每年出版 6 期
ISSN 打印: 1543-1649
ISSN 在线: 1940-4352
Indexed in
Nonlocal Gradient-Dependent Thermodynamics for Modeling Scale-Dependent Plasticity
摘要
This article is concerned with formulating the thermodynamics of nonlocal gradient-dependent plasticity based on the nonlocality energy residual introduced by Eringen and Edelen (1972). A thermodynamic based theory for small strain gradient plasticity is developed by introducing gradients for variables associated with kinematic and isotropic hardening. This theory is a three-nonlocal-parameter theory that takes into consideration large variations in the plastic strain, large variations in the accumulated plastic strain, and accumulation of plastic strain gradients. It is shown that the presence of higher-order gradients in the plastic strain enforces the presence of a corresponding history variable brought by the accumulation of the plastic strain gradients. Gradients in the plastic strain introduce anisotropy in the form of kinematic hardening and are attributed to the net Burgers vector, whereas gradients in the accumulation of the plastic strain introduce isotropic hardening attributed to the additional storage of geometrically necessary dislocations. The equilibrium, or so-called microforce balance, between the internal Cauchy stress and the microstresses that are conjugates to the higher-order gradients turns out to be the yield criterion, which can be simply retrieved from the principle of virtual power. The classical macroscopic boundary conditions are supplemented by nonclassical microscopic boundary conditions associated with plastic flow. The developed nonlocal theory preserves the classical assumption of the local plasticity theory such that the plastic flow direction is governed by the deviatoric Cauchy stress. However, it is also argued here that plastic flow direction is the same as if it is governed by the nonlocal microstress. This is not in line with Gurtin (2003), who argued that the plastic flow direction is governed by a microstress and not the deviatoric Cauchy stress. Some generalities and the utility of this theory are discussed, and comparisons with other gradient theories are given. Applications of the proposed theory for size effects in thin films are presented.
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Voyiadjis George Z., Deliktas Babur, Theoretical and Experimental Characterization for the Inelastic Behavior of the Micro-/Nanostructured Thin Films Using Strain Gradient Plasticity With Interface Energy, Journal of Engineering Materials and Technology, 131, 4, 2009. Crossref
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Voyiadjis George Z., Deliktas Babur, Faghihi Danial, Lodygowski Adam, Friction coefficient evaluation using physically based viscoplasticity model at the contact region during high velocity sliding, Acta Mechanica, 213, 1-2, 2010. Crossref
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Lodygowski A., Voyiadjis G.Z., Deliktas B., Palazotto A., Non-local and numerical formulations for dry sliding friction and wear at high velocities, International Journal of Plasticity, 27, 7, 2011. Crossref
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Voyiadjis George Z., Deliktas Babur, Formulation of strain gradient plasticity with interface energy in a consistent thermodynamic framework, International Journal of Plasticity, 25, 10, 2009. Crossref
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Clayton J.D., Modeling finite deformations in trigonal ceramic crystals with lattice defects, International Journal of Plasticity, 26, 9, 2010. Crossref
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McDowell David L., Viscoplasticity of heterogeneous metallic materials, Materials Science and Engineering: R: Reports, 62, 3, 2008. Crossref
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Voyiadjis George Z., Pekmezi Gerald, Deliktas Babur, Nonlocal gradient-dependent modeling of plasticity with anisotropic hardening, International Journal of Plasticity, 26, 9, 2010. Crossref
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Voyiadjis George Z., Faghihi Danial, Localization in stainless steel using microstructural based viscoplastic model, International Journal of Impact Engineering, 54, 2013. Crossref
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Voyiadjis George Z., Faghihi Danial, Gradient plasticity for thermo-mechanical processes in metals with length and time scales, Philosophical Magazine, 93, 9, 2013. Crossref
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Abu Al-Rub Rashid K., Darabi Masoud K., A thermodynamic framework for constitutive modeling of time- and rate-dependent materials. Part I: Theory, International Journal of Plasticity, 34, 2012. Crossref
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Voyiadjis George Z., Faghihi Danial, Thermo-mechanical strain gradient plasticity with energetic and dissipative length scales, International Journal of Plasticity, 30-31, 2012. Crossref
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Voyiadjis George Z., Deliktas Babur, Mechanics of strain gradient plasticity with particular reference to decomposition of the state variables into energetic and dissipative components, International Journal of Engineering Science, 47, 11-12, 2009. Crossref
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Pérez Pozo Luis, Campos Andy, Lascano Sheila, Oller Sergio, Rodríguez-Ferran Antonio, A Finite Points Method Approach for Strain Localization Using the Gradient Plasticity Formulation, Mathematical Problems in Engineering, 2014, 2014. Crossref
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Lin Te-Sheng, Pradas Marc, Kalliadasis Serafim, Papageorgiou Demetrios T., Tseluiko Dmitri, Coherent Structures in Nonlocal Dispersive Active-Dissipative Systems, SIAM Journal on Applied Mathematics, 75, 2, 2015. Crossref
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Voyiadjis George Z., Deliktaş Babür, Modeling High-Speed Impact Failure of Metallic Materials: Nonlocal Approaches, in Handbook of Nonlocal Continuum Mechanics for Materials and Structures, 2018. Crossref
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Darabi Masoud K., Abu Al-Rub Rashid K., Omidi Omid, A thermodynamically consistent framework to derive local/nonlocal generalized nonassociative plasticity/viscoplasticity theories, International Journal of Plasticity, 110, 2018. Crossref
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Voyiadjis George Z., Deliktaş Babür, Modeling High-Speed Impact Failure of Metallic Materials: Nonlocal Approaches, in Handbook of Nonlocal Continuum Mechanics for Materials and Structures, 2019. Crossref
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Voyiadjis George Z., Yaghoobi Mohammadreza, Future evolution: Multiscale modeling framework to develop a physically based nonlocal plasticity model for crystalline materials, in Size Effects in Plasticity, 2019. Crossref
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Voyiadjis George Z., Song Yooseob, Strain gradient continuum plasticity theories: Theoretical, numerical and experimental investigations, International Journal of Plasticity, 121, 2019. Crossref
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Voyiadjis George Z., Deliktas Babur, Kattan Peter I., Consistent Non Local Coupled Damage Model and Its Application in Impact Response of Composite Materials, in Damage Mechanics and Micromechanics of Localized Fracture Phenomena in Inelastic Solids, 525, 2011. Crossref
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Voyiadjis George Z., Song Yooseob, Review of theoretical developments on the gradient-enhanced continuum plasticity, in Gradient-Enhanced Continuum Plasticity, 2020. Crossref
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Amendola Giovambattista, Fabrizio Mauro, Golden John, Fractional Derivative Models of Materials with Memory, in Thermodynamics of Materials with Memory, 2021. Crossref
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Voyiadjis George Z., Almasri Amin H., Park Taehyo, Experimental nanoindentation of BCC metals, Mechanics Research Communications, 37, 3, 2010. Crossref