Numerical Study of Microstructures in Single-Slip Finite Elastoplasticity

Sergio Conti () and Georg Dolzmann ()
Additional contact information
Sergio Conti: Universität Bonn
Georg Dolzmann: Universität Regensburg

Journal of Optimization Theory and Applications, 2020, vol. 184, issue 1, No 4, 43-60

Abstract: Abstract A model problem in finite elastoplasticity with one active slip system in two dimensions is considered. It is based on the multiplicative decomposition of the deformation gradient and includes an elastic response, dissipation and linear hardening. The focus lies on deformation theory of plasticity, which corresponds to a single time step in the variational formulation of the incremental problem. The formation of microstructures in different regions of phase space is analyzed, and it is shown that first-order laminates play an important role in the regime, where both dissipation and hardening are relevant, with second- and third-order laminates reducing the energy even further. No numerical evidence for laminates of order four or higher is found. For large shear and bulk modulus, numerical convergence to the rigid-plastic regime is verified. The main tool is an algorithm for the efficient search for optimal microstructures, which are determined by minimization of the condensed energy. The presently used algorithm and code are extensions of those previously developed for the study of relaxation in sheets of nematic elastomers.

Keywords: Elastoplasticity; Single slip; Quasiconvexity; Relaxation; 49J45; 74B20; 74C15 (search for similar items in EconPapers)
Date: 2020
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10957-018-01460-0 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:joptap:v:184:y:2020:i:1:d:10.1007_s10957-018-01460-0

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10957/PS2

DOI: 10.1007/s10957-018-01460-0

Access Statistics for this article

Journal of Optimization Theory and Applications is currently edited by Franco Giannessi and David G. Hull

More articles in Journal of Optimization Theory and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().