I. F. Collins, A note on the interpretation of Coulomb’s analysis of the thrust on a rough retaining wall in terms of the limit theorems of plasticity theory, Geotechnique, 24, 442-447 (1973). A. Drescher and E. Detournay, Limit load in translational failure mechanisms for associative and non-associative materials, Geotechnique, 43, 443-456 (1993). J. Heyman, Coulomb’s […]

Coulomb’s retaining wall analysis was based on equilibrium of forces acting upon a wedge of soil isolated behind the retaining wall. His method is generally referred to as a limiting equilibrium analysis. It gives exactly the same result as the energy balance method used in the upper bound theorem for any translational collapse mechanism.* Moreover […]

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 concept of the uniqueness of a solution is an essential requirement to the well-posed nature of a boundary value problem. A uniqueness theorem assures us that there is only one solution possible for the governing set of equations subject to appropriate boundary conditions. In EG we have discussed a uniqueness theorem in the context […]

In Appendix E we have examined Drucker’s postulate for the stability of the material undergoing plastic deformations. To develop the plastic constitutive equations or the associated flow rule it is necessary to assume that a yield function exists, i. e. Consider the point B in Figure F.1, which is located on the yield surface f […]

An approach to the development of the constitutive equations of plasticity involves the consideration of plastic energy dissipation in an irreversible process. This is somewhat analogous to the determination of the constitutive equations for an elastic material by considering the energy stored during deformation. The notion of material stability is an important aspect of the […]

An extremum principle is basically a mathematical concept that relies on some phys­ical law. In mechanics, extremum principles such as the principle of minimum total potential energy and minimum total complementary energy form an important base of knowledge that has provided the means for obtaining approximate solutions to a variety of problems in engineering. This […]

The principles of virtual work, which bring together the concepts of equilibrium and compatibility, or kinematics, are an important development in the mechanics of solids and in applied mechanics in general. The fact that the principles do not rely on the constitutive behaviour that pertains to the material is a major advantage in their applicability […]

We can extend Mohr circle construction to three dimensions. As with the two­dimensional case the procedure is most conveniently demonstrated using the principal stress state where a1 is the maximum principal stress, a2 is the intermediate principal stress and a3 is the minimum principal stress with the result, o1 > o2 > a3. The result […]

The graphical construction for the representation of the state of stress at a point within a continuum region is generally attributed to the German engineer Otto Christian Mohr. Although the use of graphical techniques in structural and solid mechanics has been an important area of activity both for engineering calculations and stress analysis, par­ticularly in […]