Gennady Mishuris

Symmetric and skew-symmetric weight functions in 2D perturbation models for semi-infinite interfacial cracks

Abstract In this paper we address the vector problem of a 2D half-plane interfacial crack loaded by a general asymmetric distribution of forces acting on its faces. It is shown that the general integral formula for the evaluation of stress intensity factors, as well as high-order terms, requires both symmetric and skew-symmetric weight function matrices. The symmetric weight function matrix is obtained via the solution of a Wiener–Hopf functional equation, whereas the derivation of the skew-symmetric weight function matrix requires the construction of the corresponding full field singular solution. The weight function matrices are then used in the perturbation analysis of a crack advancing quasi-statically along the interface between two dissimilar media. A general and rigorous asymptotic procedure is developed to compute the perturbations of stress intensity factors as well as high-order terms.

Evaluation of the Lazarus-Leblond constants in the asymptotic model of the interfacial wavy crack

Piccolroaz, A; Mishuris, G; Movchan, AB. Evaluation of the Lazarus-Leblond constants in the asymptotic model of the interfacial wavy crack. Journal of the mechanics and Physics of Solids. 2007, 55(8), 1575-1600

Asymptotic Behaviour of the Elastic Solution near the Tip of a Crack Situated at a Nonideal Interface

The interface crack problem with a nonideal interface described by special transmission conditions is examined. The corresponding modelling boundary value problem is reduced to a system of singular integral equations with moving and fixed point singularities. The existence and uniqueness of the system solution are proved. Possible shapes of an intermediate zone as well as combinations of material parameters are investigated. Asymptotic expansions of the stresses and displacements near the crack tip are found. The obtained results are discussed from a fracture mechanical point of view. Numerical examples concerning the calculation of the stress singularity exponent as well as the generalized SIFs are presented.

Interface crack and nonideal interface concept (Mode III)

Asymptotic behaviour of displacements and stresses in a vicinity of the interface crack tip situated on a nonideal interface between two different elastic materials is investigated. The nonideal interface is described by special transmission conditions along the material bonding. The corresponding modelling boundary value problem is reduced to a singular integral equation with fixed point singularities. It is shown from the solution to the problem that asymptotic behaviour of displacement and stresses near the crack tip essentially depends on the model parameters. Some numerical examples are presented and discussed with respect to the stress singularity exponent and the generalized stress intensity factors.

Elliptical contact of thin biphasic cartilage layers: Exact solution for monotonic loading

A three-dimensional unilateral contact problem for articular cartilage layers is considered in the framework of the biphasic cartilage model. The articular cartilages bonded to subchondral bones are modeled as biphasic materials consisting of a solid phase and a fluid phase. It is assumed that the subchondral bones are rigid and shaped like elliptic paraboloids. The obtained analytical solution is valid for monotonically increasing loading conditions.

Accounting for the thickness effect in dynamic spherical indentation of a viscoelastic layer: Application to non-destructive testing of articular cartilage

Abstract In recent years, dynamic indentation tests have been shown to be useful both in identification of mechanical properties of biological tissues (such as articular cartilage) and assessing their viability. We consider frictionless flat-ended and spherical sinusoidally-driven indentation tests utilizing displacement-controlled loading protocol. Articular cartilage tissue is modeled as a viscoelastic material with a time-independent Poissons ratio. We study the dynamic indentation stiffness with the aim of formulating criteria for evaluation the quality of articular cartilage in order to be able to discriminate its degenerative state. In particular, evaluating the dynamic indentation stiffness at the turning point of the flat-ended indentation test, we introduce the so-called incomplete storage modulus. Considering the time difference between the time moments when the dynamic stiffness vanishes (contact force reaches its maximum) and the dynamic stiffness becomes infinite (indenter displacement reaches its maximum), we introduce the so-called incomplete loss angle. Analogous quantities can be introduced in the spherical sinusoidally-driven indentation test, however, to account for the thickness effect, a special approach is required. We apply an asymptotic modeling approach for analyzing and interpreting the results of the dynamic spherical indentation test in terms of the geometrical parameter of the indenter and viscoelastic characteristics of the material. Some implications to non-destructive indentation diagnostics of cartilage degeneration are discussed.

Waves and fracture in an inhomogeneous lattice structure

We analyze a crack propagating in an inhomogeneous rectangular lattice in the state of anti-plane shear. The filtering properties of such a lattice are linked to the energy dissipation due to waves initiated by the crack. The influence of the inhomogeneities within the lattice on the lattice trapping is investigated.

On the dead-zone formation and limit analysis in axially symmetric extrusion

For axisymmetric direct and indirect extrusion, a kinematically admissible velocity field based on a simple radial flow field combined with the asymptotic behaviour required of a real velocity field near a velocity discontinuity surface is proposed. The influence of the extrusion ratio on the shape of a dead zone and the extrusion pressure is investigated. The result obtained for the upper bound on the extrusion pressure is compared with other solutions. It is shown that using the asymptotic velocity field slightly improves the prediction of the extrusion pressure in comparison with the other solutions based on radial flow. The main advantages of the approach proposed are that it is applicable to a class of processes and that it accounts for the behaviour of a real velocity field in the vicinity of velocity discontinuity surfaces/maximum friction surfaces where various physical effects like local heating, recrystalization, and transformations occur.

Stress singularity at a crack tip for various intermediate zones in bimaterial structures (mode III)

The influence of the geometry of a thin intermediate zone on the stress distribution has been investigated in the vicinity of a crack tip in a bimaterial structure. Corresponding modelling boundary value problems are reduced to functional-difference equations by the Mellin transform technique, and later to singular integral equations with fixed point singularities. It has been observed that the order of the stress singularity is essentially dependent on the model parameters. Numerical results concerning the stress singularity exponents and generalized stress intensity factors are presented.

Improved algorithm for analytical solution of the heat conduction problem in doubly periodic 2D composite materials

We consider a boundary value problem (BVP) in unbounded 2D doubly periodic composite with circular inclusions having arbitrary constant conductivities. By introducing complex potentials, the BVP for the Laplace equation is transformed to a special -linear BVP for doubly periodic analytic functions. This problem is solved with use of the method of functional equations. The -linear BVP is transformed to a system of functional equations. A new improved algorithm for solution of the system is proposed. It allows one not only to compute the average property but to reconstruct the solution components (temperature and flux) at an arbitrary point of the composite. Several computational examples are discussed in details demonstrating high efficiency of the method. Indirect estimate of the algorithm accuracy has been also provided.