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.
FURTHER DEVELOPMENT OF THE THEORY OF INTERNAL BUCKLING OF MULTILAYERS
The approximate theory of internal buckling of multilayers is obtained by a direct method and generalized to nonsinusoidal deformations. The numerical discussion includes the case of unequal thickness of competent and incompetent layers. Simple expressions are derived for the dominant wave length for rigid confinement or self-confinement showing the influence of interstitial flow. The theory is presented in the context of viscous media using both solid and fluid mechanics and is valid for large compressive strain and moderate slopes. Its applicability to elastic and viscoelastic media is indicated.
Theory of Stress‐Strain Relations in Anisotropic Viscoelasticity and Relaxation Phenomena
A thermodynamic derivation is given for the representation of a system having viscoelastic or relaxationproperties by means of a potential and dissipation function familiar in Lagrangian mechanics. This leads to modes of relaxation which are used as normal coordinates to derive general expressions for operational tensors relating stress and strain. A large variety of phenomena involving interaction of diffusion,chemical reaction, heat transfer, mechanical deformation, etc., is included in this theory.