Incompatible 4-node element for gradient-dependent plasticity

Chen, G. and Baker, Graham (2004) Incompatible 4-node element for gradient-dependent plasticity. Advances in Structural Engineering, 7 (2). pp. 169-177. ISSN 1369-4332

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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 on the mesh, in addition to the usual discretization of the displacements, and the consistency condition is solved simultaneously with the equilibrium equations. The notorious disadvantage is that the plastic multiplier requires a Hermitian interpolation which has four degrees of freedom at each node. However, in this article, an incompatible (trigonometric) interpolation is proposed for the plastic multiplier. This incompatible interpolation uses only the function values of each node, but both the function and first-order derivatives are continuous across element boundaries. It greatly reduces the degrees of freedom for a problem, and is shown through numerical examples on localization to give good results.

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Item Type: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Additional Information: Awaiting Author and Publisher versions from Author. Deposited with blanket permission of Publisher.
Faculty/School / Institute/Centre: Current - USQ Other
Faculty/School / Institute/Centre: Current - USQ Other
Date Deposited: 31 Mar 2008 06:33
Last Modified: 08 Jun 2012 03:47
Uncontrolled Keywords: gradient-dependent plasticity; incompatible element; trigonometric interpolation; strain localization
Fields of Research (2008): 09 Engineering > 0905 Civil Engineering > 090506 Structural Engineering
01 Mathematical Sciences > 0103 Numerical and Computational Mathematics > 010301 Numerical Analysis
09 Engineering > 0905 Civil Engineering > 090503 Construction Materials
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