Elasticstressandstrain - Carnegie Mellon University
2
Elasticstressandstrain Kittel ch 3 Uniform dilation Uniform shear constant Volume V v n T h dilation S simple shear Who pure shear Vo ho Localstrain Fi's it Fi local displacement Tier de Y.i FitiicrI Strain Var iation of it F up f F de ti Separation DI Fi Fi DEI Fi Fi DI dii Idi t IDI't t 2dL die't OHH ha dry Strainteri Ug I t 3 symmetric dimensionless Idf 12 Idf th t 2Uijdridr t Ui 6 independent strains Uxx Ux y 4 2 Dilation S Tr Uig Uyy Uyz Uzz
Transcript of Elasticstressandstrain - Carnegie Mellon University
Elasticstressandstrain Kittel ch 3
Uniform dilation Uniform shear constant VolumeV
v n T h
dilation S simpleshearWho pure shearVo ho
Localstrain Fi's itFi
local displacement Tier de Y.i FitiicrIStrain Var iation of it F
up fF de ti
Separation DI Fi Fi DEIFi Fi DI dii
Idi t IDI't t 2dL die't OHH hadry
Strainteri Ug I t 3 symmetric dimensionless
Idf12 Idfth t 2Uijdridr t Ui 6 independent strains
Uxx Uxy 4 2
Dilation S Tr Uig Uyy UyzUzz
Stress response to strain
z tf faceEforce Stress tensor
µ I 0h2 faceof i force ong face g areay t 1 face
faceJi Tj for no net torque
x faceUnits forcelarea energylvolum
pressureHooke's law
spring f k nkmM
integrated E zkx2
Solid body Tig KijmnUmm
integrated I KijmnUijUmindependent
Elements of Kijmn ijmn x y z 34 81 elementsor
index symmetries i c Xji Mn nm ij mu 21
Crystalsymmetries cubic 3 isotropic 2 bulk shear
Netf orceA A A
T x tax 4 1 13AYAZIi i1921 1 7 04 13AxAy
F TT LAXAyaz Force density I Volume
