Commun. Comput. Phys., 11 (2012), pp. 1525-1546.

On Computational Modelling of Strain-Hardening Material Dynamics

Philip Barton 1*, Evgeniy Romenski 2

1 Graduate Aerospace Laboratories, California Institute of Technology, California 91125, USA.
2 Sobolev Institute of Mathematics, Russian Academy of Sciences, Novosibirsk 630090, Russia.

Received 17 December 2010; Accepted (in revised version) 27 May 2011
Available online 23 December 2011


In this paper we show that entropy can be used within a functional for the stress relaxation time of solid materials to parametrise finite viscoplastic strain-hardening deformations. Through doing so the classical empirical recovery of a suitable irreversible scalar measure of work-hardening from the three-dimensional state parameters is avoided. The success of the proposed approach centres on determination of a rate-independent relation between plastic strain and entropy, which is found to be suitably simplistic such to not add any significant complexity to the final model. The result is sufficiently general to be used in combination with existing constitutive models for inelastic deformations parametrised by one-dimensional plastic strain provided the constitutive models are thermodynamically consistent. Here a model for the tangential stress relaxation time based upon established dislocation mechanics theory is calibrated for OFHC copper and subsequently integrated within a two-dimensional moving-mesh scheme. We address some of the numerical challenges that are faced in order to ensure successful implementation of the proposed model within a hydrocode. The approach is demonstrated through simulations of flyer-plate and cylinder impacts.

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PACS: 81.40.Ef, 83.85.St, 83.60.La, 81.40.Lm, 83.10.Gr
Key words: Entropy, viscoplasticity, solid mechanics, relaxation time, Maxwell solid, Eulerian.

*Corresponding author.
Email:, (P. Barton), (E. Romenski)

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