Abstract
We discuss the notion of equivalence of states and the concept of symmetry of continuously defective elastic crystals, focusing primarily on states which are uniformly defective.
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References
1.
Davini
C
. A proposal for a continuum theory of defective crystals . Arch Rational Mech Anal 1986 ; 96 : 295 –317 .
2.
Palais
R
. A global formulation of the lie theory of transformation groups . Mem Amer Math Soc 1957 ; 22 : 1 –123
3.
Davini
C
Parry
G
. On defect-preserving deformations in crystals . Int J Plasticity 1989 ; 5 : 337 –369 .
4.
Elżanowski
M
Parry
G
. A kinematics of defects in solid crystals . In:
Segev
R
Epstein
M
(eds) Geometric continuum mechanics . Cham : Birkhäuser , 2020 : 303 –348 .
5.
Kobayashi
S
Nomizu
K
. Foundations of differential geometry , vol. I, II . New York : John Wiley , 1996 .
6.
Parry
G
. Group properties of defective crystal structures . Math Mech Solids 2003 ; 8 : 515 –538 .
7.
Lee
E
. Elastic-plastic deformation at finite strains . J App Mechanics 1969 ; 36 : 1 –6 .
8.
Epstein
M
Segev
R
. Regular and singular dislocations . In:
Segev
R
Epstein
M
(eds) Geometric continuum mechanics . Cham : Birkhäuser , 2020 : 223 –265
9.
Kobayashi
S
. Transformation groups in differential geometry . Berlin : Springer , 1995 .
10.
Elżanowski
M
Preston
S
. On continuously defective elastic crystals . Miskolc Math Notes 2013 ; 14 (2 ): 659 –670 .
11.
Epstein
M
. The geometrical language of continuum mechanics . Cambridge : Cambridge University Press , 2010 .
12.
Elżanowski
M
Preston
S
. A model of the self-driven evolution of a defective continuum . Math Mech Solids 2007 ; 12 (4 ): 450 –465 .
13.
Elżanowski
M
Parry
G
. Connection and curvature in crystals with non-constant dislocation density . Math Mech Solids 2019 ; 24 (6 ): 1714 –1725 .
14.
Elżanowski
M
. Geometric characterization of defective elastic crystals . Math Mech Solids 2022 ; 27 (2 ): 1212 –1221 .
15.
Parry
G
Silhavý
M
. Elastic invariants in the theory of defective crystals . Proc R Soc Lond A 1999 ; 455 : 4333 –4346 .
16.
Olver
P
. Equivalence, invariants, and symmetry . Cambridge : Cambridge University Press , 1995 .
17.
Epstein
M
Elżanowski
M
. Material inhomogeneities and their evolution: a geometric approach . Berlin : Springer , 2007 .
