Plasticity - Mathematical Theory and Numerical Analysis

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Plasticity - Mathematical Theory and Numerical Analysis

The basis for the modern theory of elastoplasticity was laid in the nineteenth-
century, by Tresca, St. Venant, Levy ́ , and Bauschinger. Further
major advances followed in the early part of this century, the chief contributors during this period being Prandtl, von Mises, and Reuss. This early phase in the history of elastoplasticity was characterized by the introduction and development of the concepts of irreversible behavior, yield criteria, hardening and perfect plasticity, and of rate or incremental constitutive equations for the plastic strain. Greater clarity in the mathematical framework for elastoplasticity theory came with the contributions of Prager, Drucker, and Hill, during the period just after the Second World War. Convexity of yield surfaces, and all its ramifications was a central theme in this phase of the development of the theory.

The mathematical community, meanwhile, witnessed a burst of progress
in the theory of partial differential equations and variational inequalities
from the early 1960s onwards. The timing of this set of developments was
particularly fortuitous for plasticity, given the fairly mature state of the
subject, and the realization that the natural framework for the study of
initial boundary value problems in elastoplasticity was that of variational
inequalities. This confluence of subjects emanating from mechanics and

mathematics resulted in yet further theoretical developments, the out-
standing examples being the articles by Moreau, and the monographs

Weimin Han B. Daya Reddy

เครดิตไฟล์ :

Weimin Han B. Daya Reddy

ผู้อัพโหลด : tumcivil

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