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On Computational Modelling Of Strain-Hardening Material Dynamics

Published online by Cambridge University Press:  20 August 2015

Philip Barton  and
Evgeniy Romenski
Philip Barton*
Affiliation:
Graduate Aerospace Laboratories, California Institute of Technology, California 91125, USA
Evgeniy Romenski*
Affiliation:
Sobolev Institute of Mathematics, Russian Academy of Sciences, Novosibirsk 630090, Russia
*
Corresponding author.Email:ptbarton@caltech.edu, phil.t.barton@gmail.com
Email:evrom@math.nsc.ru
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Abstract

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 proposedmodel within a hydrocode. The approach is demonstrated through simulations of flyer-plate and cylinder impacts.

Keywords

81.40.Ef83.85.St83.60.La81.40.Lm83.10.GrEntropyviscoplasticitysolid mechanicsrelaxation timeMaxwell solidEulerian
Type
Research Article
Information
Communications in Computational Physics , Volume 11 , Issue 5 , May 2012 , pp. 1525 - 1546
Copyright
Copyright © Global Science Press Limited 2012

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References

[1]Barton, P. T., Drikakis, D., Romenski, E. and Titarev, V. A., Exact and approximate solutions of Riemann problems in non-linear elasticity, J. Comp. Phys., 228 (2009) 7046.Google Scholar
[2]Barton, P. T., Drikakis, D. and Romenski, E., An Eulerian finite-volume scheme for large elasto-plastic deformations in solids, Int. J. Num. Meth. Eng., 81 (2010) 453.Google Scholar
[3]Barton, P. T. and Drikakis, D., AnEulerian method for multi-component problems in non-linear elasticity with sliding interfaces, J. Comp. Phys., 229 (2010) 5518.Google Scholar
[4]Besaran, C. and Nie, S., An irreversible thermodynamics theory for damage mechanics of solids, Int. J. Damage Mech., 13 (2004) 205.Google Scholar
[5]Dorovskii, V. N., Iskol’dskii, A. M. and Romenskii, E. I., Dynamics of impulsive metal heating by a current and electrical explosion of conductors, J. Appl. Mech. Tech. Phys., 24 (1984) 454.Google Scholar
[6]Favrie, N., Gavrilyuk, S.L. and Saurel, R., Solidfluid diffuse interface model in cases of extreme deformations, J. Comp. Phys., 228 (2009) 6037.Google Scholar
[7]Fedkiw, R. P., Marquina, A. and Merriman, B., An isobaric fix for the overheating problem in multimaterial compressible flows, J. Comp. Phys., 148 (1999) 545.Google Scholar
[8]Gavrilyuk, S., Favrie, N. and Saurel, R., Modelling wave dynamics of compressible elastic materials, J. Comp. Phys., 227 (2008) 2941.CrossRefGoogle Scholar
[9]Gilman, J. J., Microdynamics of plastic flow at constant stress, J. Appl. Phys., 36 (1965) 2772.Google Scholar
[10]Gilman, J. J., Dislocation mobility in crystals, J. Appl. Phys., 36 (1965) 3195.Google Scholar
[11]Gillis, P. P. and Gilman, J. J., Dynamical dislocation theory of crystal plasticity. I. The yield stress, J. Appl. Phys., 36 (1965) 3370.Google Scholar
[12]Gillis, P. P. and Gilman, J. J., Dynamical dislocation theory of crystal plasticity. II. Easy glide and strain hardening, J. Appl. Phys., 36 (1965) 3380.Google Scholar
[13]Gilman, J. J., Dislocation dynamics and the response of materials to impact, Appl. Mech. Rev., 21 (1968) 767.Google Scholar
[14]Godunov, S. K., Zabrodin, A. V., Ivanov, M. Ya., Kraiko, A. N. and Prokopov, G. P., Numerical Solution of Multidimensional Gas Dynamic Problems, Nauka, Moscow, 1976 (in Russian).Google Scholar
