A Review of Mixture and Non-Local Continuum Mechanics with Example Applications to Cohesive Sediments

Abstract

The purpose here is to assess the potential application of mixture and nonlocal continuum models to cohesive sediments. Mixture models are discussed first. A review of this theory shows that this approach requires continuity and equations of motion for each constituent. A general constitutive model based on concepts from viscoelasticity is developed. The problem of the propagation of acoustic waves is examined as a special case of the model. For a two-constituent medium two dispersive acoustical modes are found; however, one is strongly attenuated. A mixture model is also applied to the problem of plane shear. The analysis shows solid displacement and fluid velocity profiles which can differ remarkably from the classic linear solutions. Next non-local models are investigated. This approach results in stress strain relations which are integrodifferential equations. Acoustical propagation for three different integral kernels is studied. All three models exhibit dispersion at low frequencies; however, there seems to be little practical difference between the solutions associated with the different kernels. The plane shear problem is also investigated. The analysis reveals displacement profiles which differ from the classic solution. The paper is concluded with a brief summary of results and some suggestions for more realistic applications.