The functional for minimization following from the upper bound theorem depends on the constitutive law chosen. The effect of simultaneous deformation of viscoplastic and rigid perfectly plastic materials on the mathematical formulation of upper bound solutions is studied. The results show that, in contrast to the conventional formulation in the theory of rigid perfectly plastic solids, it is in general impossible to get an upper bound of the load applied. Instead, an approximate value of this load can be found. The theory is illustrated by a solution for plane-strain compression of a three-layer strip between two parallel, rough plates.
rigid perfectly plastic model viscoplastic model bi-material interface friction upsetting process
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