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Original Articles

The importance of being curved: bowing dislocations in a continuum description

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Pages 3735-3752 | Received 10 Oct 2002, Accepted 03 Apr 2003, Published online: 12 May 2010

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Read on this site (8)

Jaber Rezaei Mianroodi, Ron Peerlings & Bob Svendsen. (2016) Strongly non-local modelling of dislocation transport and pile-up. Philosophical Magazine 96:12, pages 1171-1187.
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T. Hochrainer. (2015) Multipole expansion of continuum dislocations dynamics in terms of alignment tensors. Philosophical Magazine 95:12, pages 1321-1367.
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Xiaohong Zhu & Yang Xiang. (2010) Continuum model for dislocation dynamics in a slip plane. Philosophical Magazine 90:33, pages 4409-4428.
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S. Sandfeld, T. Hochrainer, P. Gumbsch & M. Zaiser. (2010) Numerical implementation of a 3D continuum theory of dislocation dynamics and application to micro-bending. Philosophical Magazine 90:27-28, pages 3697-3728.
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Cyril Imbert, Régis Monneau & Elisabeth Rouy. (2008) Homogenization of First Order Equations with (u/ε)-Periodic Hamiltonians Part II: Application to Dislocations Dynamics. Communications in Partial Differential Equations 33:3, pages 479-516.
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R. Sedláček, C. Schwarz, J. Kratochvíl & E. Werner. (2007) Continuum theory of evolving dislocation fields. Philosophical Magazine 87:8-9, pages 1225-1260.
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M. Zaiser, N. Nikitas, T. Hochrainer & E. C. Aifantis. (2007) Modelling size effects using 3D density-based dislocation dynamics. Philosophical Magazine 87:8-9, pages 1283-1306.
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T. Hochrainer, M. Zaiser & P. Gumbsch. (2007) A three-dimensional continuum theory of dislocation systems: kinematics and mean-field formulation. Philosophical Magazine 87:8-9, pages 1261-1282.
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Articles from other publishers (47)

