By the moment method established previously on the basis of the statistical mechanics, the thermodynamic properties of a strongly anharmonic crystal with the f.c.c. structure are considered. The analytic expressions for the thermodynamic quantities as the thermal expansion coefficient, the specific heats C , and Cp, the isothermal and adiabatic compressibilities, etc. are obtained.Mit einer friiher abgeleiteten Momentenmethode auf der Grundlage der statistischen Mechanik werden die thermodynamischen Eigenschaften eines stark anharmonischen Kristalls mit k.f.z.-Struktur untersucht. Die analytischen Ausdriicke fur die thermodynamischen GrBBen, wie thermischer Ausdehnungskoeffizient, spezifische Wiirme, C , und Cp, die isothermen und adiabatischen Kompressionsvermogen usw. werden erhalten.
This in vitro study investigated the stress distribution in the bone surrounding an implant that is placed in a posterior edentulous maxilla with a sinus graft. The standard threaded implant and anatomy of the crestal cortical bone, cancellous bone, sinus floor cortical bone, and grafted bone were represented in the 3-dimensional finite element models. The thickness of the crestal cortical bone and stiffness of the graft were varied in the models to simulate different clinical scenarios, representing variation in the anatomy and graft quality. Axial and lateral loads were considered and the stresses developed in the supporting structures were analyzed. The finite element models showed different stress patterns associated with helical threads. The von Mises stress distribution indicated that stress was maximal around the top of the implant with varying intensities in both loading cases. The stress was highest in the cortical bone, lower in the grafted bone, and lowest in the cancellous bone. When the stiffness of the grafted bone approximated the cortical bone, axial loading resulted in stress reduction in all the native bone layers; however, lateral loading produced stress reduction in only the cancellous bone. When the stiffness of the graft was less than that of the cancellous bone, the graft assumed a lesser proportion of axial loads. Thus, it caused a concomitant stress increase in all the native bones, whereas this phenomenon was observed in only the cancellous bone with lateral loading. The crestal cortical bone, though receiving the highest intensity stresses, affected the overall stress distribution less than the grafted bone. The stress from the lateral load was up to 11 times higher than that of the axial load around the implant. These findings suggest that the type of loading affects the load distribution more than the variations in bone, and native bone is the primary supporting structure.
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