Classification of Concepts in Thermodynamically Consistent Generalized Plasticity
Publication: Journal of Engineering Mechanics
Volume 135, Issue 3
Abstract
A classification of various formulations coined as generalized plasticity is introduced. Thereby the authors present variants of both gradient and micromorphic plasticity, which prove thermodynamically consistent by fulfilling the second law of thermodynamics. In a structured manner, they vary key characteristic features of the formulation and compare their influence on the complexity and, in particular, on the benefit of the individual formulations.
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Acknowledgments
This work was performed at the University of Kaiserslautern. The writers gratefully acknowledge financial support by the German Science Foundation (DFG)DFG within the International Research Training Group 1131 “Visualization of Large and Unstructured Data Sets—Applications in Geospatial Planning, Modeling, and Engineering.”
References
Abu Al-Rub, R. K., and Voyiadjis, G. Z. (2006). “A physically based gradient plasticity theory.” Int. J. Plast., 22(4), 654–684.
Aifantis, E. C. (1984). “On the microstructural origin of certain inelastic models.” J. Eng. Mater. Technol., 106(4), 326–330.
Aifantis, E. C. (1992). “On the role of gradients in the localization of deformation and fracture.” Int. J. Eng. Sci., 30(10), 1279–1299.
Askes, H., and Sluys, L. J. (2003). “A classification of higher-order strain-gradient models in damage mechanics.” Arch. Appl. Mech., 73(5–6), 448–465.
Besdo, D. (1974). “Ein Beitrag zur nichtlinearen Theorie des Cosserat-Kontinuums.” Acta Mech., 20(1–2), 105–131.
Capriz, G. (1985). “Continua with latent microstructure.” Arch. Ration. Mech. Anal., 90(1), 43–56.
Capriz, G. (1989). Continua with microstructure, Springer, New York.
Capriz, G., and Virga, E. G. (1990). “Interactions in general continua with microstructure.” Arch. Ration. Mech. Anal., 109(4), 323–342.
Coleman, B. D. (1964). “On thermodynamics of materials with memory.” Arch. Ration. Mech. Anal., 17(1), 1–46.
Coleman, B. D., and Gurtin, M. E. (1967). “Thermodynamics with internal state variables.” J. Chem. Phys., 47(2), 597–613.
Collins, I. F., and Houlsby, G. T. (1997). “Application of thermomechanical principles to the modelling of geotechnical materials.” Proc. R. Soc. London, Ser. A, 453(1964), 1975–2001.
Creighton, S. L., Regueiro, R. A., Garikipati, K., Klein, P. A., Marin, E. B., and Bammann, D. J. (2004). “A variational multiscale method to incorporate strain gradients in a phenomenological plasticity model.” Comput. Methods Appl. Mech. Eng., 193(48–51), 5453–5475.
de Borst, R. (1991). “Simulation of strain localization: A reappraisal of the Cosserat continuum.” Eng. Comput., 8(4), 317–332.
de Borst, R., and Mühlhaus, H.-B. (1992). “Gradient-dependent plasticity: Formulation and algorithmic aspects.” Int. J. Numer. Methods Eng., 35(3), 521–539.
de Borst, R., and Pamin, J. (1996). “Some novel developments in finite element procedures for gradient-dependent plasticity.” Int. J. Numer. Methods Eng., 39(14), 2477–2505.
Diepolder, W., Mannl, V., and Lippmann, H. (1991). “The Cosserat continuum, a model for grain rotations in metals?” Int. J. Plast., 7(4), 313–328.
Dietsche, A., Steinmann, P., and Willam, K. (1993). “Micropolar elastoplasticity and its role in localization analysis.” Int. J. Plast., 9(7), 813–831.
Edelen, D., and Laws, N. (1971). “On the thermodynamics of systems with nonlocality.” Arch. Ration. Mech. Anal., 43(1), 24–35.
Ehlers, W., and Volk, W. (1997). “On shear band localization phenomena of liquid-saturated granular elastoplastic porous solid materials accounting for fluid viscosity and micropolar solid rotations.” Mech. Cohesive-Frict. Mater., 2(4), 301–320.
Ehlers, W., and Volk, W. (1998). “On theoretical and numerical methods in the theory of porous media based on polar and non-polar elasto-plastic solid materials.” Int. J. Solids Struct., 35(34), 4597–4617.
Eringen, A. C. (1964). “Mechanics of micromorphic materials.” Proc., 11th Int. Congress of Applied Mechanics, H. Gortler, ed., Springer, New York, 131–138.
Eringen, A. C. (1999). Microcontinuum field theories. I: Foundations and solids, Springer, New York.
Eringen, A. C. (2002). Nonlocal continuum field theories, Springer, New York.
Eringen, A. C., and Edelen, D. G. B. (1972). “On nonlocal elasticity.” Int. J. Eng. Sci., 10(3), 233–248.
