A COURSE IN MATHEMATICAL THEORY OF PLASTICITY

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     Theory of plasticity is the mathematical study of stress and strain in plastically deformable solids. It is an extension of the well-established precedent set by the “theory of elasticity” which deals with the calculation of strain and stress distributions in elastically deformable solids. Elastic and plastic deformations, however, are quite different in nature; the former is reversible, while the latter is irreversible, thereby being memory-dependent because of microstructural complexities of plastic flow. Plastic strains are residual strains, and contrary to elastic deformations, cannot be removed upon complete unloading. 
     History of plasticity as a science began in 1864 with the papers of Tresca on punching and extrusion and formulation of his famous yield criterion. Thereafter, Saint-Venant and Lévy laid some of the foundations of the present-day plasticity theory. Important contributions were made by von Mises, Henky and Prandtl. It is only after 1945 that a unified theory began to emerge and progressed with the advent of modern continuum mechanics in 1960s. 
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