Reflection of plane waves from the boundary of a pre-stressed compressible elastic half-space

The effect of pre-stress on the propagation and reflection ofplane waves in an incompressible isotropic elastic half-spacehas been examined recently by the authors (Ogden & Sotiropoulos,1997). In the present paper the corresponding analysis for compressiblematerials is detailed. In the two-dimensional context consideredfor incompressible materials the (homogeneous) plane waves werenecessarily shear waves. By contrast, in the compressible contextpure shear waves can propagate only in specific directions inthe considered principal plane and, in a general direction,a quasi-shear wave may be accompanied by a quasi-longitudinalwave, as is the case in the anisotropic linear theory. The dependenceof the (in-plane) slowness section on the pre-stress (and finitedeformation) and on the choice of constitutive law is elucidated.This information is used to determine the reflection coefficientsfor reflection of either a (quasi-) shear wave or a (quasi-)longitudinal wave from the boundary of the half-space and tocharacterize the different cases which arise depending on thegeometry of the slowness section. The theoretical results are illustrated by numerical calculationsfor the range of possible types of behaviour with referenceforms of strain-energy function and different states of finitedeformation and to the question of stability of the half-space.     

Estimating lean mass over a wide range of body composition: a calibration of deuterium dilution in the arctic ground squirrel

Calculating body water through isotope dilution has become a useful way to nondestructively estimate body composition in many species. The most accurate estimates using this method require calibration against proximate chemical analysis of body composition for individual species, but no studies to our knowledge have calibrated this method on a hibernating mammal that seasonally undergoes dramatic changes in body composition. We use deuterium oxide to estimate total body water in captive arctic ground squirrels, Urocitellus parryii, and compare two approaches of calculating lean mass from total body water, both calibrated against lean mass based on proximate analysis. The first method uses a single tissue hydration constant to calculate lean mass from total body water; the second method uses a predictive equation to calculate lean mass from total body water and body mass. We found that the predictive equation performs better over the large range of body composition common to this species. Distillation of blood samples did not affect lean mass estimates from either calculation method. These findings indicate that isotope dilution using a predictive equation should work well as an alternative to destructive methods in other small mammals that undergo radical changes in body composition across their annual cycle.