changes in solutions. Considering various loading and symmetry conditions we show that the stresses may have logarithmic or square root singularity or be bounded in the vicinity of a crack tip

Influence of fracture criteria on dynamic fracture propagation in a discrete chain

The extent to which time-dependent fracture criteria affect the dynamic behavior of fracture in a discrete structure is discussed in this work. The simplest case of a semi-infinite isotropic chain of oscillators has been studied. Two history-dependent criteria are compared to the classical one of threshold elongation for linear bonds. The results show that steady-state regimes can be reached in the low subsonic crack speed range where it is impossible according to the classical criterion. Repercussions in terms of load and crack opening versus velocity are explained in detail. A strong qualitative influence of history-dependent criteria is observed at low subsonic crack velocities, especially in relation to achievable steady-state propagation regimes

Iakovleva Functional characterization of Littorina littorea blood cells

The main functional characteristics of haemocytes from the common periwinkle Littorina littorea (phagocytic ability, acid phosphatase activity, cytotoxic properties and generation of reactive oxygen intermediates) were investigated. The blood cells of L. littorea demonstrated phagocytic activity for zymozan particles in both plasma and seawater. However, the level of phagocytosis in plasma was higher than in seawater, suggesting the presence of some soluble factors with opsonizing activity for yeast cell walls in the snail haemolymph. Acid phosphatase was detected in haemocytes following phagocytosis of zymosan. Zymosan particles as well as soluble inducers of respiratory burst (mannan, phorbol-myristate acetate, lipopolysaccharide from Escherichia coli) were shown to trigger superoxide anion production in L. littorea blood cells as evidenced by nitroblue tetrazolium (NBT) reduction. Haemocytes exposed simultaneously to both inducer and the superoxide scavenger enzymeösuperoxide dismutase demonstrated a lower ability to reduce nitrobluetetrazolium. Periwinkle blood cells showed plasma-independent cytotoxic activity for human erythrocytes which may be due to the release of superoxide intermediates into the extracellular environment. These results, together with previously obtained data, suggest that haemocytes are the main e¡ectors in the internal defence system of L. littorea, with humoral factors playing an accessory role in recognition and elimination of pathogens