
atiushna samagri

hyperlastic kinwa hiravi lavchik samagri heey aadarsh lavchik samagrisathi eka prakarche rachnatmak model aahe jyasathi taana-taana sambandh taana urja ghanata karyatoon prapt hoto. hyperlastic samagri hii eka vishesh cases aahe, jee eka kachee elastic samagri aahe.
anek samagrisathi, resheey lavchik models nirikshan kelelya bhautik vartanache achook varnan karat naheet. yaa prakarchya samagriche sarvat samanya udaharan mhanje rubber, jyacha taana-taana sambandh haah resheey nasalela lavchik, samasthanik aanee asampidya mhanoon paribhashit keela jaau shakato. atilambata asha samgrichya taana-taana vartanache pratirupan karnyache eka sadhan pradan karate. naan bharalelya, vulcanised elastomersche vartan anekada hyperlastic idealshi jawalun julate. bharalele elastomers aanee jaivik ootee dekhil anekada hyperlastic aadarshikaranachya madhyamatoon tayar kelya jaatat.
ronald rivlin aanee melvin mooney yanni neo-hookian aanee mooney-rivlin ghan padarth heey pahile hyperlastic model vikasit kele. tyanantar itar anek hyperlastic models vikasit karnyat aalya aahet. mothya pramanavar vaparlya jaanarya itar hyperlastic samagri modelmadhye ogden model aanee aruda-boyce modelcha samavesh aahe.
hyperlastic samagri model.
seent venant-kirchoff model.
sarvat sope hyperlastic materiyal model mhanje seent venant-kirchoff model jeey bhaumitikdrushtya rekheey lavchik materiyal modelcha keval bhaumitikdrushtya araikhik vyavastheparyant vistar aahe. yaa pratimeche sarvasadharan swaroop aanee samasthanik swaroop anukrame aahe.
sootra _ 1
jethe sootra _ 2 heey tensor aakunchan aahe, sootra _ 3 heey dusare piola-kirchoff taana aahe, sootra _ 4 heey chauthya kramankache kadakpana tensor aahe aanee sootra _ 5 heey lagrangian green strain aahe jeey
sootra _ 6
sootra _ 7 aanee sootra _ 8 heey lamey sthirank aahet aanee sootra _ 9 heey dusya kramankache ekak tensor aahe.
seent venant-kirchoff modelsathi taana-urja ghanata karya aahe
sootra _ 10
aanee dusra piola-kirchoff taana yaa sambandhatun midavata yeto.
sootra _ 11
atiushna samagri pratikrutinche vargikaran.
hyperlastic samagri modelsche vargikaran asey kele jaau shakateh
samanyatah, hyperlastic modelane drucker sthiratecha nikash purn keela pahije.
kahee hyperlastic models valenis-landell gruhitak purn karatat jeey asey sangatat qee taana urja karya heey mukhya taana sootra _ 12 chya swatantra karyanchya bereejmadhye vibhagale jaau shakateh
sootra _ 13
tanav-taana sambandh.
sankuchit hyperlastic samagri.
pahila piola-kirchoff taana.
jarr sootra _ 14 heey taana urja ghanata karya asel, tarr hyperlastic samagrisathi pahila piola-kirchoff taana tensor asha prakare mojala jaau shakato
sootra _ 15
jethe sootra _ 16 haah virupan pravanata aahe. lagrangian green strainchya sandarbhat (sootra _ 5)
sootra _ 18
ujavya kachee-green vikrutee tensorchya sandarbhat (sootra _ 19)
sootra _ 20
dusra piola-kirchoff taana.
jarr sootra _ 3 haah dusra piola-kirchoff taana tanak asel tarr
sootra _ 22
lagrangian green strainchya sandarbhat
sootra _ 23
ujavya kachee-green vikrutee tensorchya sandarbhat
sootra _ 24
vareel sambandhala bhautik sanrachanet doil-ericson sootra mhanoon dekhil olakhale jaate.
kachakach tanav.
tyachpramane, kachee taana haah yaa dware deela jaato
sootra _ 25
lagrangian green strainchya sandarbhat
sootra _ 26
ujavya kachee-green vikrutee tensorchya sandarbhat
sootra _ 27
vareel abhivyakti agadi anisotropic madhyamansathi dekhil vaidh aahet (asha paristhitit, sambhavya karya prarambhik fiber abhimukhata sarkhya sandarbh dishatmak pramananvar "apratyakshapane" avalambun asalyache samajale jaate). isotropychya vishesh prakaranat, kachee taana khalilpramane "davikadil" kachee-hiravya virupanachya tensorchya sandarbhat vyakt keela jaau shakatoh
sootra _ 28
asampidit hyperlastic samagri.
