Incompatible 3-node interpolation for gradient-dependent plasticity

Chen, G. and Baker, Graham (2004) Incompatible 3-node interpolation for gradient-dependent plasticity. Structural Engineering and Mechanics , 17 (1). pp. 87-97. ISSN 1225-4568

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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 die 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.

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Item Type: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Additional Information: Abstract only. Author version not held.
Faculty / Department / School: Historic - Faculty of Engineering and Surveying - Department of Agricultural, Civil and Environmental Engineering
Date Deposited: 17 May 2010 23:27
Last Modified: 18 May 2010 03:09
Uncontrolled Keywords: gradient-dependent plasticity; incompatible element; strain localization; trigonometric interpolation
Fields of Research : 09 Engineering > 0905 Civil Engineering > 090503 Construction Materials
09 Engineering > 0905 Civil Engineering > 090506 Structural Engineering

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