Fleck, N. A., and Hutchinson, J. W. (1993). “A phenomenological theory for strain gradient effects in plasticity.” J. Mech. Phys. Solids, 41(12), 1825–1857.
Fleck, N. A., and Hutchinson, J. W. (1997). “Strain gradient plasticity.” Advanced applied mechanics, Vol. 33, Academic, San Diego, 295–362.
Fleck, N. A., and Hutchinson, J. W. (2001). “A reformulation of strain gradient plasticity.” J. Mech. Phys. Solids, 49(10), 2245–2271.
Forest, S. (1998). “Modeling slip, kink and shear banding in classical and generalized single crystal plasticity.” Acta Mater., 46(9), 3265–3281.
Forest, S. (2007). “Generalized continuum modelling of crystal plasticity.” Lecture notes of the CISM advanced course—“Generalised continua and dislocation theory. Theoretical concepts, computational methods, and experimental verification.”
Forest, S., and Sievert, R. (2003). “Elastoviscoplastic constitutive frameworks for generalized continua.” Acta Mech., 160(1–2), 71–111.
Forest, S., and Sievert, R. (2006). “Nonlinear microstrain theories.” Int. J. Solids Struct., 43(24), 7224–7245.
Fried, E. (1996). “Continua described by a microstructural field.” ZAMP, 47(1), 168–175.
Garikipati, K. (2003). “Variational multiscale methods to embed the macromechanical continuum formulation with fine-scale strain gradient theories.” Int. J. Numer. Methods Eng., 57(9), 1283–1298.
Geers, M. G. D., Ubachs, R. L. J. M., and Engelen, R. A. B. (2003). “Strongly nonlocal gradient-enhanced finite strain elastoplasticity.” Int. J. Numer. Methods Eng., 56(14), 2039–2068.
Grammenoudis, P., and Tsakmakis, C. (2001). “Hardening rules for finite deformation micropolar plasticity: Restrictions imposed by the second law of thermodynamics and the postulate of Il’Iushin.” Continuum Mech. Thermodyn., 13(5), 325–363.
Grammenoudis, P., and Tsakmakis, C. (2005a). “Finite element implementation of large deformation micropolar plasticity exhibiting isotropic and kinematic hardening effects.” Int. J. Numer. Methods Eng., 62(12), 1691–1720.
Grammenoudis, P., and Tsakmakis, C. (2005b). “Predictions of microtorsional experiments by micropolar plasticity.” Proc. R. Soc. London, Ser. A, 461(2053), 189–205.
Green, A. E., and Naghdi, P. M. (1965). “A general theory of an elastic-plastic continuum.” Arch. Ration. Mech. Anal., 18(4), 251–281.
Gudmundson, P. (2004). “A unified treatment of strain gradient plasticity.” J. Mech. Phys. Solids, 52(6), 1379–1406.
Gurtin, M. E. (2000). “On the plasticity of single crystals: Free energy, microforces, plastic-strain gradients.” J. Mech. Phys. Solids, 48(5), 989–1036.
Gurtin, M. E. (2003). “On a framework for small-deformation viscoplasticity: Free energy, microforces, strain gradients.” Int. J. Plast., 19(1), 47–90.
Gurtin, M. E., and Podio-Guidugli, P. (1992). “On the formulation of mechanical balance laws for structured continua.” ZAMP, 43(1), 181–190.
Haupt, P. (2000). Continuum mechanics and theory of materials, Springer, Berlin.
Hirschberger, C. B., Kuhl, E., and Steinmann, P. (2006). “Computational modelling of micromorphic continua—Theory, numerics, and visualisation challenges.” Visualization of large and unstructured data sets, GI-Edition Lecture Notes in Informatics (LNI), Vol. S-4, H. Hagen, A. Kerren, and P. Dannenmann, eds., Gesellschaft für Informatik (German Society for Computer Science), Bonn, Germany, 155–164.
Hirschberger, C. B., Kuhl, E., and Steinmann, P. (2007). “On deformational and configurational mechanics of micromorphic hyperelasticity—Theory and computation.” Comput. Methods Appl. Mech. Eng., 196(41–44), 4027–4044.
Kirchner, N., and Steinmann, P. (2005). “A unifying treatise on variational principles for gradient and micro-morphic continua.” Philos. Mag., 85(33–35), 3875–3895.
Koiter, W. T. (1964). “Couple-stresses in the theory of elasticity: I and II.” Proc. K. Ned. Akad. Wet.: Biol., Chem., Geol., Phys. Med. Sci. (Proc. R. Netherlands Academy of Science), 67, 17–44.
Kröner, E. (1967). “Elasticity theory of materials with long range cohesive forces.” Int. J. Solids Struct., 3(5), 731–742.
Liebe, T., Menzel, A., and Steinmann, P. (2003). “Theory and numerics of geometrically nonlinear gradient plasticity.” Int. J. Eng. Sci., 41(13–14), 1603–1629.
