Mathematical Modelling of Structures, Solids and Fluids
Browse by
Recent Submissions
-
Piccolroaz, Andrea; Radi, Enrico; Mishuris, Gennady (2012)[more][less]
Abstract: In this paper we are concerned with the problem of a crack lying at the interface between dissimilar materials with microstructure undergoing antiplane deformations. The micropolar behaviour of the materials is described by the theory of couple-stress elasticity developed by Koiter (1964). This constitutive model includes the characteristic lengths in bending and torsion and thus it is able to account for the underlying microstructure of the two materials. We perform an asymptotic analysis to investigate the behaviour of the solution near the crack tip. It turns out that the stress singularity at the crack tip is strongly influenced by the microstructural parameters and it may or may not show oscillatory behaviour depending on the ratio between the characteristic lengths. URI: http://hdl.handle.net/2160/7832 Files in this item: 1
1010.1822v2.pdf (250.2Kb) -
Mishuris, Gennady; Piccolroaz, Andrea; Movchan, Alexander; Movchan, Natasha (Elsevier, February , 2012)[more][less]
Abstract: The interaction of an interfacial crack with small impurities is analysed on the basis of an asymptotic formula derived by the authors. The interaction between the main crack and the defects (e.g. small cracks or inclusions) is described asymptotically by analysing the dipole fields and the corresponding dipole matrices of the defects in question. The method is generic, and it serves interfacial cracks with general distributed loading on the crack faces, taking into account possible asymmetry in the boundary conditions, and in a particular configuration for a crack in a homogeneous medium results agree with those obtained earlier by Gong [1]. Shielding and amplification effects of the defects on the propagation of the main crack along the interface are investigated. Numerical computations based on the explicit analytical formulae show potential applications in the design of composite and fibre reinforced materials. URI: http://hdl.handle.net/2160/7831 Files in this item: 1
1010.6223v4.pdf (3.991Mb) -
Piccolroaz, Andrea; Mishuris, Gennady; Movchan, Alexander; Movchan, Natasha (2012)[more][less]
Abstract: The paper addresses the problem of a Mode III interfacial crack advancing quasi-statically in a heterogeneous composite material, that is a two-phase material containing elastic inclusions, both soft and stiff, and defects, such as microcracks, rigid line inclusions and voids. It is assumed that the bonding between dissimilar elastic materials is weak so that the interface is a preferential path for the crack. The perturbation analysis is made possible by means of the fundamental solutions (symmetric and skew-symmetric weight functions) derived in Piccolroaz et al. (2009). We derive the dipole matrices of the defects in question and use the corresponding dipole fields to evaluate effective tractions along the crack faces and interface to describe the interaction between the main interfacial crack and the defects. For a stable propagation of the crack, the perturbation of the stress intensity factor induced by the defects is then balanced by the elongation of the crack along the interface, thus giving an explicit asymptotic formula for the calculation of the crack advance. The method is general and applicable to interfacial cracks with general distributed loading on the crack faces, taking into account possible asymmetry in the boundary conditions. The analytical results are used to analyse the shielding and amplification effects of various types of defects in different configurations. Numerical computations based on the explicit analytical formulae allows for the analysis of crack propagation and arrest. URI: http://hdl.handle.net/2160/7829 Files in this item: 1
1105.3497v2.pdf (1.215Mb) -
Davies, I. T.; Cox, Simon (The Society of Rheology, Inc., American Institute of Physics, March , 2012)[more][less]
Abstract: The effect of the interplay between surface tension and gravity on the sedimentation of objects in structured fluids is investigated by simulating the quasi-static motion of a spherical particle through an ordered foam. We describe the path which a sphere takes as it descends through bamboo (1,1,0), staircase (2,1,1), chiral (3,2,1), and double staircase (4,2,2) foams, and measure the degree of control of the sphere’s motion that each foam offers. For an ordered foam contained within a vertical cylinder, the resulting sphere motion depends strongly on the structure itself, on how the films are deformed near the sphere, and on how the motion of the sphere deforms them further. For staircase and chiral foams, the distance that a sphere is pulled away from the center-line of the cylinder by the foam is found to depend on the Bond number with a power-law relation. By tilting the cylinder at an angle to the vertical, we show that there exists a critical tilt angle above which the sphere falls out of the foam. This angle is dependent on the choice of foam structure and the Bond number. For a sphere of given size and given Bond number in the ordered foams studied here, the greatest tilt can be imposed on the double staircase foam URI: http://hdl.handle.net/2160/7813 Files in this item: 1
JOR000473.pdf (454.5Kb) -
Jones, Sian; Cox, Simon (The Society of Rheology, Inc., American Institute of Physics, March , 2012)[more][less]
Abstract: A comprehensive set of experiments on a two-dimensional constriction flow of a foam are described. Image analysis of the flow is used to ascertain bubble shape and flow dynamics. The bubble velocity, elongation (texture), stress, and deformation rate for a reference case are used to validate a quasistatic simulation. Changes to the constriction geometry, most especially in the rounding of the corners, have a significant effect on the response of the foam, captured in both experiment and simulation. On the other hand, foam properties such as bubble size have little C impact on the rheological behavior of the foam in the range considered here. URI: http://hdl.handle.net/2160/7812 Files in this item: 1
online_JOR000457.pdf (2.335Mb)