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Structural Engineering and Mechanics Volume 17, Number 1, January 2004 , pages 087-97 DOI: https://doi.org/10.12989/sem.2004.17.1.087 |
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Incompatible 3-node interpolation for gradient-dependent plasticity |
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G. Chen and G. Baker
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| Abstract | ||
| In gradient-dependent plasticity theory, the yield strength depends on the Laplacian of an equivalent plastic strain measure (hardening parameter), and the consistency condition results in a differential equation with respect to the plastic multiplier. The plastic multiplier is then discretized in addition to the usual discretization of the displacements, and the consistency condition is solved simultaneously with the equilibrium equations. The disadvantage is that the plastic multiplier requires a Hermitian interpolation that has four degrees of freedom at each node. Instead of using a Hermitian interpolation, in this article, a 3-node incompatible (trigonometric) interpolation is proposed for the plastic multiplier. This incompatible interpolation uses only the function values of each node, but it is continuous across element boundaries and its second-order derivatives exist within the elements. It greatly reduces the degrees of freedom for a problem, and is shown through a numerical example on localization to yield good results. | ||
| Key Words | ||
| gradient-dependent plasticity; incompatible element; trigonometric interpolation; strain localization. | ||
| Address | ||
| Faculty of Engineering & Surveying, The University of Southern Queensland, Toowoomba, QLD 4350, Australia | ||