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Numerical Implementation of Continuum Dislocation Dynamics with the Discontinuous-Galerkin Method.

Published online by Cambridge University Press:  09 January 2014

Alireza Ebrahimi*
Affiliation:
Universität Bremen, Am Biologischen Garten 2, 28359 Bremen, Germany
Mehran Monavari
Affiliation:
Friedrich-Alexander-Universität Erlangen-Nürnberg, Dr.-Mack-Str. 77, Fürth, Germany
Thomas Hochrainer
Affiliation:
Universität Bremen, Am Biologischen Garten 2, 28359 Bremen, Germany
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Abstract

In the current paper we modify the evolution equations of the simplified continuum dislocation dynamics theory presented in [T. Hochrainer, S. Sandfeld, M. Zaiser, P. Gumbsch, Continuum dislocation dynamics: Towards a physical theory of crystal plasticity. J. Mech. Phys. Solids. (in print)] to account for the nature of the so-called curvature density as a conserved quantity. The derived evolution equations define a dislocation flux based crystal plasticity law, which we present in a fully three-dimensional form. Because the total curvature is a conserved quantity in the theory the time integration of the equations benefit from using conservative numerical schemes. We present a discontinuous Galerkin implementation for integrating the time evolution of the dislocation state and show that this allows simulating the evolution of a single dislocation loop as well as of a distributed loop density on different slip systems.

Type
Articles
Copyright
Copyright © Materials Research Society 2014 

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References

Acharya, A., J. Mech. Phys. Solids 49, 761784 (2001).CrossRef
Hochrainer, T., Zaiser, M., Gumbsch, P., Philos. Mag. 87, 12611282 (2007)CrossRef
Hochrainer, T., Sandfeld, S., Zaiser, M., Gumbsch, P., J. Mech. Phys. Solids. (in print)
Hochrainer, T. MRS Proceedings, 1535, mmm2012-a-0343 doi:10.1557/opl.2013.451. (2013)CrossRef
Bangerth, W., Hartmann, R. and Kanschat, G., ACM Trans. Math. Softw. 33 (4) 24/1–24/27 (2007)CrossRef
Hartmann, R., Houston, P., J. Comput. Phys., 183 508532, (2002)CrossRef
Hochrainer, T., MRS Proceedings (this volume)

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Numerical Implementation of Continuum Dislocation Dynamics with the Discontinuous-Galerkin Method.
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