A Crack Model of a Bone Cement Interface

1984 ◽  
Vol 106 (3) ◽  
pp. 235-243 ◽  
Author(s):  
J. P. Clech ◽  
L. M. Keer ◽  
J. L. Lewis
Keyword(s):  
Bone Cement ◽  
Cohesive Zone ◽  
Edge Crack ◽  
Crack Problem ◽  
Bimaterial Interface ◽  
Fracture Mechanisms ◽  
Homogeneous Material ◽  
Crack Model ◽  
Cement Interface ◽  
Crack Faces

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.

A Model of Tension and Compression Cracks With Cohesive Zone at a Bone-Cement Interface

1985 ◽  
Vol 107 (2) ◽  
pp. 175-182 ◽  
Author(s):  
J. P. Clech ◽  
L. M. Keer ◽  
J. L. Lewis
Keyword(s):  
Bone Cement ◽  
Uniaxial Tension ◽  
Cancellous Bone ◽  
Cohesive Zone ◽  
Stress Singularity ◽  
Continuum Theory ◽  
Strengthening Mechanism ◽  
Bimaterial Interface ◽  
Cement Interface ◽  
Crack Faces

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 Superposition Framework for Discrete Dislocation Plasticity

2004 ◽  
Vol 71 (6) ◽  
pp. 805-815 ◽  
Author(s):  
M. P. O’Day ◽  
W. A. Curtin
Keyword(s):  
Boundary Conditions ◽  
Crack Growth ◽  
Cohesive Zone ◽  
Cohesive Zone Model ◽  
Bimaterial Interface ◽  
Homogeneous Material ◽  
Plastic Behavior ◽  
Zone Model ◽  
Discrete Dislocation ◽  
Wide Range

A superposition technique is introduced that allows for the application of discrete dislocation (DD) plasticity to a wide range of thermomechanical problems with reduced computational effort. Problems involving regions of differing elastic and/or plastic behavior are solved by superposing the solutions to i) DD models only for those regions of the structure where dislocation phenomena are permitted subject to either zero traction or displacement at every point on the boundary and ii) an elastic (EL) (or elastic/cohesive-zone) model of the entire structure subject to all desired loading and boundary conditions. The DD subproblem is solved with standard DD machinery for an elastically homogeneous material. The EL subproblem requires only a standard elastic or elastic/cohesive-zone finite element (FE) calculation. The subproblems are coupled: the negative of the tractions developed at the boundaries of the DD subproblem are applied as body forces in the EL subproblem, while the stress field of the EL subproblem contributes a driving force to the dislocations in the DD subproblem structure. This decomposition and the generic boundary conditions of the DD subproblem permit the DD machinery to be easily applied as a “black-box” constitutive material description in an otherwise elastic FE formulation and to be used in a broader scope of applications due to the overall enhanced computational efficiency. The method is validated against prior results for crack growth along a plastic/rigid bimaterial interface. Preliminary results for crack growth along a metal/ceramic bimaterial interface are presented.

No-slip crack model for damaged bone/cement interface

2003 ◽  
Vol 70 (6) ◽  
pp. 757-773 ◽  
Author(s):  
Robert Rizza ◽  
Kevin Meade
Keyword(s):  
Bone Cement ◽  
Crack Model ◽  
Cement Interface

Mutual influence of the faces contact area and the pre-fracture zone near the tip of the interfacial crack

2020 ◽  
Vol 13 (3) ◽  
pp. 143-161
Author(s):  
M.V. Dudyk
Keyword(s):  
Contact Area ◽  
Fracture Zone ◽  
Mutual Influence ◽  
Interfacial Crack ◽  
Normal Displacement ◽  
Crack Model ◽  
Hopf Equation ◽  
Resistant Material ◽  
Order Of Magnitude ◽  
Crack Faces

