Page 231 - Analysis and Design of Energy Geostructures

204 Analysis and Design of Energy Geostructures

modelled material (or general system) is characterised by a thermo-
elastic, thermoplastic behaviour.
dd. The yield criterion defines all of the possible stress states that are
associated with a reversible mechanical behaviour of the material
as well as those that are associated with an irreversible mechanical
behaviour of the material (depending on the loading situation).
The limit of the elastic domain characterising the mechanical
behaviour of a material can be expressed mathematically through
the following general yield surface (or yield function)

f 5 0

ee. If the unit normal to the plastic potential approaches a finite num-
ber of linearly independent limiting values as the stress point
approaches the singular point in question, the following generalised
flow rule can be considered:
N @g
X
p
dε 5 dλ p k
ij k
@σ ij
k51
ff. Materials behaving according to the theory of hardening plasticity are char-
acterised by a size, location or shape of the yield surface that may change
under the development of plastic deformations:
a. True
b. False
gg. The yield function of hardening materials only depends the stress state:
a. True
b. False
hh. Materials characterised by hardening and an elastic limit that is
considered to be sensitive to temperature are characterised by the
following yield function:

~
f 5 f σ ij ;h i ;T 5 0
ii. The condition of consistency for materials characterised by hard-
ening and an elastic limit that is considered to be sensitive to tem-
perature reads:
@f @f @f
~
df 5 dσ ij 1 dh i 1 dT 5 0
~
@σ ij @h i @T