Abstract
We look for the simplest configuration which will lead to the problems most characteristic of plasticity—the contrast between incremental flow laws and deformation theory, and between the collapse of a perfectly plastic structure and its continued stresses and strains when hardening is allowed. The problems are to be continuous rather than discrete, and not one-dimensional; they will be governed by linear partial differential equations with inequality constraints. Each has a primal form in which the stresses are the unknowns, and a dual in terms of velocities or displacements. Our main goal is to clarify these different possibilities, in the case known as antiplane shear.
The preparation of this paper was supported by the National Science Foundation (MCS 76-22289).
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Strang, G. (1979). A family of model problems in plasticity. In: Glowinski, R., Lions, J.L., Laboria, I. (eds) Computing Methods in Applied Sciences and Engineering, 1977, I. Lecture Notes in Mathematics, vol 704. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0063627
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DOI: https://doi.org/10.1007/BFb0063627
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