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http://dx.doi.org/10.3795/KSME-A.2014.38.10.1057

Non-Local Plasticity Constitutive Relation for Particulate Composite Material Using Combined Back-Stress Model and Shear Band Formation  

Yun, Su-Jin (Advanced Propulsion Technology Center, The 4th R&D Institute, Agency for Defense Development)
Kim, Shin Hoe (Advanced Propulsion Technology Center, The 4th R&D Institute, Agency for Defense Development)
Park, Jae-Beom (Advanced Propulsion Technology Center, The 4th R&D Institute, Agency for Defense Development)
Jung, Gyoo Dong (Advanced Propulsion Technology Center, The 4th R&D Institute, Agency for Defense Development)
Publication Information
Transactions of the Korean Society of Mechanical Engineers A / v.38, no.10, 2014 , pp. 1057-1068 More about this Journal
Abstract
This paper proposes elastic-plastic constitutive relations for a composite material with two phases-inclusion and matrix phases-using a homogenization scheme. A thermodynamic framework is employed to develop non-local plasticity constitutive relations, which are specifically represented in terms of the second-order gradient terms of the internal state variables. A combined two back-stress evolution equation is also established and the degradation of the state and internal variables is expressed by continuum damage mechanics in terms of the damage factor. Then, deformation localization is analyzed; the analysis results show that the proposed model yields a wide range of shear band formation behaviors depending on the evolution of the specific internal state variables. The analysis results also show good agreement with the results of simplified Rice instability analyses.
Keywords
Non-Local Plastic Deformation; Constitutive Relation; Homogenization; Rice's Instability Criterion; Shear Band; Kinematic Hardening;
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1 Sabar, H., Berveiller, M., Favier, V. and Berbenni, S., 2002, "A New Class of Micro-Macro Models for Elastic-Viscoplastic Heterogeneous Materials," Int. J. Sol. Struc., Vol. 39, pp. 3257-3276.   DOI   ScienceOn
2 Mercier, S., Jacques, N. and Molinari, A., 2005, "Validation of an Interaction Law for the Eshelby Inclusion Problem in Elasto-Viscoplasticity," Int. J. Sol. Struc., Vol. 42, pp. 1923-1941.   DOI   ScienceOn
3 Pensee, V. and He, Q.-C., 2007, "Generalized Self-Consistent Estimation of the Apparent Isotropic Elastic Moduli and Minimum Representative Volume Element Size of Heterogeneous Media," Int. J. Sol. Struc., Vol. 44, pp. 2225-2243.   DOI   ScienceOn
4 Ramtani, S., Bui, H. Q. and Dirras, G., 2009, "A Revisited Generalized Self-Consistent Polycrystal Model Following an Incremental Small Strain Formulation and Including Grain-Size Distribution Effect," Int. J. Eng. Sci., Vol. 47, pp. 537-553.   DOI   ScienceOn
5 Berbenni, S., Favier, V. and Berveiller, M., 2007, "Impact of the Grain Size Distribution on the Yield Stress of Heterogeneous Materials," Int. J. Plas. Vol. 23, pp. 114-142.   DOI   ScienceOn
6 Ponte Castaneda P., 1991, "The Effective Mechanical Properties of Nonlinear Isotropic Composites," J. Mech. Phys. Solids, Vol. 39. No. 1, pp. 45-71.   DOI   ScienceOn
7 Hutter, G., Linse, T., Muhlich, U. and Kuna, M., 2013, "Simulation of Ductile Crack Initiation and Propagation by Means of a Non-Local Gurson-Model," Int. J. Eng. Sci., Vol. 50, pp 662-671.
