A priori time regularity estimates and a simplified proof of existence in perfect plasticity |
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Authors: | Francesco Solombrino |
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Institution: | Faculty of Mathematics, Technische Universit?t München, Garching, Germany |
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Abstract: | We revisit the time‐incremental method for proving existence of a quasistatic evolution in perfect plasticity. We show how, as a consequence of a priori time regularity estimates on the stress and the plastic strain, the piecewise affine interpolants of the solutions of the incremental minimum problems satisfy the conditions defining a quasistatic evolution up to some vanishing error. This allows for a quicker proof of existence: furthermore, this proof bypasses the usual variational reformulation of the problem and directly tackles its original mechanical formulation in terms of an equilibrium condition, a stress constraint, and the principle of maximum plastic work. |
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Keywords: | Quasistatic evolution rate‐independent processes perfect plasticity Prandtl‐Reuss plasticity shear bands incremental problems variational problems in BD 74C05 74G65 49J45 47J20 35Q72 |
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