asampidit bhautik sutrasathi _ 29. asampiditata adthala mhanoon sootra _ 30 aahe. hyperlastic samagrichi asampiditata sunishchit karnyasathi, taana-urja karya swarupat lihile jaau shakateh
sootra _ 31
jethe hydrostatic daab sootra _ 32 heey asampidankshamatechya nirbandhala lagoo karnyasathi lagrangian gunak mhanoon karya karate. pahila piola-kirchoff taana aata hoto
sootra _ 33
yaa taana tankala nantar itar konatyahi paramparik taana tankamadhye rupantarit kele jaau shakate, jase qee kachee taana tanak jeey dware dile jaate
sootra _ 34
kachee tanavasathi abhivyakti.
sankuchit samasthanik hyperlastic samagri.
samasthanik hyperlastic samagrisathi, davi daabee daabee davi davi davi davi davi davi davi davi davi davi davi davi davi davi davi davi davi davi davi davi davi davi davi davi davi davi davi davi davi davi davi davi davi davi davi davi davi davi davi davi davi davi davi davi davi davi davi davi davi davi davi davi davi davi davi davi davi davi davi davi davi davi davi davi davi davi davi davi davi davi davi davi davi davi davi davi davi davi davi davi davi davi davi davi davi davi davi davi davi davi davi davi davi davi davi davi davi davi davi davi davi davi davi davi davi davi davi davi davi davi davi davi davi davi davi davi davi davi davi jarr taana urja ghanata karya sootra _ 35 asel tarr
sootra _ 36
(yaa chinhanchya vyakhyansathi davya bajula asalelya kachee-green virupan tenservaril paan pahaa).
 </ganeet>
jethe sootra _ 37 heey yogya kachee-green virupan tensor aahe aanee sootra _ 16 heey virupan pravanata aahe. dandga taana deela jaato
sootra _ 39
jethe sootra _ 40. sootra _ 41 heey sootra _ 19 chey teen pramukh aparivartak asoo dya.
sootra _ 43
samamiteey tensor sootra _ 19 chya aparivartananche vyutpann aahet
sootra _ 45
mhanoon, aapan lihu shakato
sootra _ 46
kachee stressathi abhivyaktimadhye jodale jaane dete
sootra _ 47
davikadil kachee-green virupan tensor sootra _ 48 vaparoon aanee teey sootra _ 49 lakshat gheuun aapan lihu shakato.
sootra _ 50
asampidit naan karata yenyajogya samagri sutrasathi _ 51 aanee mhanoon formula_52.then
sootra _ 53
tyamule, kachee taana haah yaa dware deela jaato
sootra _ 54
jethe sootra _ 32 haah eka anirdharit daab aahe joou asampidankshamatechya nirbandhala lagoo karnyasathi lagrange gunak mhanoon karya karato.
jarr, yavyatirikt, sootra _ 56, tarr aaplyakade sootra _ 57 aahe aanee mhanoon
sootra _ 58
asha paristhitit kachee taana mhanoon vyakt keela jaau shakato
sootra _ 59
sootra _ 61 chey aparivartak aahet
sootra _ 62
vikrutipoorn vartanachi vyakhya karnyasathi vaparale jaanare aparivartanancha sanch heey samaroop davya kachee-hiravya vikrutee tensor tensorche pahile done aparivartak aahet, (jeey ujavya kachee hiravya taana tensorsathi samaan aahet) aanee aakarman vartanache varnan karnyasathi sharyatit sootra _ 63 joda.
aparivartaniy sutranusar kachee taana vyakt karnyasathi _ 64 lakshat thewa qee
sootra _ 65
vibhedacha sakhali niyam aaplyala deto
sootra _ 66
lakshat thewa qee kachee taana haah yaa dware deela jaato
sootra _ 50
aparivartaniy sootra _ 64 chya sandarbhat aamchyakade aahe
sootra _ 69
sootra _ 70 chya vyutpannansathi sootra _ 64 chya sandarbhat abhivyakti jodat, aamchyakade aahe
sootra _ 72
kinwa,
sootra _ 73
sootra _ 74 chya vichalanachya drushtine, aapan lihu shakato
sootra _ 75
asampidit naan karata yenyajogya samagri sutrasathi _ 76 aanee mhanoon formula_77.then
dandga taana deela jaato
sootra _ 78
jethe sootra _ 32 hii anirdharit dabasarkhi lagrange gunak sandnya aahe. yavyatirikt, jarr sootra _ 80 asel tarr, aaplyakade sootra _ 81 aahe aanee mhanoon
kachee taana mhanoon vyakt keela jaau shakato
sootra _ 82
 = \frac {1} {2\lambda _ i} ~ \boldsymbol {r} ^ t\cdot (\mathbf {n} _ i\otymes\mathbf {n} _ i) \cdot\boldsymbol {r} ~;
 i = 1,2,3 ~.