Liebe, T., and Steinmann, P. (2001). “Theory and numerics of a thermodynamically consistent framework for geometrically linear gradient plasticity.” Int. J. Numer. Methods Eng., 51(12), 1437–1467.
Lubliner, J. (1973). “On the structure of the rate equations of materials with internal variables.” Acta Mech., 17(1–2), 109–119.
Maugin, G. A. (1979). “Nonlocal theories or gradient-type theories: A matter of convenience?” Arch. Mech., 31(1), 15–26.
Menzel, A., and Steinmann, P. (2000). “On the continuum formulation of higher gradient plasticity for single and polycrystals.” J. Mech. Phys. Solids, 48(8), 1777–1796.
Menzel, A., and Steinmann, P. (2001). “Erratum for ‘On the continuum formulation of higher gradient plasticity for single and polycrystals.’” J. Mech. Phys. Solids, 49, 1179–1180.
Mindlin, R. D. (1964). “Micro-structure in linear elasticity.” Arch. Ration. Mech. Anal., 16(1), 51–78.
Mindlin, R. D. (1965). “Second gradient of strain and surface-tension in linear elasticity.” Int. J. Solids Struct., 1(4), 417–438.
Mindlin, R. D., and Tiersten, H. F. (1962). “Effects of couple-stress in linear elasticity.” Arch. Ration. Mech. Anal., 11(1), 415–448.
Mühlhaus, H. B., and Aifantis, E. C. (1991). “A variational principle for gradient plasticity.” Int. J. Solids Struct., 28(7), 845–857.
Papenfuss, C., and Forest, S. (2006). “Thermodynamical framework for higher grade material theories with internal variables or additional degrees of freedom.” J. Non-Equil. Thermodyn., 31(4), 319–353.
Peerlings, R. H. J. (2007). “On the role of moving elastic-plastic boundaries in strain-gradient plasticity.” Modell. Simul. Mater. Sci. Eng., 15(1), 109–120.
Peerlings, R. H. J., de Borst, R., Brekelmans, W. A. M., and de Vree, J. H. P. (1996). “Gradient enhanced damage for quasi-brittle materials.” Int. J. Numer. Methods Eng., 39(19), 3391–3403.
Peerlings, R. H. J., Geers, M. G. D., de Borst, R., and Brekelmans, W. A. M. (2001). “A critical comparison of nonlocal and gradient-enhanced softening continua.” Int. J. Solids Struct., 38(44–45), 7723–7746.
Polizzotto, C. (2007). “Strain-gradient elastic-plastic material models and assessment of the higher order boundary conditions.” Eur. J. Mech. A/Solids, 26(2), 189–211.
Polizzotto, C., and Borino, G. (1998). “A thermodynamics-based formulation of gradient-dependent plasticity.” Eur. J. Mech. A/Solids, 17(5), 741–761.
Regueiro, R. A., Bammann, D. J., Marin, E. B., and Garikipati, K. (2002). “A nonlocal phenomenological anisotropic finite deformation plasticity model accounting for dislocation defects.” J. Eng. Mater. Technol., 124(3), 380–387.
Simo, J. C., and Hughes, T. J. R. (1998). Computational inelasticity, Springer, New York.
Steinmann, P. (1994). “A micropolar theory of finite deformation and finite rotation multiplicative elastoplasticity.” Int. J. Solids Struct., 31(8), 1063–1084.
Steinmann, P., and Willam, K. (1991). “Localization within the framework of micro-polar elastoplasticity.” Advances in continuum mechanics, O. Brüller, V. Mannl, and J. Najar, eds., Springer, Heidelberg, Germany, 296–313.
Toupin, R. A. (1962). “Elastic materials with couple-stress.” Arch. Ration. Mech. Anal., 11(1), 385–414.
Toupin, R. A. (1964). “Theory of elasticity with couple-stress.” Arch. Ration. Mech. Anal., 17(2), 85–112.
Valanis, K. C. (1996). “A gradient theory of internal variables.” Acta Mech., 116(1–4), 1–14.
Vardoulakis, I., and Aifantis, E. C. (1991). “A gradient flow theory of plasticity for granular materials.” Acta Mech., 87(3–4), 197–217.
Voyiadjis, G. Z., and Abu Al-Rub, R. K. (2005). “Gradient plasticity theory with a variable length scale parameter.” Int. J. Solids Struct., 42(14), 3998–4029.
Zhao, J., Sheng, D., and Collins, I. F. (2006). “Thermomechanical formulations of strain-gradient plasticity for geomaterials.” J. Mech. Mater. Struct., 1(5), 837–863.
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© 2009 ASCE.
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Received: Sep 5, 2007
Accepted: Sep 26, 2008
Published online: Mar 1, 2009
Published in print: Mar 2009
Notes
Note. Associate Editor: George Z. Voyiadjis
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