Michael Ryvkin

Mode III crack in a laminated medium

Antiplane deformation of a laminated medium with a semi-infinite crack parallel to the interfaces between the layers is considered. The homogeneous, elastic and isotropic layers of two different types are arranged periodically. This allows the reduction of the initial boundary value problem to the Wiener-Hopf equation by combined application of the Laplace and the discrete Fourier transforms. For the specific case of an exponentially decaying load the solution is obtained in closed form by means of rapidly convergent triple integrals. The simple expressions for the stress intensity factor and the energy release rate are derived. For some limiting cases the solution is found to be consistent with previous results. A parametric study gave an opportunity to examine the accuracy of the known approximate sandwich model of multilayered composites.

Optimal design of infinite repetitive structures

An approach for designing optimal repetitive structures under arbitrary static loading is presented. It is shown that the analysis of such infinite structures can be reduced to the analysis of the repeating module under transformed loading and boundary conditions. Consequently, both the design parameters and the analysis variables constitute a relatively small set which facilitates the optimization process. The approach hinges on the representative cell method. It is based on formulating the analysis equations and the continuity conditions for a sequence of typical modules. Then, by means of the discrete Fourier transform this problem translates into a boundary value problem of a representative cell in transformed variables, which can be solved by any appropriate analytical or numerical method. The real structural response any-where in the structure is then obtained by the inverse transform. The sensitivities can also be calculated on the basis of the sensitivities of the representative cell. The method is illustrated by the design for minimum compliance with a volume constraint of an infinite plane truss. It is shown that by employing this analysis method within an optimal design scheme one can incorporate a reduced analysis problem in an intrinsically small design space.

The Cardiocoil stent-artery interaction.

An analytical approach for the mechanical interaction of the self-expanding Cardiocoil stent with the stenosed artery is presented. The damage factor as the contact stress at the stent-artery interface is determined. The stent is considered as an elastic helical rod having a nonlinear pressure-displacement dependence, while the artery is modeled by an elastic cylindrical shell. An influence of a moderate relative thickness of the shell is estimated. The equations for both the stent and the artery are presented in the stent-associated helical coordinates. The computational efficiency of the model enabled to carry out a parametric study of the damage factor. Comparative examinations are conducted for the stents made of the helical rods with circular and rectangular cross sections. It was found, in particular, that, under same other conditions, the damage factor for the stent with a circular cross section may be two times larger than that for a rectangular one.

On the scale effect in the thin layer delamination problem

Influence of layer thickness on the stress distribution in the vicinity of a crack tip is examined, taking into account the fact that the conventional stress intensity factor concept becomes invalid if the thickness of the layer is not much more than the size of the fracture process zone. An eigen-problem is considered which is characterized by two asymptotes. The first is a near one; it is formed in a small vicinity of the crack tip in the layer thickness scale. The second asymptote is a far one in the same scale. The regions of validity of these asymptotes are determined and shown to depend upon layer thickness, material parameters and crack tip speed. The complete stress distribution in front of the crack is obtained, as well. Some conclusions are made concerning the stress distribution and energy release rate for the general problem. Mode III crack propagation is considered in detail.

Antiplane deformation of a periodically layered composite with a crack. A non-homogenization approach

Fracture behaviour of an infinite periodically layered composite body, with a Mode 3 crack parallel to the layering, is investigated. Upon deriving the Green function for a dislocation in a layered space, the problem is reduced to a singular integral equation of the first kind. The specific case of the bimaterial multilayered composite is considered in detail. The numerical results obtained for the stress intensity factor allows one to estimate the accuracy of the known approximate models with a reduced number of layers. It is found that for certain parameter combinations the stress intensity factor for the interface crack may exceed the corresponding value for a crack in a homogeneous space.