8 Liu, X. and Hu, G., 2005, "A Continuum Micromechanical Theory of Overall Plasticity for Particulate Composites Including Particle Size Effect," Int. J. of Plas., Vol. 21, pp. 777-799.   DOI   ScienceOn
9 Li, J. and Weng, G. J., 1998, "A Unified Approach from Elasticity to Viscoelasticity to Viscoplascity of Particle-Reinforced Solids," Int. J. Plas. Vol. 14, No. 1-3, pp. 193-208.   DOI   ScienceOn
10 Coulibaly, M. and Sabar, H., 2011, "New Integral Formulation and Self-Consistent Modeling of Elastic-Viscoplastic Heterogeneous Materials," Int. J. Sol. Struc., Vol. 48, pp. 753-763.   DOI   ScienceOn
11 Bardella, L., 2003, "An Extension of the Secant Method for the Homogenization of the Nonlinear Behavior of Composite Materials," Int. J. Eng. Sci., Vol. 41, pp. 741-768.   DOI   ScienceOn
12 Pierard, O., Gonzalez, C., Segurado, J., LLorca, J. and Doghri, I., 2007 "Micromechanics of Elasto-Plastic Materials Reinforced with Ellipsoidal Inclusions," Int. J. Sol. Struc., Vol. 44, pp. 6945-6962.   DOI   ScienceOn
13 Shen, L. and Yi, S., 2001, "An Effective Inclusion Model for Effective Moduli of Heterogeneous Materials with Ellipsoidal Inhomogeneities," Int. J. Sol. Struc., Vol. 38 pp. 5789-5805.   DOI   ScienceOn
14 Hui, T. and Oskay, C., 2013, "A Nonlocal Homogenization Model for Wave Dispersion in Dissipative Composite Materials," Int. J. Sol. Struc., Vol. 50, pp. 38-48.   DOI   ScienceOn
15 Phillips, A., Tang, J. L. and Ricciuti, M., 1974, "Some New Observation on Yield Surfaces," Acta Mech, Vol. 20 pp. 23-39.   DOI
16 Lee, E. H., 1969, "Elastic-Plastic Deformation at Finite Strains," J. Appl. Mech., Vol. 36, pp. 1-6.   DOI
17 Prawoto, Y., 2012, "How to Compute Plastic Zones of Heterogeneous Materials: A Simple Approach Using Classical Continuum and Fracture Mechanics," Int. J. Sol. Struc., Vol. 49, pp. 2195-2201.   DOI   ScienceOn
18 Stromberg, L., 2008, "A Special Case of Equivalence Between Nonlocal Plasticity and Gradient Plasticity in a One-Dimensional Formulation," Int. J. Eng. Sci., Vol. 46, pp. 835-841.   DOI   ScienceOn
19 Polizzotto, C., Fuschi, P. and Pisano, A. A., 2004, "A Strain-Difference-Based Nonlocal Elasticity Model," Int. J. Sol. Struc., Vol. 41, 2383-2401   DOI   ScienceOn
20 Chung, P. W. and Namburu, R. R., 2003, "On a Formulation for a Multiscale Atomistic-Continuum Homogenization Method," Int. J. Sol. Struc., Vol. 40, pp. 2563-2588.   DOI   ScienceOn
21 Voyiadjis, G. Z. and Park, T., 1999, "Kinematics Description of Damage for Finite Strain Plasticity," Int. J. Eng. Sci., Vol. 56, Nos 4, pp. 483-511.
