Cracks emanating from slipping inclusions near a bone-implant interface.

It has been hypothesized that mechanical fracture at the bone-cement-implant interface is the initial cause for loosening of orthopedic implants. Previous investigators have observed cracks to emanate from methacrylate beads, apparently acting as inclusions within the cement. It is believed that the bond between these inclusions and the surrounding matrix breaks prior to emanation of radial cracks from the inclusion. An analytical model is developed for radial cracks emanating from circular inclusions that allow slip along their interface. The solution to the interaction of a single dislocation and a slipping inclusion is used as a Green's Function to model the crack. The Mode I stress intensity factors are calculated for arbitrary orientations of the crack and for varying relative stiffness of the matrix and the inclusion to test feasibility of crack growth.

Normal contact of elastic spheres with two elastic layers as a model of joint articulation.

An analytical model of two elastic spheres with two elastic layers in normal, frictionless contact is developed which simulates contact of articulating joints, and allows for the calculation of stresses and displacements in the layered region of contact. Using various layer/layer/substrate combinations, the effects of variations in layer and substrate properties are determined in relation to the occurrence of tensile and shear stresses as the source of crack initiation in joint cartilage and bone. Vertical cracking at the cartilage surface and horizontal splitting at the tidemark have been observed in joints with primary osteoarthritis. Deep vertical cracks in the calcified cartilage and underlying bone have been observed in blunt trauma experiments. The current model shows that cartilage stresses for a particular system are a function of the ratio of contact radius to total layer thickness (a/h). Surface tension, which is observed for a/h small, is alleviated as a/h is increased due to increased load, softening and/or thinning of the cartilage layer. Decreases in a/h due to cartilage stiffening lead to increased global compressive stresses and increased incidence of surface tension, consistent with impact-induced surface cracks. Cartilage stresses are not significantly affected by variations in stiffness of the underlying material. Tensile radial strains in the cartilage layer approach one-third of the normal compressive strains, and increase significantly with cartilage softening. For cases where the middle layer stiffness exceeds that of the underlying substrate, tensile stresses occur at the base of the middle layer, consistent with impact induced cracks in the zone of calcified cartilage and subchondral bone. The presence of the superficial tangential zone appears to have little effect on underlying cartilage stresses.

An analytical model of joint contact.

The stress distribution in the region of contact between a layered elastic sphere and a layered elastic cavity is determined using an analytical model to stimulate contact of articulating joints. The purpose is to use the solution to analyze the effects of cartilage thickness and stiffness, bone stiffness and joint curvature on the resulting stress field, and investigate the possibility of cracking of the material due to tensile and shear stresses. Vertical cracking of cartilage as well as horizontal splitting at the cartilage-calcified cartilage interface has been observed in osteoarthritic joints. The current results indicate that for a given system (material properties mu and nu constant), the stress distribution is a function of the ratio of contact radius to layer thickness (a/h), and while tensile stresses are seen to occur only when a/h is small, tensile strain is observed for all a/h values. Significant shear stresses are observed at the cartilage-bone interface. Softening of cartilage results in an increase in a/h, and a decrease in maximum normal stress. Cartilage thinning increases a/h and the maximum contact stress, while thickening has the opposite effect. A reduction in the indenting radius reduces a/h and increases the maximum normal stress. Bone softening is seen to have negligible effect on the resulting contact parameters and stress distribution.

Cracks emanating from circular voids or elastic inclusions in PMMA near a bone-implant interface.

Mechanical fracture is believed to be a primary reason for loss of fixation at the bone-cement-implant interface. In addition to the expected cracks at the bone-cement interface, cracks are also observed to be formed at voids and inclusions within the cement. An analytical solution is presented for cracks emanating from circular voids or elastic inclusions under uniaxial tension using the solution for a single dislocation as a Green's function. Stress intensity factors are calculated for arbitrary orientations of the cracks, and for varying relative stiffnesses of the inclusion and the matrix, to determine the most favorable combination of parameters for crack growth.

Cracks emanating from a fluid filled void loaded in compression: application to the bone-implant interface.

Loosening of orthopedic implants is believed to be caused, in part, by fracture at the bone-cement interface. This loosening occurs even in regions where the interfacial load is primarily compressive. A model is developed whereby cracks can radiate from an elliptical fluid filled void. The incompressible fluid is allowed to penetrate into the cracks when the system is loaded compressively. The mode I stress intensity factor is calculated to test the feasibility of crack growth, and a numerical scheme which uses piecewise quadratic polynomials is used to solve the resulting singular integral equations. The results show the combinations of parameters for which cracks are likely to grow.

A model of tension and compression cracks with cohesive zone at a bone-cement interface.

This paper gives an insight about compression and tension cracks as encountered at a bone-cement interface. Within the context of continuum theory of fracture, an analytical solution is presented for the problem of a bimaterial interface edge crack under uniaxial tension or compression, assuming no tangential slip along the crack faces since cement pedicles penetrate into the cancellous bone several millimeters. Also essential to the solution are cohesive zone effects that account for a strengthening mechanism over the crack faces. The solution provides a methodological framework for quantifying the influence of the cohesive zone on the magnitude of the stress singularity. Mode I crack tip stress intensity factors are calculated at different stages of the loading and unloading phases under uniaxial tension or compression. Finally, an inelastic mechanism is presented that gives theoretical support to explain the formation of interfacial compression cracks, a phenomenon that was not previously appreciated and that arises from the rigid cement being forced into the more compliant cancellous bone.

A crack model of a bone cement interface.

This paper is concerned with the fracture mechanics of a bone-cement interface that includes a cohesive zone effect on the crack faces. This accounts for the experimentally observed strengthening mechanism due to the mechanical interlock between the crack faces. Edge crack models are developed where the cohesive zone is simulated by a continuous or a discrete distribution of linear or nonlinear springs. It is shown that the solution obtained by assuming a homogeneous material is fairly close to the exact solution for the bimaterial interface edge crack problem. On the basis of that approximation, the analysis is conducted for the problem of two interacting edge cracks, one at the interface, and the other one in the cement. The small crack that was observed to initiate in the cement, close to the bone-cement interface, does not affect much the mode I stress-intensity factor at the tip of the interface crack. However it may grow, leading to a catastrophic breakdown of the cement. The analysis and following discussion point out an interdependency between bone-cement interface strength and cement strength not previously appreciated. The suggested crack models provide a framework for quantifying the fracture mechanisms at the bone-cement interface.