NON-HOMOGENEITY IN RHEOLOGY Stability Problems of Inhomogeueous Viscoelastic Media

The phenomenon of buckling in compression of an elastic inhomogeneous medium under initial stress is well known. It is illustrated by the instability of a longitudinally compressed ‘elastic plate embedded in a medium of lower rigidity. Under a critical load buckling appears suddenly in the form of a sinusoidal folding of a certain wave-length. Such sudden buckling ,will, of course, not occur in general if the solids involved are viscoelastic. The interest in studying the stability problem of viscoelastic media lies partly in some technological applications connected with the use of polymers or with the thermomechanics of metallic structures. Our main interest, however, was directed to geodynamics in an attempt to furnish the beginnings of a quantitative approach to problems of deformation of the earth’s crust. A systematic program to this effect was initiated about ten years ago and embodies several distinct areas of investigation. One such investigation was the development of general stress-strain relations: derived from the thermodynamics of irreversible processes [l]. We alsoi . had to establish a theoretical approach for the treatment of stability problems in viscoelastic media [2]. This was applied to the gradual clarification of the qualitative as well as quantitative nature of the phenomena. Along with the theoretical work a model testing program has also been initiated as an intermediate check toward its application to full-scalegeophysical configurations. The simplest problem is that of a layer embedded in an infinite medium or lying on the surface of a half-space. A longitudinal compression acts in the layer. This problem has been treated quite simply by analogy with the corresponding elastic problem [3]. The stress-strain relations are formulated operationally in the same form as in the elastic case, but the elastic moduli are replaced by operators in conformity with a general “correspondence rule”. The nature of these operators was derived from the thermodynamics of irreversible processes and Onsager’s relations. The correspondence rule leads to an immediate solution by using the