arXiv subjects

Gennady Mishuris

Publications and source records attributed to Gennady Mishuris.

41 records · Page 3Linked to original sources

arXiv2012

On modeling hydraulic fracture in proper variables: stiffness, accuracy, sensitivity

The problem of hydraulic fracture propagation is considered by using its recently suggested modified formulation in terms of the particle velocity, the opening in the proper degree, appropriate spatial coordinates and $\varepsilon$-regularization. We show that the formulation may serve for significant increasing the efficiency of numerical tracing the fracture propagation. Its advantages are illustrated by re-visiting the Nordgren problem. It is shown that the modified formulation facilitates (i) possibility to have various stiffness of differential equations resulting after spatial discretization, (ii) obtaining highly accurate and stable numerical results with moderate computational effort, and (iii) sensitivity analysis. The exposition is extensively illustrated by numerical examples.

physics.geo-ph↗

arXiv2011

Perturbation analysis of Mode III interfacial cracks advancing in a dilute heterogeneous material

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.

math-ph↗

arXiv2011

Interaction of an interfacial crack with linear micro-defects under out-of-plane shear loading

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 (1995). 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 fiber reinforced materials.

math-ph↗

arXiv2011

Mode III interfacial crack in the presence of couple stress elastic materials

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.

math-ph↗

arXiv2008

Remarks on the accuracy of algorithms for motion by mean curvature in bounded domains

Simulations of motion by mean curvature in bounded domains, with applications to bubble motion and grain growth, rely upon boundary conditions that are only approximately compatible with the equation of motion. Three closed form solutions for the problem exist, governing translation, rotation and expansion of a single interface [1], providing the only benchmarks for algorithm verification. We derive new identities for the translation solution. Then we estimate the accuracy of a straightforward algorithm to recover the analytical solution for different values of the velocity V given along the boundary. As expected, for large V the error can reach unacceptable levels especially near the boundary. We discuss factors influencing the accuracy and propose a simple modification of the algorithm which improves the computational accuracy.

cond-mat.soft↗