Mode III delamination of a viscoelastic strip from a dissimilar viscoelastic half-plane

Abstract The problem of a semi-infinite crack propagating steadily along the interface of a viscoelastic bimaterial composite is investigated. One of the constituents of the composite is a strip and the other is a dissimilar half-plane. The viscoelastic behavior of both materials is modeled as a standard solid. The crack is driven by an arbitrary traveling shear load applied to the crack faces, producing a state of antiplane strain (mode 3). The boundary value problem is reduced to a Wiener-Hopf equation and solved in closed form by means of Cauchy-type integrals. For the specific case of an exponentially decaying load, the expression for the stress intensity factor is derived and its behavior as a function of crack-tip speed for different material combinations is examined. For some limiting cases, the solution is seen to coincide with known results. The important problem of an elastic-viscoelastic composite is also considered.

STEADY-STATE MODE III PROPAGATION OF AN INTERFACE CRACK IN AN INHOMOGENEOUS VISCOELASTIC STRIP

Abstract The problem of a steady propagating semi-infinite crack between two bonded, viscoelastic infinite strips subjected to mode III deformation is investigated. A Wiener-Hopf equation is formulated and solved in closed form by means of a Cauchy-type integral. The integral is evaluated yielding the stress intensity factor for various material combinations including a homogeneous Maxwell material, two bonded Maxwell materials, a bonded elastic and Maxwell material and two standard solids. The correspondence principle is employed to obtain the stress intensity factor value for a standing crack ( i . e . v = 0). Results are presented in graphical form for some cases of interest.

Numerical models of net-structure stents inserted into arteries

INTRODUCTION Restenosis is strongly attributed to stresses caused by stent-artery interactions generated in the artery after balloon angioplasty. Numerical methods are often used to examine the stent-artery mechanical interactions. To overcome the extensive computational requirements demanded by these simulations, simplifications are needed. OBJECTIVE We introduce simplified models to calculate the mechanical interactions between net-structured stents and arteries, and discuss their validity and implications. METHODS 2D simplified numerical models are suggested, which allow cost effective assessment of arterial stresses and the potential damage factor (DF). In these models, several contact problems were solved for arteries with hyper elastic mechanical properties. Stresses were calculated for a large range of cases and for different numerical model types. The effects of model simplifications, oversizing mismatch and stenosis rate and length and symmetry on the resulting stresses were analyzed. RESULTS & CONCLUSIONS Results obtained from planar 2D models were found in good agreement with results obtained from complex 3D models for cases with axisymmetric constant or varying stenosis. This high correlation between the results of 3D cases with varying stenosis and the more simple 2D cases can be used as a simplified and convenient tool for calculating the arterial wall stresses in complex cases. Maximal stresses obtained by the 2D model with an asymmetric stenosis are lower than the maximal stresses obtained in the axisymmetric case with the same stenosis percentage. Therefore, axisymmetric models may provide the worst-case estimation values for a stent of interest.

An Inverse Shielding Effect in a Periodically Layered Composite

A plane problem for a periodically layered bimaterial composite with an interface crack is considered. After deriving the closed form analytic expression of the Green function for the point dislocation in a layered media the problem is solved by means of singular integral equations. It is found that similar to a previously considered case of antiplane deformation, increasing the stiffness of the thinner layers may lead either to increasing or to decreasing of the absolute value of the stress intensity factor. As a result, it can exceed appreciably the corresponding value for the crack in a homogeneous material. On the other hand, compared to the sandwich composite this effect is found to be limited.

Flaw Nucleation In A Brittle Open-Cell Kelvin Foam

Open-cell Kelvin foam is considered as a spatial lattice consisting of brittle elastic struts rigidly connected to each other at the nodal points. The lattice is subjected to remote uniaxial tensile loading, an initial imperfection is introduced and sequential break of the struts is observed. Different loading directions and material densities are examined and it is found that the broken struts form a plane flaw, which may be either a bridged or a usual crack. The possible crack propagation planes to be used in the fracture toughness analysis are determined.