-
Previous Article
Modelling of implicit standard materials. Application to linear coaxial non-associated constitutive laws
- DCDS-S Home
- This Issue
-
Next Article
A velocity-based time-stepping scheme for multibody dynamics with unilateral constraints
Non-local elasto-viscoplastic models with dislocations and non-Schmid effect
1. | Faculty of Mathematics and Computer Science, University of Bucharest, Str. Academiei nr. 14, 010014 Bucharest, Romania, Romania |
References:
[1] |
R. J. Asaro and J. R, Rice, Strain localization in ductile single crystals, J. Mech. Phys. Solids, 25 (1977), 309-338.
doi: 10.1016/0022-5096(77)90001-1. |
[2] |
L. Bortoloni and P. Cermelli, Dislocation patterns and work-hardening in crystalline plasticity, Journal of Elasticity, 76 (2004), 113-138.
doi: 10.1007/s10659-005-0670-1. |
[3] |
P. Cermelli and M. E. Gurtin, Geometrically necessary dislocations in viscoplastic single crystals and bicrystals undergoing small deformations, International Journal of Solids and Structures, 39 (2002), 6281-6309.
doi: 10.1016/S0020-7683(02)00491-2. |
[4] |
S. Cleja-Ţigoiu, Bifurcations of homogeneous deformations of the bar in finite elasto-plasticity, European Journal of Mechanics A Solids, 15 (1996), 761-786. |
[5] |
S. Cleja-Ţigoiu, Non-local elasto-viscoplastic models with dislocations in finite elasto-plasticity. Part I: Constitutive framework, Mathematics and Mechanics of Solids, (2012), accepted.
doi: 10.1177/1081286512439059. |
[6] |
S. Cleja-Ţigoiu, Material forces in finite elastoplasticity with continuously distributed dislocations, Int. J. Fracture, 147 (2007), 67-81. |
[7] |
S. Cleja-Ţigoiu, Elasto-plastic materials with lattice defects modeled by second order deformations with non-zero curvature, in "Recent Progress in the Mathematics of Defects," Springer, Dordrecht, (2011), 61-75. |
[8] |
S. Cleja-Ţigoiu and R. Paşcan, Non-local elasto-viscoplastic models with dislocations in finite elasto-plasticity. Part II: Dislocation density, International Journal of the Physics and Mechanics of Solids, (2011), submitted. |
[9] |
S. Cleja-Ţigoiu and E. Soós, Elastoplastic models with relaxed configurations and internal state variables, Applied Mechanics Reviews, 43 (1990), 131-151.
doi: 10.1115/1.3119166. |
[10] |
M. Dao and R. J. Asaro, Localized deformation modes and non-Schmid effects in crystalline solids. Part I. Critical conditions of localization, Mechanics of Materials, 23 (1996), 71-102.
doi: 10.1016/0167-6636(96)00012-9. |
[11] |
P. Grudmundson, A unified treatment of strain gradient plasticity, J. Mech. Phys. Solids, 52 (2004), 1379-1406.
doi: 10.1016/j.jmps.2003.11.002. |
[12] |
M. E. Gurtin and L. Anand, The decomposition F=F$^e$F$^p$, material symmetry, and plastic irrotationality for solids that are isotropic-viscoplastic or amorphous, Int. J. Plast., 21 (2005), 1686-1719. |
[13] |
P. Howard, "Partial Equations in Matlab 7.0," 2005. Available from: http://www.math.tamu.edu/~phoward/m308/matbasics.pdf. |
[14] |
M. Kuroda, Crystal plasticity model accounting for pressure dependence of yielding and plastic expansion, Scripta Materialia, 48 (2003), 605-610.
doi: 10.1016/S1359-6462(02)00465-7. |
[15] |
J. Mandel, "Plasticité Classique et Viscoplasticité," Course held at the Department of Mechanics of Solids, September-October 1971, International Centre for Mechanical Sciences, Udine, Courses and Lectures, No. 97, Springer-Verlag, Vienna-New York, 1972. |
[16] |
G. W. Recktenwald, "Numerical Methods with Matlab," Prentice Hall, New Jersey, 2000. |
[17] |
C. Teodosiu, A dynamic theory of dislocations and its applications to the theory of the elastic- plastic, in "Fundamental Aspects of Dislocation Theory," Vol. II (eds. J. A. Simmons, R. de Witt and R. Bullough), Conference Proceedings, National Bureau of Standards, (1970), 837-876. |
[18] |
C. Teodosiu and F. Sidoroff, A physical theory of finite elasto-viscoplastic behaviour of single crystal, International Journal of Engineering Science, 14 (1976), 165-176. |
show all references
References:
[1] |
R. J. Asaro and J. R, Rice, Strain localization in ductile single crystals, J. Mech. Phys. Solids, 25 (1977), 309-338.
doi: 10.1016/0022-5096(77)90001-1. |
[2] |
L. Bortoloni and P. Cermelli, Dislocation patterns and work-hardening in crystalline plasticity, Journal of Elasticity, 76 (2004), 113-138.
