Hageman, T. orcid.org/0000-0001-7770-7440, Sabet, S.A. and Borst, R. (2021) Convergence in non‐associated plasticity and fracture propagation for standard, rate‐dependent, and Cosserat continua. International Journal for Numerical Methods in Engineering, 122 (3). pp. 777-795. ISSN 0029-5981
Abstract
The use of pressure‐dependent plasticity models with a non‐associated flow rule causes a loss of the well‐posedness for sufficiently low hardening rates. Apart from a mesh dependence, this can result in poor convergence, or even divergence of the iterative procedure employed to find an equilibrium configuration. This can be aggravated when other nonlinear, dissipative mechanisms are introduced, for instance the propagation of cracks. This is demonstrated rigorously, as well as the regularizing effect of adding viscosity or employing a Cosserat continuum. In both cases the regularization is independent of the value of the internal length scale for a fairly wide range of parameters. The spatial discretization has been done using T‐splines, and the fracture is modeled using interface elements and propagated using mesh line insertions. The time integration has been done by an implicit Newmark scheme. The use of proper regularization techniques makes an implicit scheme feasible, resulting in a reduction in the number of time steps by an order of magnitude.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2020 The Authors. International Journal for Numerical Methods in Engineering published by John Wiley & Sons Ltd. This is an open access article under the terms of the Creative Commons Attribution‐NonCommercial‐NoDerivs License, which permits use and distribution in any medium, provided the original work is properly cited, the use is non‐commercial and no modifications or adaptations are made. |
Keywords: | Cosserat continuum; fracture; non‐associated plasticity; T‐splines; viscoplasticity |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Engineering (Sheffield) > Department of Civil and Structural Engineering (Sheffield) |
Funding Information: | Funder Grant number EUROPEAN COMMISSION - HORIZON 2020 664734 |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 03 Nov 2020 15:37 |
Last Modified: | 02 Feb 2022 12:37 |
Status: | Published |
Publisher: | Wiley |
Refereed: | Yes |
Identification Number: | 10.1002/nme.6561 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:167317 |