TY  - JOUR
PB  - American Physical Society
ID  - 10.1103/PhysRevB.63.174103
DO  - 10.1103/PhysRevB.63.174103
TI  - Symmetry-general least-squares extraction of elastic coefficients from ab initio total energy calculations
PY  - 2001/03/29/
UR  - https://link.aps.org/doi/10.1103/PhysRevB.63.174103
JF  - Physical Review B
JA  - Phys. Rev. B
J1  - PRB
VL  - 63
IS  - 17
SP  - 174103
EP  - 
A1  - Le Page, Y.
AU  - Saxe, Paul
ER  -

TY  - JOUR
PB  - American Physical Society
ID  - 10.1103/PhysRevB.65.104104
DO  - 10.1103/PhysRevB.65.104104
TI  - Symmetry-general least-squares extraction of elastic data for strained materials from ab initio calculations of stress
PY  - 2002/02/13/
UR  - https://link.aps.org/doi/10.1103/PhysRevB.65.104104
JF  - Physical Review B
JA  - Phys. Rev. B
J1  - PRB
VL  - 65
IS  - 10
SP  - 104104
EP  - 
A1  - Le Page, Yvon
AU  - Saxe, Paul
ER  -

TY  - JOUR
T1  - Estimating elastic constants by averaging over simulated structures
AU  - Suter, U.W.
AU  - Eichinger, B.E.
JO  - Polymer
VL  - 43
IS  - 2
SP  - 575
EP  - 582
PY  - 2002
DA  - 2002/01/01/
SN  - 0032-3861
DO  - https://doi.org/10.1016/S1089-3156(01)00007-1
UR  - https://www.sciencedirect.com/science/article/pii/S1089315601000071
KW  - Elastic constants
KW  - Atomistic simulations
KW  - Disordered structures
AB  - In the context of atomistic simulations of solids, two situations often occur: that in which disordered structures (e.g. from “amorphous cell” simulations) are deemed to occur with essentially equal likelihood to form a “glass”, and that in which a particular orientational average over one crystal unit cell is desired, e.g. when a fiber modulus is deduced surmising that identical crystallites are oriented in the direction of the fiber axis with a specified direction of the unit cell frame while all orientations in the transverse directions are equally likely (“fiber symmetry”). The common averaging of elastic constants yields inappropriate results. We apply methods introduced by Hill and by Walpole more than three decades ago and show that with these methods, physically reasonable, self-consistent averages for elastic constants can be obtained as well as bounds considerably narrower than the well-known ones after Voigt and Reuss.
ER  -