Principles of Hyperplasticity is concerned with the theoretical
modelling of the behaviour of solids which undergo nonlinear and
irreversible deformation. The approach to plasticity theory
developed here is firmly rooted in thermodynamics, so that the
models developed are guaranteed to obey the First and Second Laws.
Major emphasis is placed on the use of potentials, and the
derivation of constitutive models for irreversible behaviour
entirely from two scalar potentials is shown. It is to accentuate
this feature that the authors use the term "hyperplasticity," by
analogy with the use of "hyperelasticity" in elasticity theory.
The use of potentials has several advantages. First it allows
models to be very simply defined, classified and, if necessary,
developed. Secondly, by employing Legendre Transformations, it
permits dependent and independent variables to be interchanged,
making possible different forms of the same model for different
applications. Emphasis is also placed on the derivation of
incremental response, which is necessary for numerical
analysis.
In the later parts of the book the theory is extended to include
treatment of rate-dependent materials. A new and powerful concept,
in which a single plastic strain is replaced by a plastic strain
function, allowing smooth transitions between elastic and plastic
behaviour is also introduced.
Illustrated with many examples of models derived within this
framework, and including material particularly relevant to the
field of geomechanics, this monograph will benefit academic
researchers in mechanics, civil engineering and geomechanics and
practising geotechnical engineers; it will also interest numerical
analysts inengineering mechanics.
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