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  1. Zeitschrift für angewandte Mathematik und Physik
  2. Zeitschrift für angewandte Mathematik und Physik : Volume 65
  3. Zeitschrift für angewandte Mathematik und Physik : Volume 65, Issue 3, June 2014
  4. Thermodynamic forces in single crystals with dislocations
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Zeitschrift für angewandte Mathematik und Physik : Volume 67
Zeitschrift für angewandte Mathematik und Physik : Volume 66
Zeitschrift für angewandte Mathematik und Physik : Volume 65
Zeitschrift für angewandte Mathematik und Physik : Volume 65, Issue 6, December 2014
Zeitschrift für angewandte Mathematik und Physik : Volume 65, Issue 5, October 2014
Zeitschrift für angewandte Mathematik und Physik : Volume 65, Issue 4, August 2014
Zeitschrift für angewandte Mathematik und Physik : Volume 65, Issue 3, June 2014
Justification of a nonlinear Schrödinger model for laser beams in photopolymers
Transient electroosmotic flow of general Maxwell fluids through a slit microchannel
Global existence and blowup for a degenerate and singular parabolic system with nonlocal source and absorptions
Global existence, large time behavior, and life span for a degenerate parabolic equation with inhomogeneous density and source
Algebro-geometric solutions for the Hunter–Saxton hierarchy
A free boundary problem for a reaction-diffusion system with nonlinear memory
Longitudinal counterflow in turbulent liquid helium: velocity profile of the normal component
Thermodynamic forces in single crystals with dislocations
Modeling the onset of shear boundary layers in fibrous composite reinforcements by second-gradient theory
Zeitschrift für angewandte Mathematik und Physik : Volume 65, Issue 2, April 2014
Zeitschrift für angewandte Mathematik und Physik : Volume 65, Issue 1, February 2014
Zeitschrift für angewandte Mathematik und Physik : Volume 64
Zeitschrift für angewandte Mathematik und Physik : Volume 63
Zeitschrift für angewandte Mathematik und Physik : Volume 62
Zeitschrift für angewandte Mathematik und Physik : Volume 61
Zeitschrift für angewandte Mathematik und Physik : Volume 60
Zeitschrift für angewandte Mathematik und Physik : Volume 59
Zeitschrift für angewandte Mathematik und Physik : Volume 58
Zeitschrift für angewandte Mathematik und Physik : Volume 57
Zeitschrift für angewandte Mathematik und Physik : Volume 56
Zeitschrift für angewandte Mathematik und Physik : Volume 55
Zeitschrift für angewandte Mathematik und Physik : Volume 54
Zeitschrift für angewandte Mathematik und Physik : Volume 53
Zeitschrift für angewandte Mathematik und Physik : Volume 52
Zeitschrift für angewandte Mathematik und Physik : Volume 51
Zeitschrift für angewandte Mathematik und Physik : Volume 50
Zeitschrift für angewandte Mathematik und Physik : Volume 49
Zeitschrift für angewandte Mathematik und Physik : Volume 48

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Thermodynamic forces in single crystals with dislocations

Content Provider SpringerLink
Author Goethem, Nicolas
Copyright Year 2013
Abstract A simple model for the evolution of macroscopic dislocation regions in a single crystal is presented. This model relies on maximal dissipation principle within Kröner’s geometric description of the dislocated crystal. Mathematical methods and tools from shape optimization theory provide equilibrium relations at the dislocation front, similarly to previous work achieved on damage modelling (J Comput Phys 33(16):5010–5044, 2011). The deformation state variable is the incompatible strain as related to the dislocation density tensor by a relation involving the Ricci curvature of the crystal underlying elastic metric. The time evolution of the model variables follows from a novel interpretation of the Einstein–Hilbert flow in terms of dislocation microstructure energy. This flow is interpreted as the dissipation of non-conservative dislocations, due to the climb mechanism, modelled by an average effect of mesoscopic dislocations moving normal to their glide planes by adding or removing points defects. The model equations are a fourth-order tensor parabolic equation involving the operator “incompatibility,” here appearing as a tensorial counterpart of the scalar Laplacian. This work encompasses and generalizes results previously announced (C R Acad Sci Paris Ser I 349:923–927, 2011), with in addition a series of physical interpretations to give a meaning to the newly introduced concepts.
Ending Page 586
Page Count 38
Starting Page 549
File Format PDF
ISSN 00442275
e-ISSN 14209039
Journal Zeitschrift für angewandte Mathematik und Physik
Issue Number 3
Volume Number 65
Language English
Publisher Springer Basel
Publisher Date 2013-07-10
Publisher Place Basel
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword Principle of maximal dissipation Shape optimization Dynamics of phase boundaries Geometrical methods Theoretical and Applied Mechanics Problems involving partial differential equations Dislocations Applications to physics Thermodynamics of continua Single crystals PDEs in connection with mechanics of deformable solids Mathematical Methods in Physics Strain incompatibility Thermodynamic model Einstein–Hilbert flow
Content Type Text
Resource Type Article
Subject Applied Mathematics Physics and Astronomy
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