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A model for elastic-viscoplastic deformations of crystalline solids based on material symmetry: theory and plane-strain simulations. (English) Zbl 1423.74168

Summary: A model for the elastic-viscoplastic response of metallic single crystals is developed on the basis of the modern finite-deformation theory of plasticity combined with considerations of material symmetry. This is proposed as an alternative to conventional crystal plasticity theory, based on a decomposition of the plastic deformation rate into a superposition of slips on active slip systems. A simple special case of the general theory, modeling evolving geometrically necessary dislocations and their effect on hardening, is developed and used as the basis of numerical experiments.

MSC:

74C15 Large-strain, rate-independent theories of plasticity (including nonlinear plasticity)
74A05 Kinematics of deformation
74C10 Small-strain, rate-dependent theories of plasticity (including theories of viscoplasticity)
74E15 Crystalline structure

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[1] Anand, L.; Balasubramanian, S.; Kothari, M., Constitutive modeling of polycrystalline metals at large strains, (Large plastic deformation of crystalline aggregates, (1997), Springer Berlin)
[2] Bell, J. F.; Green, R. E., An experimental study of the double-slip deformation hypothesis for face-centered cubic crystals, Philosophical Magazine, 15, 469-476, (1967)
[3] Cermelli, P.; Gurtin, M. E., On the characterization of geometrically necessary dislocations in finite plasticity, Journal of the Mechanics and Physics of Solids, 49, 1539-1568, (2001) · Zbl 0989.74013
[4] Cleja-Tigoiu, S.; Soos, E., Elastoviscoplastic models with relaxed configurations and internal variables, Applied Mechanics Reviews, 43, 131-151, (1990)
[5] Cullity, B., Elements of X-ray diffraction, (1978), Addison-Wesley · Zbl 0043.43903
[6] Del Piero, G.; Owen, D. R., Structured deformations of continua, Archive for Rational Mechanics and Analysis, 124, 99-155, (1993) · Zbl 0795.73005
[7] Deseri, L.; Owen, D. R., Invertible structured deformations and the geometry of multiple slip in single crystals, International Journal of Plasticity, 18, 833-849, (2002) · Zbl 1006.74022
[8] Edmiston, J. (2012). Continuum plasticity: Phenomenological modeling and X-ray diffraction experiments. Dissertation. UC Berkeley.
[9] Epstein, M.; Elzanowski, M., Material inhomogeneities and their evolution, (2007), Springer Berlin · Zbl 1130.74001
[10] Green, A. E.; Adkins, J. E., Large elastic deformations, (1970), Oxford University Press · Zbl 0227.73067
[11] Gupta, A.; Steigmann, D. J.; Stölken, J. S., On the evolution of plasticity and incompatibility, Mathematics and Mechanics of Solids, 12, 583-610, (2007) · Zbl 1133.74009
[12] Gupta, A.; Steigmann, D. J.; Stölken, J. S., Aspects of the phenomenological theory of elastic–plastic deformation, Journal of Elasticity, 104, 249-266, (2011) · Zbl 1320.74027
[13] Gurtin, M. E.; Fried, E.; Anand, L., Mechanics and thermodynamics of continua, (2010), Cambridge University Press
[14] Ha, S.; Kim, K. T., Heterogeneous deformation of al single crystal: experiments and finite element analysis, Mathematics and Mechanics of Solids, 16, 652-661, (2011) · Zbl 1269.74044
[15] Havner, K. S., Finite plastic deformation of crystalline solids, (1992), Cambridge University Press · Zbl 0774.73001
[16] Lubarda, V. A., Elastoplasticity theory, (2002), CRC Press Boca Raton, FL · Zbl 1014.74001
[17] Lucchesi, M.; Silhavy, M., Il’yushin’s conditions in non-isothermal plasticity, Archive for Rational Mechanics and Analysis, 113, 121-163, (1991) · Zbl 0717.73037
[18] Nagdhi, P. M., A critical review of the state of finite-strain plasticity, ZAMP, 41, 315-394, (1990) · Zbl 0712.73032
[19] Nagdhi, P. M.; Srinivasa, Characterization of dislocations and their influence on plastic deformation in single crystals, International Journal of Engineering Science, 32, 1157-1182, (1994) · Zbl 0899.73456
[20] Naghdi, P. M.; Srinivasa, A., Some general results in the theory of crystallographic slip, ZAMP, 45, 687-732, (1994) · Zbl 0812.73009
[21] Noll, W., Materially uniform simple bodies with inhomogeneities, Archive for Rational Mechanics and Analysis, 27, 1-32, (1967) · Zbl 0168.45701
[22] Owen, D. (2012). Private e-mail communication dated June 6.
[23] Pipkin, A. C.; Rivlin, R. S., The formulation of constitutive equations in continuum physics (I), Archive for Rational Mechanics and Analysis, 2, 129-144, (1959), Reprinted In Collected works of R.S. Rivlin, Vol. 1 (G.I. Barenblatt and D.D. Joseph, eds.). Springer, NY, 1997. · Zbl 0092.40402
[24] Prager, W., Introduction to the mechanics of continua, (1961), Ginn & Co. Boston · Zbl 0094.18602
[25] Rajagopal, K.; Srinivasa, A., Inelastic behavious of materials. part 1: theoretical underpinnings, International Journal of Plasticity, 14, 945, (1998) · Zbl 0978.74013
[26] Rajagopal, K.; Srinivasa, A., On the role of the eshelby energy-momentum tensor in materials with multiple natural configurations, Mathematics and Mechanics of Solids, 10, 3, (2005) · Zbl 1104.74012
[27] Rengarajan, G.; Rajagopal, K., On the form for the plastic velocity gradient L_{p} in crystal plasticity, Mathematics and Mechanics of Solids, 6, 471-480, (2001) · Zbl 1077.74007
[28] Silling, S. A., Finite difference modelling of phase changes and localization in elasticity, Computer Methods in Applied Mechanics and Engineering, 70, 251-273, (1988) · Zbl 0635.73119
[29] Smith, G. F.; Smith, M. M.; Rivlin, R. S., Integrity bases for a symmetric tensor and a vector – the crystal classes, Archive for Rational Mechanics and Analysis, 12, 93-133, (1963), Reprinted In Collected works of R.S. Rivlin, Vol. 1 (G.I. Barenblatt and D.D. Joseph, Eds.), Springer, NY, 1997. · Zbl 0125.00802
[30] Steigmann, D. J.; Gupta, A., Mechanically equivalent elastic–plastic deformations and the problem of plastic spin, Theoretical and Applied Mechanics, 38, 397-417, (2011) · Zbl 1299.74030
[31] Steigmann, D. J.; Ogden, R. W., Note on residual stress, lattice orientation and dislocation density in crystalline solids, Journal of Elasticity, 109, 275-283, (2012) · Zbl 1253.74016
[32] Zangwill, W. I., Nonlinear programming, (1969), Prentice-Hall Englewood Cliffs, N.J · Zbl 0191.49101
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