THEORY OF VISCOUS BUCKLING AND GRAVITY INSTABILITY OF MULTILAYERS WITH LARGE DEFORMATION
An exact treatment of the stability of multilayered viscous fluids in slow motion with large deformations leads to an analog model which includes the effect of gravity. A distinction can be made between true mechanical instability and an apparent instability of purely kinematic nature. A mechanism for concentric folding is derived, leading to predictions in good agreement with experimental results (De Sitter, 1939). Exact equations are obtained for the time history of viscous buckling of multilayered fluids for small deflections superimposed upon a large variable compressible strain. A numerical application to the single embedded layer checks the practical validity of the simplified thin-layer theory with interfacial slip. For gravity instability, the analog model provides a method of analysis applicable to very large deformations in salt structures.
Rheological stability with couple stresses and its application to geological folding
The author’s theory of elasticity and viscoelasticity of initially stressed anisotropic solids is extended to include couple stresses and an additional refinement represented by a dependence of the deformation on the second gradient of the stress. The theory is intended to provide an approximate continuous model valid over a wide range for the mechanics of laminated media. The equations derived for the continuous model are rigorous for a medium initially at rest under the initial stress but are applicable as an approximation to stability problems of viscous and plastic media which exhibit initial strain rate with finite strain. The effect of gravity is included. A ‘couple-stress analogy’ renders immediately applicable to the medium with couple stresses a large class of solutions obtained earlier for plates and multilayers under initial stress. The problem of internal buckling is discussed. The theory is particularly suited to the analysis of folding and gravity instability of stratified sedimentary rock and remarkably simple results are shown to provide striking verification when applied to a wide variety of geological structures.
Hill country sheep production. I. The influence of age, flock, and year on some components of reproduction rate in Romney and Border Leicester × Romney ewes.
Data from 7,091 straightbred Romney and Border Leicester × Romney ewes grazed at the Whatawhata Hill Country Research Station over the period 1959 to 1967 have been used to obtain estimates of flock and age-of-ewe effects on reproduction rate and its components and of year-to-year variation. The ewes were from six groups: a Romney control (RCR) flock, a Romney flock in which ewes were mated either to Romney (RER) or to Border Leicester rams (REB), and flocks of first-cross (F1), second-cross (F2), and third-cross (F3) Border Leicester × Romney ewes mated to first-cross Border Leicester × Romney rams. The ewes' ages at lambing varied from 2 to 5 years and no selection was practised. The ratio of number of lambs weaned per ewe present at lambing increased from the RCR (0.84) to the F1 (1.07), then declined with interbreeding to the F2 (0.92) and further to the F3 (0.87) ewes. Similar changes were evident for the percentage of ewes lambing, of multiple births, and of lambs surviving to weaning. Over...