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.
Buckling instability in arteries.
Arteries can become tortuous in response to abnormal growth stimuli, genetic defects and aging. It is suggested that a buckling instability is a mechanism that might lead to artery tortuosity. Here, the buckling instability in arteries is studied by examining asymmetric modes of bifurcation of two-layer cylindrical structures that are residually stressed. These structures are loaded by an axial force, internal pressure and have nonlinear, anisotropic, hyperelastic responses to stresses. Strain-softening and reduced opening angle are shown to lower the critical internal pressure leading to buckling. In addition, the ratio of the media thickness to the adventitia thickness is shown to have a dramatic impact on arterial instability.
Folding of a layered viscoelastic medium derived from an exact stability theory of a continuum under initial stress
A layer of viscoelastic material embedded in an infinite medium also viscoelastic tends to fold through instability when the system is compressed in a direction parallel with the layer. This phenomenon which was treated previously by using an approximate plate theory, (l, 21, is analyzed here by using an exact theory for the deformation of a continuum under prestress (3, 4, 5, 61. The effect of the compressive prestress in the embedding medium is taken into account, and it is found that although it is not always negligible, it tends to be very small under conditions where the instability of the layer is strong. The same conclusion holds for the error involved in the use of a plate theory for the layer instead of the exact equations for a prestressed continuum. In the course of the analysis we have also treated the problem of a semi-infinite visco- elastic half space subject to a uniform internal compression parallel with the boundary and a surface load normal to this boundary. The compressive load produces an increase of the surface deflection under the normal load. This effect appears through an ampli- fication factor which is evaluated numerically for the particular example of an elastic body. It is shown that under certain conditions the free surface of the compressed semi- infinite medium may become unstable and will tend to wrinkle. This is suggested as a probable explanation for the wrinkles which appear on the surface of a body subjected to a plastic compression. 1. Introduction. We consider a layer of viscoelastic material surrounded by an un- bounded medium also viscoelastic, the whole system being subject to compressive stresses parallel with the direction of the layer. Such stresses may be set up for instance if the whole system is subject to a uniform compressive strain parallel with the layer.