Principles of Hyperplasticity

The approach to plasticity theory developed here is firmly rooted in thermodynamics. Emphasis is placed on the use of potentials and the derivation of incremental response, necessary for numerical analysis. This monograph benefits academic researchers in mechanics, civil engineering and geomechanics and practising geotechnical engineers. 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 in engineering mechanics.