Fabio Sozio & Arash Yavari. (2023) A Geometric Field Theory of Dislocation Mechanics. Journal of Nonlinear Science 33:5.
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Xi Luo & Michael Zaiser. (2023) A computationally efficient implementation of continuum dislocation dynamics: Formulation and application to ultrafine-grained Mg polycrystals. Journal of the Mechanics and Physics of Solids 172, pages 105166.
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Serena Dipierro, Stefania Patrizi & Enrico Valdinoci. 2023. Geometric and Functional Inequalities and Recent Topics in Nonlinear PDEs. Geometric and Functional Inequalities and Recent Topics in Nonlinear PDEs 103 135 .
Binh Duong Nguyen & Stefan Sandfeld. 2021. Wide Bandgap Semiconductors for Power Electronics. Wide Bandgap Semiconductors for Power Electronics 199 223 .
Stefania Patrizi & Tharathep Sangsawang. (2021) From the Peierls–Nabarro model to the equation of motion of the dislocation continuum. Nonlinear Analysis 202, pages 112096.
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Mehran Monavari & Michael Zaiser. (2018) Annihilation and sources in continuum dislocation dynamics. Materials Theory 2:1.
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A. H. W. Ngan. (2017) Dislocation-density kinematics: a simple evolution equation for dislocation density involving movement and tilting of dislocations. MRS Communications 7:3, pages 583-590.
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Ronghai Wu, Michael Zaiser & Stefan Sandfeld. (2017) A continuum approach to combined γ/γ′ evolution and dislocation plasticity in Nickel-based superalloys. International Journal of Plasticity 95, pages 142-162.
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Mehran Monavari, Stefan Sandfeld & Michael Zaiser. (2016) Continuum representation of systems of dislocation lines: A general method for deriving closed-form evolution equations. Journal of the Mechanics and Physics of Solids 95, pages 575-601.
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Alireza Ebrahimi & Thomas Hochrainer. (2016) Three-Dimensional Continuum Dislocation Dynamics Simulations of Dislocation Structure Evolution in Bending of a Micro-Beam. MRS Advances 1:24, pages 1791-1796.
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Stefan Sandfeld & Giacomo Po. (2015) Microstructural comparison of the kinematics of discrete and continuum dislocations models. Modelling and Simulation in Materials Science and Engineering 23:8, pages 085003.
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Yichao Zhu & Yang Xiang. (2015) A continuum model for dislocation dynamics in three dimensions using the dislocation density potential functions and its application to micro-pillars. Journal of the Mechanics and Physics of Solids 84, pages 230-253.
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Stefan Sandfeld, Ekkachai Thawinan & Christian Wieners. (2015) A link between microstructure evolution and macroscopic response in elasto-plasticity: Formulation and numerical approximation of the higher-dimensional continuum dislocation dynamics theory. International Journal of Plasticity 72, pages 1-20.
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Yichao Zhu, Hanquan Wang, Xiaohong Zhu & Yang Xiang. (2014) A continuum model for dislocation dynamics incorporating Frank–Read sources and Hall–Petch relation in two dimensions. International Journal of Plasticity 60, pages 19-39.
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C. Reuber, P. Eisenlohr, F. Roters & D. Raabe. (2014) Dislocation density distribution around an indent in single-crystalline nickel: Comparing nonlocal crystal plasticity finite-element predictions with experiments. Acta Materialia 71, pages 333-348.
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K Schulz, D Dickel, S Schmitt, S Sandfeld, D Weygand & P Gumbsch. (2014) Analysis of dislocation pile-ups using a dislocation-based continuum theory. Modelling and Simulation in Materials Science and Engineering 22:2, pages 025008.
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Mehran Monavari, Michael Zaiser & Stefan Sandfeld. (2014) Comparison of closure approximations for continuous dislocation dynamics. MRS Proceedings 1651.
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Thomas Hochrainer. (2014) Continuum Dislocation Dynamics Based on the Second Order Alignment Tensor. MRS Proceedings 1651.
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Jan Kratochvíl. 2014. Plasticity and Beyond. Plasticity and Beyond 199 304 .
Stefan Sandfeld, Mehran Monavari & Michael Zaiser. (2013) From systems of discrete dislocations to a continuous field description: stresses and averaging aspects. Modelling and Simulation in Materials Science and Engineering 21:8, pages 085006.
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T. Hochrainer. (2012) Moving dislocations in finite plasticity: a topological approach. ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik 93:4, pages 252-268.
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Thomas Hochrainer. (2013) Higher order alignment tensors for continuum dislocation dynamics. MRS Proceedings 1535.
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J. Kratochvíl. (2012) Crystal Plasticity Treated as a Quasi-Static Material Flow through Adjustable Crystal Lattice. Acta Physica Polonica A 122:3, pages 482-484.
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Katerina E. Aifantis, Daniel Weygand, Christian Motz, Nikolaos Nikitas & Michael Zaiser. (2011) Modeling microbending of thin films through discrete dislocation dynamics, continuum dislocation theory, and gradient plasticity. Journal of Materials Research 27:3, pages 612-618.