 </ganeet>
sakhali niyam deto
sootra _ 83
dandga taana deela jaato
sootra _ 84
sootra _ 70 chya vyutpattisathi abhivyakti jodalyane
sootra _ 86
sootra _ 87 chey varnakrameey vighatan vaparoon aamchyakade aahe
sootra _ 88
hehee lakshat ghya qee
sootra _ 89
mhanoon, kachee tanavachi abhivyakti ashee lihili jaau shakate
sootra _ 90
asampidit naan karata yenyajogya bhautik sutrasathi _ 91 aanee mhanoon sootra _ 92. augden pii. chey anusaran karane. 485, aapan lihu shakato
sootra _ 93
yaa tappyavar thodi kalji ghene aavashyak aahe kaaran, jevha igenvaluechy punaravrutti hote, tevha teey sarvasadharanpane keval gatox differentiable asate, parantu freckett differentiable nasate. aanakhi eka eigenvalue samasya sodavunach kathor tensor vyutpann shodhale jaau shakate.
jarr aapan ghatakanmadhil farkanchya sandarbhat taana vyakt keela,
sootra _ 94
jarr asampidikaranachya vyatirikt aaplyakade sootra _ 95 asel tarr samasyevar sambhavya upay
sootra _ 96 aavashyak aahe aanee aapan tanavache farak asey lihu shakato
sootra _ 97
asampidit samasthanik hyperlastic samagri.
asampidit samasthanik hyperlastic samagrisathi, taana urja ghanata karya sootra _ 98 aahe. tyanantar kachee taana deela jaato
sootra _ 99
jethe sootra _ 32 haah anirdharit daab aahe. tanavachya farkanusar
sootra _ 101
jarr sootra _ 56 vyatirikt asel, tarr
sootra _ 59
jarr sootra _ 95 asel, tarr
sootra _ 97
resheey lavchiktesah susangatata.
hyperlastic samagri modelsche kahee mapdand nishchit karnyasathi resheey lavchiktesah susangatata anekada vaparali jaate. yaa susangatatechya paristhiti hukchya niyamachi tulana lahan tananvar rekheey hyperlasticityshy karoon shodhalya jaau shakatat.
samasthanik hyperlastic modelsasathi susangatatechya atty.
samasthanik hyperlastic samagri samasthanik resheey lavchikteshi susangat honyasathi, taana-taana sambandhat anant taana maryadet khaleel swaroop asaveh
sootra _ 106
jethe sootra _ 107 heey lamey sthirank aahet. vareel sambandhanshi sambandhit taana urja ghanata karya aahe
sootra _ 108
asampidit naan karata yenyajogya samgrichya sutrasathi _ 109 aanee aamchyakade aahe
sootra _ 110
konatyahi taana urja ghanata karya sutrasathi _ 111 lahan tanansathi vareel swarupanmadhye qamee karnyasathi khaleel atty purn karavya lagtil
sootra _ 112
jarr samagri asampidit karnyayogya nasel, tarr vareel atty khaleel swarupat vyakt kelya jaau shakatat.
sootra _ 113
yaa atincha vapar dilelya hyperlastic modelche mapdand aanee katarane aanee mothya pramanat modulinmadhil sambandh shodhanyasathi keela jaau shakato.
asampidak aadharit rubber samagrisathi susangatatechya atty.
anek elastomersche, taana urja ghanata karyadvare purese pratirupan kele jaate jeey keval sootra _ 114 varr avalambun asate. asha samagrisathi aaplyakade sootra _ 57 aahe.
sootra _ 116 sathee asampidit samagrisathi susangatatechya atty nantar asha prakare vyakt kelya jaau shakatat
sootra _ 117
vareel dusari susangatata aut hii lakshat gheuun ghetali jaau shakate qee
sootra _ 118
heey sambandh nantar samasthanik asampidit hyperlastic samagrisathi susangatatechya sthiteet badalale jaau shakatat.