Stress analysis of contact models for isotropic articular cartilage under impacting loads shows high shear stresses at the interface with the subchondral bone and normal compressive stresses near the surface of the cartilage. These stress distributions are not consistent, with lesions observed on the cartilage surface of rabbit patellae from blunt impact, for example, to the patello-femoral joint. The purpose of the present study was to analyze, using the elastic capabilities of a finite element code, the stress distribution in more morphologically realistic transversely isotropic biphasic contact models of cartilage. The elastic properties of an incompressible material, equivalent to those of the transversely isotropic biphasic material at time zero, were derived algebraically using stress-strain relations. Results of the stress analysis showed the highest shear stresses on the surface of the solid skeleton of the cartilage and tensile stresses in the zone of contact. These results can help explain the mechanisms responsible for surface injuries observed during blunt insult experiments.
Experimental evidence suggests that the tensile behavior of tendons and ligaments is in part a function of tissue hydration. The models currently available do not offer a means by which the hydration effects might be explicitly explored. To study these effects, a finite element model of a collagen sub-fascicle, a substructure of tendon and ligament, was formulated. The model was microstructurally based, and simulated oriented collagen fibrils with elastic-orthotropic continuum elements. Poroelastic elements were used to model the interfibrillar matrix. The collagen fiber morphology reflected in the model interacted with the interfibrillar matrix to produce behaviors similar to those seen in tendon and ligament during tensile, cyclic, and relaxation experiments conducted by others. Various states of hydration and permeability were parametrically investigated, demonstrating their influence on the tensile response of the model.
Several candidate predictors for the occurrence of surface fissures in cartilage, including impact force, shear stress, and tensile strain have been previously proposed without an analytic basis. In this study a controlled impact experiment was performed where a dropped mass and three impact interfaces were used to identify loads associated with the initiation of fissuring. A Finite Element Model of each experiment was used to obtain stresses and strains associated with each impact event. The resulting experimental and analytical data were analyzed using logistic regression in order to determine the strongest predictor of a fissure, and thus to propose a failure criterion for articular cartilage during a blunt insult. The logistic regression indicated that shear stress, rather than impact force or drop height (an indicator of impact energy), was the strongest predictor for the occurrence of a fissure.
In this paper the connection is developed between the direct and indirect boundary-integral equation methods of linear elastostatics from both a physical and a mathematical viewpoint. It is shown that the indirect method in its various forms, like the direct method, can be derived from Somigliana's identity, and one particular indirect formulation is presented which reduces the mixed problem of elastostatics to a system of Cauchy singular integral equations.
RgSUM~Dans ce texte la relation est developpe entre la direct et l'indirect m6thode d'6quations int~grales de la fronti6re de l'elasticite linear des deux points de vue mathematique et physique.I1 est demonstre que la methode indirecte dans ses differents aspects resemble a la methode direct pouvant etre tire de l'identite de Somigliana. Et une formulation particuliere indirecte a ete presente. Elle reduit le problemes mixte de l'elasticite a un systeme d'equation d'integration singulier de Cauchy.
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