Plasticity and Geomechanics

When a continuum region consists of either a rigid strain hardening or an elastic strain hardening material, the strains and displacements of the region for a given history of loading can be determined. If, on the other hand, the continuum region is made of either a rigid perfectly plastic or an elastic perfectly plastic material the situation is quite different. A qualitative picture of the behaviour of such a material was discussed at the very start of this volume. For example, at sufficiently small loads the region can either remain rigid or experience small elastic deformations. As the loading increases parts of the continuum region can become plastic, but the region as a whole can withstand collapse due to the restraining effect of elastic regions. As the loads increase, larger regions of the continuum can experience plastic yield and eventually the continuum region can undergo ‘indefinite’ plastic deformations leading to what we term ‘collapse’ of the region. Two interesting examples that illustrate the definition of a ‘collapse’ state in the context of limit analysis are given by Drucker et al. (1952). In this process we implicitly assume that the deformations experienced by the continuum region are small enough so that changes in the geometry of the region may be neglected and that all the deformations take place in a quasi-static fashion so that any dynamic effects can be ignored.