Page 164 - Analysis and Design of Energy Geostructures

CHAPTER 4

Deformation in the context of energy

geostructures

4.1 Introduction
Deformation and heat transfer phenomena arise because of the gradient of physical
variables and may be considered independently from each other. Deformation charac-
terises the mechanical behaviour of materials and is often associated with the influence
of mechanical loads. Heat transfer characterises the thermal behaviour of materials and
is often associated with the influence of thermal loads. However, deformation and
heat transfer are coupled phenomena, similar to heat transfer and mass transfer. That is
heat transfer can influence the deformation of materials and the opposite is true. This
fact implies that the thermal and mechanical behaviours of materials are coupled.
Deformation phenomena under nonisothermal conditions characterise energy geos-
tructures through the thermomechanical response of the materials involved.
Understanding the physical principles governing deformation phenomena under noni-
sothermal conditions and accounting in a suitable way for these phenomena in the
analysis and design of energy geostructures is paramount.
This chapter presents a theoretical analysis of deformation phenomena that can
occur under nonisothermal conditions associated with heat transfer processes in the
context of energy geostructures. The topic is addressed by focusing on the essentials of
the theories of thermoelasticity, plasticity and thermoplasticity that may be considered
for the characterisation of the thermomechanical behaviour of materials and the related
analysis and design of energy geostructures. Comments on the coupling between
deformation and heat transfer are also provided.
To this aim, idealisations and assumptions are presented first: in this context, the
objective is to propose a summary of the conceptual descriptions and hypotheses that
are employed for describing deformation phenomena under nonisothermal conditions.
Second, the concepts of strain, compatibility and stress are addressed: the purpose of this
part is to expand on fundamental variables and principles governing the description of
the mechanical response of materials. Third, the momentum equilibrium equation and
boundary conditions are presented: the purpose of this part is to define the equations
governing the equilibrium of materials under loading. Next, generalities about stress
strain relations are introduced: the goal of this section is to elaborate on mathematical
expressions relating strains to stresses and the opposite. Later, thermoelasticity is

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Analysis and Design of Energy Geostructures
DOI: https://doi.org/10.1016/B978-0-12-816223-1.00004-7 All rights reserved. 137