doi: 10.1007/s10659-005-0670-1. |
[3] |
P. Cermelli and M. E. Gurtin, Geometrically necessary dislocations in viscoplastic single crystals and bicrystals undergoing small deformations, International Journal of Solids and Structures, 39 (2002), 6281-6309.
doi: 10.1016/S0020-7683(02)00491-2. |
[4] |
S. Cleja-Ţigoiu, Bifurcations of homogeneous deformations of the bar in finite elasto-plasticity, European Journal of Mechanics A Solids, 15 (1996), 761-786. |
[5] |
S. Cleja-Ţigoiu, Non-local elasto-viscoplastic models with dislocations in finite elasto-plasticity. Part I: Constitutive framework, Mathematics and Mechanics of Solids, (2012), accepted.
doi: 10.1177/1081286512439059. |
[6] |
S. Cleja-Ţigoiu, Material forces in finite elastoplasticity with continuously distributed dislocations, Int. J. Fracture, 147 (2007), 67-81. |
[7] |
S. Cleja-Ţigoiu, Elasto-plastic materials with lattice defects modeled by second order deformations with non-zero curvature, in "Recent Progress in the Mathematics of Defects," Springer, Dordrecht, (2011), 61-75. |
[8] |
S. Cleja-Ţigoiu and R. Paşcan, Non-local elasto-viscoplastic models with dislocations in finite elasto-plasticity. Part II: Dislocation density, International Journal of the Physics and Mechanics of Solids, (2011), submitted. |
[9] |
S. Cleja-Ţigoiu and E. Soós, Elastoplastic models with relaxed configurations and internal state variables, Applied Mechanics Reviews, 43 (1990), 131-151.
doi: 10.1115/1.3119166. |
[10] |
M. Dao and R. J. Asaro, Localized deformation modes and non-Schmid effects in crystalline solids. Part I. Critical conditions of localization, Mechanics of Materials, 23 (1996), 71-102.
doi: 10.1016/0167-6636(96)00012-9. |
[11] |
P. Grudmundson, A unified treatment of strain gradient plasticity, J. Mech. Phys. Solids, 52 (2004), 1379-1406.
doi: 10.1016/j.jmps.2003.11.002. |
[12] |
M. E. Gurtin and L. Anand, The decomposition F=F$^e$F$^p$, material symmetry, and plastic irrotationality for solids that are isotropic-viscoplastic or amorphous, Int. J. Plast., 21 (2005), 1686-1719. |
[13] |
P. Howard, "Partial Equations in Matlab 7.0," 2005. Available from: http://www.math.tamu.edu/~phoward/m308/matbasics.pdf. |
[14] |
M. Kuroda, Crystal plasticity model accounting for pressure dependence of yielding and plastic expansion, Scripta Materialia, 48 (2003), 605-610.
doi: 10.1016/S1359-6462(02)00465-7. |
[15] |
J. Mandel, "Plasticité Classique et Viscoplasticité," Course held at the Department of Mechanics of Solids, September-October 1971, International Centre for Mechanical Sciences, Udine, Courses and Lectures, No. 97, Springer-Verlag, Vienna-New York, 1972. |
[16] |
G. W. Recktenwald, "Numerical Methods with Matlab," Prentice Hall, New Jersey, 2000. |
[17] |
C. Teodosiu, A dynamic theory of dislocations and its applications to the theory of the elastic- plastic, in "Fundamental Aspects of Dislocation Theory," Vol. II (eds. J. A. Simmons, R. de Witt and R. Bullough), Conference Proceedings, National Bureau of Standards, (1970), 837-876. |
[18] |
C. Teodosiu and F. Sidoroff, A physical theory of finite elasto-viscoplastic behaviour of single crystal, International Journal of Engineering Science, 14 (1976), 165-176. |
[1] |
Michael Herty, Reinhard Illner. Coupling of non-local driving behaviour with fundamental diagrams. Kinetic and Related Models, 2012, 5 (4) : 843-855. doi: 10.3934/krm.2012.5.843 |
[2] |
Felisia Angela Chiarello, Paola Goatin. Non-local multi-class traffic flow models. Networks and Heterogeneous Media, 2019, 14 (2) : 371-387. doi: 10.3934/nhm.2019015 |
[3] |