[15]Godunov, S. K. and Romenskii, E. I., Elements of Continuum Mechanics and Conservation Laws, Kluwer Academic/Plenum Publishers, 2003.Google Scholar
[16] W. -Guo, G., Flow stress and constitutive model of OFHC Cu for large deformation, different temperatures and different strain rates, Baozha Yu Chongji/Explosion and Shock Waves, 25 (2005) 244 (in Chinese).Google Scholar
[17]Hill, D.J., Pullin, D., Ortiz, M. and Meiron, D., An Eulerian hybrid WENO centered-difference solver for elasticplastic solids, J. Comp. Phys., 229 (2010) 9053.Google Scholar
[18]Jiang, G. S. and Shu, C. W., Efficient implementation of weighted ENO schemes, J. Comp. Phys., 126 (1996) 202.Google Scholar
[19]Keshavan, M. K. and Gillis, P. P., On dislocation multiplication, J. Phys. F: Metal Phys., 5 (1975) 903.Google Scholar
[20]Kluth, G., Despreés, B., Discretization of hyperelasticity on unstructured mesh with a cell-centered Lagrangian scheme, J. Comp. Phys., 229 (2010) 9092.CrossRefGoogle Scholar
[21]Ludwik, P., Elemente der Technologischen Mechanik, Julius Springer, 1909.CrossRefGoogle Scholar
[22]Merzhievskii, L. A. and Shamonin, S. A., Construction of the time dependence of the relaxation of tangential stresses on the state parameters of a medium, J. Appl. Mech. Tech. Phys., 21 (1980) 716.Google Scholar
[23]Merzhievskii, L. A. and Resnyanskii, A. D., Shock-wave processes in metals, Combust. Exp-los., 20 (1984) 580.Google Scholar
[24]Merzhievskii, L. A. and Paletsky, A. V., Calculations for diagrams of dynamic deformation of metals and alloys, Phys. Mesomechanics, 4 (2001) 79.Google Scholar
[25]Miller, G. H. and Colella, P., A high-order Eulerian Godunov method for elastic-plastic flow in solids, J. Comp. Phys., 167 (2001) 131.CrossRefGoogle Scholar
[26]Miller, G. H. and Colella, P., A conservative three-dimensional Eulerian method for coupled solid-fluid shock capturing, J. Comp. Phys., 183 (2002) 26.CrossRefGoogle Scholar
[27]Nelder, J. A. and Mead, R., A simplex method for function minimization, Comp. J., 7 (1965) 308.Google Scholar
[28]Orowan, E., Problems of plastic gliding, Proc. Phys. Soc., 52 (1940) 8.Google Scholar
[29]Radhakrishnan, K. and Hindmarsh, A. C., Description and use of LSODE, the Livermore solver for ordinary differential equations, LLNL report UCRL-ID-113855, 1993.Google Scholar
[30]Romenski, E. I., Thermodynamics and hyperbolic systems of balance laws in continuum mechanics, in: Godunov Methods: Theory and Applications, Toro, E. F. (Ed.), Kluwer Academic/Plenum Publishers, 2001.Google Scholar
[31]Schreyer, H. L. and Maudlin, P. J., Thermodynamically consistent relations involving plasticity, internal energy and thermal effects, Phil. Trans. R. Soc. A, 363 (2010) 2517.Google Scholar
[32]Taylor, G. I., The mechanism of plastic deformation of crystals, Proc. R. Soc. A, 145 (1934) 362.Google Scholar
[33]Titarev, V. A., Romenski, E. and Toro, E. F., MUSTA-type upwind fluxes for non-linear elasticity, Int. J. Numer. Meth. Eng., 73 (2008) 897.CrossRefGoogle Scholar
[34]Zel’dovich, Y. B. and Raizer, Y. P., Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena, v2, Academic Press, 1967.Google Scholar
[35]Zerilli, F. J. and Armstrong, R. W., Dislocation-mechanics-based constitutive relations for material dynamics, J. Appl. Phys., 61 (1987) 1816.CrossRefGoogle Scholar