Page 201 - Analysis and Design of Energy Geostructures

174 Analysis and Design of Energy Geostructures

thorough modelling of the mechanical behaviour of geomaterials, although flow rules
based on associated flow are typically employed for simplicity.

4.10.4 Perfect plasticity
The concept of perfect plasticity is associated with the mechanical behaviour of mate-
rials that while yielding do not present a further increase of stress for an increase in
strain (i.e. a plateau is observed in two dimensions, cf. Fig. 4.19). The concept of per-
fect plasticity has been initially used to solve geotechnical stability problems involving
geomaterials by Coulomb (1773) and Rankine (1857), and has been successively
applied to the analysis of other materials such as metals by Saint Venant (1870) and
Lévy (1870), for example.
Materials behaving according to the theory of perfect plasticity are characterised by
the same size and shape of the yield surface under the development of plastic deforma-
tions. In these situations, the yield function is only a function of the stress state. In the
other words, the elastic domain characterising the mechanical behaviour of perfectly
plastic materials is always the same.
The simplest mathematical expression of the yield surface for a perfectly plastic
material reads

f 5 f σ ij 5 0 ð4:88Þ
where σ ij is the relevant stress (i.e. total or effective stress). The stress conditions char-
acterising the reversible and irreversible response of materials with a thermoelastic (or
elastic), perfectly plastic behaviour are as follows

Reversible behaviour f σ ij , 0or df , 0 ð4:89Þ

Irreversible behaviour f σ ij 5 0 and df 5 0 ð4:90Þ

Figure 4.19 Concept of perfect plasticity.