22 Bonora, N., 1997, "A Nonlinear CDM Model for Ductile Failure," Engng. Fracture Mech., Vol. 58(1/2): pp. 11-28.   DOI   ScienceOn
23 Voyiadjis, G. Z., Al-Rub, R. A. and Palazotto, A. N., 2004, "Thermodynamic Framework for Coupling of Anisotropic Viscodamage for Dynamic Localiztion Problems Using Gradient Theory," Int. J. Plast., Vol. 20, pp. 981-1038.   DOI   ScienceOn
24 Engelen, R. A. B., Geers, M. G. D. and Baaijen, F. P. T., 2003, "Nonlocal Implicit Gradient-Enhanced Elasto-Plasticity for the Modelling of Softening Behavior, Int. J. of Plas., Vol. 19, pp. 403-433.   DOI   ScienceOn
25 Kouznetsova, V. G., Geers, M. G. D. and Brekelmans, W. A. M., 2004, "Multi-Scale Second-Order Computational Homogenization of Multi-Phase Materials: A Nested Finite Element Solution Strategy," Compt. Meth. Appl. Mech. Engrg., Vol. 193, pp. 5525-5550.   DOI   ScienceOn
26 Aifantis, E. C., 1992, "On the Role of Gradients in the Localization of Deformation and Fracture," Int. J. Engr. Sci., Vol. 30, pp. 1279-1299.   DOI   ScienceOn
27 Mroz, Z., Shrivastava, H. P. and Dubey, R. N., 1976, "A Non-Linear Hardening Model and Its Application to Cyclic Loading," Acta Mech., Vol. 25, pp. 51-61.   DOI   ScienceOn
28 Aravas, N. and Ponte Castaneda P., 2004, "Numerical Methods for Porous Metals with Deformation-Induced Anisotropy," Comput. Methods Appl. Mech. Engrg. Vol. 193, pp. 3767-3805.   DOI   ScienceOn
29 Tohgo, K. and Itoh, T., 2005, "Elastic and Elastic-Plastic Singular Fields Around a Crack-Tip in Particulate-Reinforced Composites with Progressive Debonding Damage," Int. J. Sol. Struc., Vol. 42, pp. 6566-6585.   DOI   ScienceOn
30 Li, C. and Ellyin, F., 2000, "A Mesomechanical Approach to Inhomogeneous Particulate Composite Undergoing Localized Damage: Part II Theory And Application," Int. J. Sol. Struc., Vol. 37, pp. 1389-1401.   DOI   ScienceOn
31 Ganghoffer, J. F. and de Borst, R., 2000, "A New Framework in Nonlocal Mechanics," Int. J. Eng. Sci., Vol. 38, pp. 453-486.   DOI   ScienceOn
32 Voyiadjis, G. Z. and Thiagarajan, G., 1997, "Micro and Macro Anisotropic Cyclic Damage-Plasticity Models for MMCS," Int. J. Eng. Sci., Vol. 35, No. 5, pp. 467-184.   DOI   ScienceOn
33 Voyiadjis, G. Z. and Park, T., 1995, "Local and Interfacial Damage Analysis of Metal Matrix Composite," Int. J. Eng. Sci., Vol. 33, No. 11, pp. 1595-1621.   DOI   ScienceOn
34 Voyiadjis, G. Z. and Deliktas, B., 2009, "Mechanics of Strain Gradient Plasticity with Particular Reference to Decomposition of the State Variables into Energetic and Dissipative Components," Int. J. Eng. Sci., Vol. 47, pp. 1405-1423.   DOI   ScienceOn
35 Makowski, J., Stumpf, H. and Hackl, K., 2006, "The Fundamental Role of Nonlocal and Local Balance Laws of Material Forces in Finite Elastoplasticity and Damage Mechanics," Int. J. Sol. Struc., Vol. 43, pp. 3940-3959.   DOI   ScienceOn
36 Buryachenko, V. A., 2011, "On Thermoelastostatics of Composites with Nonlocal Properties of Constituents I. General Representation for Effective Material and Field Parameters," Int. J. Sol. Struc., Vol. 48, pp. 1818-1828.   DOI   ScienceOn
37 Xun, F., Hu, G. and Huang, Z., 2004, "Size-Dependence of Overall In-Plane Plasticity for Fiber Composites," Int. J. Sol. Struc., Vol. 41, pp. 4713-4730.   DOI   ScienceOn
38 Mercier, S. and Molinari, A., 2009, "Homogenization of Elastic-Viscoplastic Heterogeneous Materials: Self-Consistent and Mori-Tanaka Schemes," Int. J. Plas., Vol. 25, pp. 1024-1048.   DOI   ScienceOn
39 Mori, T. and Tanaka, K., 1973, "Average Sress in Matrix and Average Elastic Energy of Materials with Misfitting Inclusions," Acta Metal., Vol. 21, May, pp. 571-574.   DOI   ScienceOn
40 Jirasek, M. and Rolshoven, S., 2003, "Comparison of Integral-Type Nonlocal Plasticity Models for Strain-Softening Materials," Int. J. Eng. Sci., Vol. 41, pp. 1553-1602.   DOI   ScienceOn
41 Xu, F., Sofronis, P., Aravas, N. and Meyer, S., 2007, "Constitutive Modeling of Porous Viscoelastic Materials," European J. Mech. A/Solids, Vol. 26, pp. 936-955.   DOI