Parametric Study on an Integral-Type Nonlocal Elastoplasticity Model Regularized with Tikhonov-Phillips Method
Publication: Journal of Engineering Mechanics
Volume 146, Issue 12
Abstract
An integral-type nonlocal elastoplasticity model is proposed and formulated in a one-dimensional scenario to address the strain-softening problem. This nonlocal model includes not only the nonlocal plasticity but also the nonlocal elasticity. The resulting elastic constitutive equation and the plastic consistency condition are ill-posed Fredholm integral equations of the first kind whose solutions are instable without appropriate regularization. In this paper, the Tikhonov-Phillips regularization method is used to reformulate the integral-differential consistency condition to obtain an approximate solution of the local internal variable, which is stable and smooth. A detailed parametric study is carried out to examine the influences of the regularization parameter, the internal length scale, the plastic modulus ratio, and the tolerance of the nonlocal yield condition on the regularized solutions. A numerical example shows that the solutions from the proposed model and the regularization method are mesh-independent. A comparison of the results from the proposed model with those from the nonlocal plasticity model and from the gradient-dependent plasticity model shows good agreement.
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Data Availability Statement
All data, models, and code generated or used during the study appear in the published article.
Acknowledgments
The research has been supported by the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry of China. This support is gratefully acknowledged.
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Published In
Journal of Engineering Mechanics
Volume 146 • Issue 12 • December 2020
Copyright
© 2020 American Society of Civil Engineers.
History
Received: Feb 10, 2019
Accepted: Aug 23, 2020
Published online: Oct 15, 2020
Published in print: Dec 1, 2020
Discussion open until: Mar 15, 2021
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