Page 165 - Analysis and Design of Energy Geostructures

138 Analysis and Design of Energy Geostructures

addressed: in this context, the aim is to characterise the reversible mechanical behav-
iour of materials through the essentials of the theory of thermoelasticity. Afterward,
plasticity and thermoplasticity are addressed: in this part, the objective is to characterise
the irreversible mechanical behaviour of materials through the essentials of the theories
of plasticity and thermoplasticity. Finally, questions and problems are proposed: the pur-
pose of this part is to fix and test the understanding of the subjects covered in this
chapter by addressing a number of exercises.

4.2 Idealisations and assumptions

As highlighted in Chapter 3, Heat and mass transfers in the context of energy geostruc-
tures, the materials constituting energy geostructures, soils and rocks arediscreteinnature.
However, mathematical models based on the continuum medium idealisation and the
concept of Representative Elementary Volume (REV) allow describing, predicting and
analysing key aspects of the behaviour of materials (discrete in particular). In the follow-
ing, the continuum idealisation and the REV concept are employed to model the
mechanical behaviour of materials, by further assuming that they are isotropic and homo-
geneous unless otherwise specified (cf. Fig. 4.1A). According to the continuum medium
idealisation, the heterogeneous nature of geomaterials is neglected, and, in the simplest
case, the presence of at least one fluid phase in addition to the solid phase constituting
the structure of materials is also neglected. The consideration of at least one fluid phase in
addition to the solid phase in the structural characterisation of materialsinvolveschal-
lenges in the analysis of deformation phenomena. These challenges are discussed in
Appendix B for both isothermal and nonisothermal conditions while providing the essen-
tials of a framework for the hydromechanical and thermohydromechanical modelling of
geomaterials.
Among the various theories that may be considered for describing the mechanical
behaviour of materials (and general structural systems) subjected to perturbations (e.g.
loads) under nonisothermal conditions, the theories of thermoelasticity, (isothermal)
plasticity and thermoplasticity are addressed in the following because of their relevance
for the analysis and design of energy geostructures. The mathematical formalisation of
the theory of thermoelasticity has been developed by Duhamel (1835), based on the
classical (or isothermal) theory of elasticity (see, e.g. Hooke, 1678; Navier, 1821;
Cauchy, 1823; Lamé and Clapeyron, 1831; Saint Venant, 1870). In a similar way, the
theory of thermoplasticity has been expanded by Prager (1958), based on the unified
framework characterising the theory of isothermal plasticity (see, e.g. Prager, 1949;
Drucker and Prager, 1952).
The theories of elasticity and thermoelasticity address a reversible mechanical behav-
iour of materials (and general structural systems) by neglecting and considering sensi-
tivity to temperature variations for this behaviour, respectively. In the former