BACKGROUND: Under plane strain conditions, a crack model was developed on a plane interface between two different materials, which assumes the existence near its tip of the faces contact area and a narrow lateral pre-fracture zone in a less crack-resistant material of the composite compound. The pre-fracture zone is modeled by the line of normal displacement rupture, on which the normal stress is equal to the tensile strength of the material. Assuming that the dimensions of the pre-fracture zone and the contact zone have the same order of magnitude and are significantly smaller than the crack length, the problem is reduced to the vector Wiener–Hopf equation. METHODS: An approximate method for solving the vector Wiener–Hopf equation was developed, which was used to obtain the equations for determining the sizes of the pre-fracture zone and the contact faces area. The pre-fracture zone orientation was determined from the condition of the potential energy maximum accumulated in the zone. Numerical calculations of the indicated parameters and analysis of their dependences on the configuration and module of external load are executed. RESULTS: A significant mutual influence of the pre-fracture zone and crack faces contact on their sizes and orientation of the zone was revealed.

scholarly journals Modified duality methods for solving an elastic crack problem with Coulomb friction on the crack faces

2020 ◽  
Vol 10 (1) ◽  
pp. 276-282
Author(s):  
Robert V. Namm ◽  
Georgiy I. Tsoy
Keyword(s):  
Variational Inequality ◽  
Elastic Body ◽  
Approximation Method ◽  
Coulomb Friction ◽  
Auxiliary Problem ◽  
Crack Problem ◽  
Successive Approximation Method ◽  
Elastic Crack ◽  
Quasi Variational Inequality ◽  
Crack Faces

AbstractWe consider an equilibrium problem for an elastic body with a crack, on the faces of which unilateral non-penetration conditions and Coulomb friction are realized. This problem can be formulated as quasi-variational inequality. To solve it, the successive approximation method is applied. On each outer step of this method, we solve an auxiliary problem with given friction. We solve the auxiliary problem by using modified Lagrange functionals. Numerical results are presented.

Mechanical consequences of fibrous membrane formation at the bone/cement interface in proximal femoral arthroplasty

1986 ◽  
Vol 19 (6) ◽  
pp. 479
Author(s):  
T.D. Brown ◽  
D.R. Pedersen ◽  
E.L. Radin ◽  
R.M. Rose
Keyword(s):  
Bone Cement ◽  
Fibrous Membrane ◽  
Membrane Formation ◽  
Cement Interface

Influence of revision arthroplasty on bone/cement interface shear strength

1987 ◽  
Vol 20 (8) ◽  
pp. 824
Author(s):  
J.E. Bechtold ◽  
Y. Dohmae ◽  
R.E. Sherman ◽  
R.B. Gustilo
Keyword(s):  
Shear Strength ◽  
Bone Cement ◽  
Revision Arthroplasty ◽  
Interface Shear Strength ◽  
Interface Shear ◽  
Cement Interface

THE INFLUENCE OF TIBIAL PROSTHESIS DESIGN FEATURES ON STRESSES RELATED TO ASEPTIC LOOSENING AND STRESS SHIELDING

2011 ◽  
Vol 11 (01) ◽  
pp. 55-72 ◽  
Author(s):  
DESMOND Y. R. CHONG ◽  
ULRICH N. HANSEN ◽  
ANDREW A. AMIS
Keyword(s):  
Bone Resorption ◽  
Bone Cement ◽  
Aseptic Loosening ◽  
Cancellous Bone ◽  
Stress Shielding ◽  
Cement Mantle ◽  
Shear Stresses ◽  
Knee Prostheses ◽  
Design Features ◽  
Cement Interface

Aseptic loosening caused by mechanical factors is a recognized failure mode for tibial components of knee prostheses. This parametric study investigated the effects of prosthesis fixation design changes, which included the presence, length and diameter of a central stem, the use of fixation pegs beneath the tray, all-polyethylene versus metal-backed tray, prosthesis material stiffness, and cement mantle thickness. The cancellous bone compressive stresses and bone–cement interfacial shear stresses, plus the reduction of strain energy density in the epiphyseal cancellous bone, an indication of the likelihood of component loosening, and bone resorption secondary to stress shielding, were examined. Design features such as longer stems reduced bone and bone–cement interfacial stresses thus the risk of loosening is potentially minimized, but at the expense of an increased tendency for bone resorption. The conflicting trend suggested that bone quality and fixation stability have to be considered mutually for the optimization of prosthesis designs. By comparing the bone stresses and bone–cement shear stresses to reported fatigue strength, it was noted that fatigue of both the cancellous bone and bone–cement interface could be the driving factor for long-term aseptic loosening for metal-backed tibial trays.

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