Two Concepts of Continuum Deformation Kinematics: Displacement Field of Points and Displacement Fields of Material Planes

The author discusses the deformation kinematics method using the concept of displacement of material planes in a medium. Displacements of planes can be described by two vector fields of displacement or, by way of alternative, by one tensor field which is a field of relative displacement of planes. This is an asymmetric tensor, and its components are uncorrelated by Saint-Venant’s compatibility conditions. This approach recovers an “equality” between the kinematic-based and force-based descriptions of deformation in a medium. The adopted notion of stresses relates to the forces that affect planes inside a body, and the notion of deformation relates to the change of distances between pairs of points. The article gives a case-study of modeling an initially isotropic geomedium using this approach.