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Samuel Forest. 2012. Generalized Continua and Dislocation Theory. Generalized Continua and Dislocation Theory 181 287 .
Stefan Sandfeld, Thomas Hochrainer, Michael Zaiser & Peter Gumbsch. (2011) Continuum modeling of dislocation plasticity: Theory, numerical implementation, and validation by discrete dislocation simulations. Journal of Materials Research 26:5, pages 623-632.
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David L. McDowell. (2010) A perspective on trends in multiscale plasticity. International Journal of Plasticity 26:9, pages 1280-1309.
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Ray S. Fertig & Shefford P. Baker. (2009) Simulation of dislocations and strength in thin films: A review. Progress in Materials Science 54:6, pages 874-908.
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Yang Xiang. (2009) Continuum approximation of the Peach–Koehler force on dislocations in a slip plane. Journal of the Mechanics and Physics of Solids 57:4, pages 728-743.
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Radan Sedláček, Cornelia Schwarz, Robert Wesenjak & Adrien Bensimon. (2009) Bauschinger effect in thin metal films simulated by the continuum dislocation-based model. International Journal of Materials Research 100:3, pages 326-328.
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Stefan Sandfeld, Thomas Hochrainer & Michael Zaiser. (2011) Application of a 3D-Continuum Theory of Dislocations to a Problems of Constrained Plastic Flow: Microbending of a Thin Film. MRS Proceedings 1224.
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Péter Dusán Ispánovity & István Groma. (2008) The probability distribution of internal stresses in externally loaded 2D dislocation systems. Journal of Statistical Mechanics: Theory and Experiment 2008:12, pages P12009.
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Péter Dusán Ispánovity, István Groma & Géza Györgyi. (2008) Evolution of the correlation functions in two-dimensional dislocation systems. Physical Review B 78:2.
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Jan Kratochvíl & Radan Sedláček. (2008) Statistical foundation of continuum dislocation plasticity. Physical Review B 77:13.
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V. Taupin, T. Richeton, J. Chevy, C. Fressengeas, J. Weiss, F. Louchet & M.C. Miguel. (2008) Rearrangement of dislocation structures in the aging of ice single crystals. Acta Materialia 56:7, pages 1555-1563.
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Radan Sedláček, Cornelia Schwarz & Ewald Werner. (2008) Modeling of size-dependent internal stresses in dislocation cell structures. Materials Science and Engineering: A 474:1-2, pages 323-327.
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Cornelia Schwarz, Radan Sedláček & Ewald Werner. (2008) Refined short-range interactions in the continuum dislocation-based model of plasticity at the microscale. Acta Materialia 56:3, pages 341-350.
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Cornelia Schwarz, Radan SedlácÌek, Christian Krempaszky & Ewald Werner. (2007) Dislocation-based modeling of size effects in microscale plasticity. PAMM 7:1, pages 4080003-4080004.
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V. Taupin, S. Varadhan, J. Chevy, C. Fressengeas, A. J. Beaudoin, M. Montagnat & P. Duval. (2007) Effects of Size on the Dynamics of Dislocations in Ice Single Crystals. Physical Review Letters 99:15.
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C. Schwarz, R. Sedláček & E. Werner. (2007) Towards a 2D finite element implementation of a continuum dislocation-based model. Computational Materials Science 39:1, pages 85-90.
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Cornelia Schwarz, Radan Sedláček & Ewald Werner. (2007) Plastic deformation of a composite and the source-shortening effect simulated by a continuum dislocation-based model. Modelling and Simulation in Materials Science and Engineering 15:1, pages S37-S49.
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B. Bakó, I. Groma, G. Györgyi & G. Zimányi. (2006) Dislocation patterning: The role of climb in meso-scale simulations. Computational Materials Science 38:1, pages 22-28.
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Michael Zaiser & Thomas Hochrainer. (2006) Some steps towards a continuum representation of 3D dislocation systems. Scripta Materialia 54:5, pages 717-721.
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C. Schwarz, R. Sedláček & E. Werner. (2005) Application of a continuum dislocation-based model to a tensile test on a thin film. Materials Science and Engineering: A 400-401, pages 443-447.
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R. Sedláček. (2005) Bending of thin crystalline strips: Comparison of continuum dislocation-based models. Materials Science and Engineering: A 400-401, pages 439-442.
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Radan Sedláček. (2005) Orowan-type size effect in plastic bending of free-standing thin crystalline strips. Materials Science and Engineering: A 393:1-2, pages 387-395.
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Radan Sedláček & Ewald Werner. (2004) Constrained shearing of a thin crystalline strip: Application of a continuum dislocation-based model. Physical Review B 69:13.
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