Analysis of Tikhonov Regularization on the Integral-Type Nonlocal Plasticity Model
Publication: Journal of Engineering Mechanics
Volume 143, Issue 9
Abstract
Tikhonov regularization on the integral-type nonlocal plasticity model is proposed to obtain a mesh-independent solution of strain localization. A detailed parametric study on the Tikhonov-regularized model is carried out for a one-dimensional and a two-dimensional problem. The influence of the regularization parameter, the tolerance of the nonlocal yield criterion, and the internal length scale on the finite-element solutions are examined. The width of the localization zone was found to be six times the internal length scale for a Gaussian-type weighting function. The solutions of the two-dimensional shear banding problem are compared with those of the one-dimensional strain localization. With the proposed model, no additional boundary conditions have to be introduced in the constitutive level, and only continuity is needed at element interfaces.
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Acknowledgments
The author acknowledges the financial support provided by the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry of China. Partial results described in this paper are obtained on the China Scientific Computing Grid (ScGrid).
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Published In
Journal of Engineering Mechanics
Volume 143 • Issue 9 • September 2017
Copyright
©2017 American Society of Civil Engineers.
History
Received: Sep 11, 2016
Accepted: Mar 30, 2017
Published online: Jul 12, 2017
Published in print: Sep 1, 2017
Discussion open until: Dec 12, 2017
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