Christos V. Nikolopoulos, Georgios E. Zouraris. Numerical solution of a non-local elliptic problem modeling a thermistor with a finite element and a finite volume method. Conference Publications, 2007, 2007 (Special) : 768-778. doi: 10.3934/proc.2007.2007.768 |
[4] |
Paola Goatin, Sheila Scialanga. Well-posedness and finite volume approximations of the LWR traffic flow model with non-local velocity. Networks and Heterogeneous Media, 2016, 11 (1) : 107-121. doi: 10.3934/nhm.2016.11.107 |
[5] |
Jan Friedrich, Oliver Kolb, Simone Göttlich. A Godunov type scheme for a class of LWR traffic flow models with non-local flux. Networks and Heterogeneous Media, 2018, 13 (4) : 531-547. doi: 10.3934/nhm.2018024 |
[6] |
José A. Carrillo, Raluca Eftimie, Franca Hoffmann. Non-local kinetic and macroscopic models for self-organised animal aggregations. Kinetic and Related Models, 2015, 8 (3) : 413-441. doi: 10.3934/krm.2015.8.413 |
[7] |
Qiyu Jin, Ion Grama, Quansheng Liu. Convergence theorems for the Non-Local Means filter. Inverse Problems and Imaging, 2018, 12 (4) : 853-881. doi: 10.3934/ipi.2018036 |
[8] |
Gabriel Peyré, Sébastien Bougleux, Laurent Cohen. Non-local regularization of inverse problems. Inverse Problems and Imaging, 2011, 5 (2) : 511-530. doi: 10.3934/ipi.2011.5.511 |
[9] |
Olivier Bonnefon, Jérôme Coville, Guillaume Legendre. Concentration phenomenon in some non-local equation. Discrete and Continuous Dynamical Systems - B, 2017, 22 (3) : 763-781. doi: 10.3934/dcdsb.2017037 |
[10] |
Henri Berestycki, Nancy Rodríguez. A non-local bistable reaction-diffusion equation with a gap. Discrete and Continuous Dynamical Systems, 2017, 37 (2) : 685-723. doi: 10.3934/dcds.2017029 |
[11] |
Matteo Focardi. Vector-valued obstacle problems for non-local energies. Discrete and Continuous Dynamical Systems - B, 2012, 17 (2) : 487-507. doi: 10.3934/dcdsb.2012.17.487 |
[12] |
Chiu-Yen Kao, Yuan Lou, Wenxian Shen. Random dispersal vs. non-local dispersal. Discrete and Continuous Dynamical Systems, 2010, 26 (2) : 551-596. doi: 10.3934/dcds.2010.26.551 |
[13] |
Hongjie Dong, Doyoon Kim. Schauder estimates for a class of non-local elliptic equations. Discrete and Continuous Dynamical Systems, 2013, 33 (6) : 2319-2347. doi: 10.3934/dcds.2013.33.2319 |
[14] |
Tao Wang. Global dynamics of a non-local delayed differential equation in the half plane. Communications on Pure and Applied Analysis, 2014, 13 (6) : 2475-2492. doi: 10.3934/cpaa.2014.13.2475 |
[15] |
Florent Berthelin, Paola Goatin. Regularity results for the solutions of a non-local model of traffic flow. Discrete and Continuous Dynamical Systems, 2019, 39 (6) : 3197-3213. doi: 10.3934/dcds.2019132 |
[16] |
Jared C. Bronski, Razvan C. Fetecau, Thomas N. Gambill. A note on a non-local Kuramoto-Sivashinsky equation. Discrete and Continuous Dynamical Systems, 2007, 18 (4) : 701-707. doi: 10.3934/dcds.2007.18.701 |
[17] |
Antonio Greco, Vincenzino Mascia. Non-local sublinear problems: Existence, comparison, and radial symmetry. Discrete and Continuous Dynamical Systems, 2019, 39 (1) : 503-519. doi: 10.3934/dcds.2019021 |
[18] |
Niels Jacob, Feng-Yu Wang. Higher order eigenvalues for non-local Schrödinger operators. Communications on Pure and Applied Analysis, 2018, 17 (1) : 191-208. doi: 10.3934/cpaa.2018012 |
[19] |
Rafael Abreu, Cristian Morales-Rodrigo, Antonio Suárez. Some eigenvalue problems with non-local boundary conditions and applications. Communications on Pure and Applied Analysis, 2014, 13 (6) : 2465-2474. doi: 10.3934/cpaa.2014.13.2465 |
[20] |
Walter Allegretto, Yanping Lin, Shuqing Ma. On the box method for a non-local parabolic variational inequality. Discrete and Continuous Dynamical Systems - B, 2001, 1 (1) : 71-88. doi: 10.3934/dcdsb.2001.1.71 |
2021 Impact Factor: 1.865
Tools
Metrics
Other articles
by authors
[Back to Top]