Elasticity 1. 10th April c 2003, Michael Marder
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1 Elasticity 0th Apil 003 c 003, Michal Mad
2 Gnal Thoy of Lina Elasticity Bfo dfomation Aft dfomation Many ways to div lasticity. Cold div fom thoy of atoms and thi intactions. Howv, this appoach is not histoically accat, and not flly gnal. 0th Apil 003 c 003, Michal Mad (L)
3 n Gnal Thoy of Lina Elasticity 3 Most gnal appoach modld by Landa; constct f ngy simply by considing symmty and sing fact that dfomations a small: vanishs in qilibim F ngy invaiant nd tanslation. Smallst allowd pows o Divativs of lowst allowd od Unifom otation costs no ngy. Uniq (?) f ngy consistnt with ths constaints: d E (L) 45 indpndnt E aft considing symmty nd intchang of indics. (L3) 0th Apil 003 c 003, Michal Mad
4 E Gnal Thoy of Lina Elasticity 4 d n n 0(L4) E E E E 0(L5) 0th Apil 003 c 003, Michal Mad
5 Dfin stain tnso E C Stain tnso 5 (L6) (L7) d E 8 8 E E E E E E E (L8) d (L9) C 4 E E E (L0) and also (L) 0th Apil 003 c 003, Michal Mad
6 Stss Tnso 6 d (L) wh th stss tnso is C (L3) zz zy zx yz z xz yx yy x Eqation of motion y xx xy 0th Apil 003 c 003, Michal Mad
7 y Solids of Cbic Symmty 7 C xyyy vanishs bcas it mltiplis? xy yy bt xy flips sign whn x x. Also invaiant nd x z x Th paamts sviv: C xxxx C xxyy C xyxy 0th Apil 003 c 003, Michal Mad
8 yy yyzz yz Solids of Cbic Symmty 8 C xxxx xx zz d Cxxyy xx yy zz xx (L4) 4Cxyxy xy zx xx yy zz yz zx xy (L5) C xxxx C xxyy C xxzz C yzxx C zxxx C xyxx tc (L6) C C C 3 C 4 C 5 C 6 tc 0th Apil 003 c 003, Michal Mad
9 C Solids of Cbic Symmty 9 d 6 (L7) Cachy lation: C 44 C 0th Apil 003 c 003, Michal Mad
10 Solids of Cbic Symmty 0 Elmnt C C 44 C Elmnt C C 44 C (GPa) (GPa) (GPa) (GPa) (GPa) (GPa) Al Li (95K) A (80 K) Mo Ag Na A N (6 K) Cs (78 K) Ni Ca 6 8 Nb C O (54.4 K) C Pd C (diamond) Pt F Rb G (ndopd) Si (ndopd) G (n-dopd,0 9 Sb) Si (n-dopd, 0 9 As) G (p-dopd,0 0 Ga) S H 3 (0.4 K, 4 cm 3 /mol) Ta H 4 (.6 K, cm 3 /mol) Th I W K V K (5 K) X (56 K) Pb th Apil 003 c 003, Michal Mad
11 Solids of Cbic Symmty B xx yy zz 3 6 C C (L8) B 3 C C (L9) 0th Apil 003 c 003, Michal Mad
12 Isotopic Solids Distingish btwn otating all mass points and otating a pattn of distotion in mass points that othwis main fixd. R R (L0a) with Rand R (L0b) 0 Cxyxy Cxxyy Cxxxx yy xy xx yy xy xx (L) Cxxxx Cxxyy C xyxy(l) d (L3) Kintic ngy: 0th Apil 003 c 003, Michal Mad
13 Eqation of motion: Stss fig Isotopic Solids 3 T d (L4) (L5) C (L6) d d n (L8) 0th Apil 003 c 003, Michal Mad (L7)
14 3 3 with 3 Isotopic Solids 4 t (L30) Yzz(L3) Y (L3) xx yy (L33) (L34) 0th Apil 003 c 003, Michal Mad (L9)
15 Isotopic Solids 5 L L Y zzy Gyz G y z L L G xzg (L35) L L z L L x (A) (B) 0th Apil 003 c 003, Michal Mad
16 Isotopic Solids 6 Matial Yong s Modls Y (GPa) Poisson Ratio Lad (cast) Tin (cast) Glass Alminm (cast) Copp (cast) Zinc (cast) Copp (soft, woght) Ion (cast) Copp (had dawn) Ion (woght) Cabon stl Tngstn th Apil 003 c 003, Michal Mad
17 is of fom 0 i k i i t t (L36) Wavs 7 t and t t t (L37) t (L38) cl (L39) ct (L40) 0th Apil 003 c 003, Michal Mad
18 Dicto n. n(l4a) Liqid Cystals 8 n n n(l4b) n(l4c) n n (L4) d d C n n (L43) 0 nz nz n n (L44) nz (L45) 0th Apil 003 c 003, Michal Mad
19 0 n Liqid Cystals 9 n n R R n (L46) R (L47) n y n C x n x n C y nx n Cy ny n Cx (L48) nx z ny y (L49) 0 Cyzyy Cyxxz Cxyxz (L50) 0th Apil 003 c 003, Michal Mad
20 Liqid Cystals 0 nx x ny y (L5a) nx z ny z (L5b) ny x nx y (L5c) ny x nx y ny y nx x (L5d) ny x nx y ny y nx x (L5) n (L5a) n n (L5b) n n (L5c) n n n(l5d) 0th Apil 003 c 003, Michal Mad
21 Liqid Cystals n n n n (L5) K n K n n K3 n splay twist bnd n (L53) 0th Apil 003 c 003, Michal Mad
22 Rbb 0 kbt Np j j I N I 3 B n Cn 3 (L54) I j j j (L55) x x y y z z (L56) (L57) 0th Apil 003 c 003, Michal Mad
23 kbt I j Rbb 3 j j j j j (L58) Np j j kbtnp 3 j 3 Np I 3 (L59) (L60) kbtnp 3 (L6) kbtnp 3 kbt Np 3 (L63) (L6) 0th Apil 003 c 003, Michal Mad
24 Foc p lngth (N/cm) 50 0 R0 Rbb 4 kbt Np 3 3 (L64) kbt Np 3 R R0 R0 R 3 (L65) Extnsion R 0th Apil 003 c 003, Michal Mad
25 Composit and Ganla Matials 5 Fig : Avalanch in mstad sds: Jag, Univsity of Chicago Univsity of Chicago Ganla Gop Dk Univsity Ganla Pag 0th Apil 003 c 003, Michal Mad
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