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Sandwich vaj huam sib luag qauv yog dav siv nyob rau hauv ntau lub lag luam vim lawv cov khoom siv tshuab siab. Lub interlayer ntawm cov qauv no yog qhov tseem ceeb heev hauv kev tswj hwm thiab txhim kho lawv cov khoom siv kho tshuab raws li ntau yam kev thauj khoom. Concave lattice structures yog cov neeg sib tw zoo tshaj plaws rau kev siv los ua interlayers hauv cov qauv sandwich rau ntau qhov laj thawj, xws li kho lawv cov elasticity (piv txwv li, Poisson tus piv thiab elastic stiffness qhov tseem ceeb) thiab ductility (xws li, siab elasticity) rau simplicity. Lub zog-rau-hnyav piv zog yog ua tiav los ntawm kev kho tsuas yog cov ntsiab lus geometric uas tsim los ntawm chav tsev cell. Ntawm no, peb tshawb xyuas cov lus teb flexural ntawm 3-txheej concave core sandwich vaj huam sib luag siv analytical (ie, zigzag theory), kev suav (ie, finite element) thiab kev sim. Peb kuj tau txheeb xyuas qhov cuam tshuam ntawm ntau yam geometric tsis ntawm concave lattice qauv (xws li lub kaum sab xis, thickness, chav cell ntev mus rau qhov siab piv) ntawm tag nrho cov neeg kho tshuab tus cwj pwm ntawm cov qauv sandwich. Peb tau pom tias cov qauv tseem ceeb nrog tus cwj pwm auxetic (xws li qhov tsis zoo Poisson tus piv) pom muaj zog dua flexural thiab tsawg kawg nkaus tawm ntawm lub dav hlau shear stress piv rau cov pa gratings. Peb qhov kev tshawb pom tuaj yeem ua rau txoj hauv kev rau kev txhim kho cov txheej txheem ua haujlwm siab tshaj plaws nrog cov txheej txheem tsim vaj tsev rau kev siv aerospace thiab biomedical.
Vim lawv lub zog siab thiab qhov hnyav, cov khoom siv sandwich tau siv dav hauv ntau qhov kev lag luam, nrog rau cov khoom siv kho tshuab thiab kev ua kis las tsim, marine, aerospace, thiab biomedical engineering. Concave lattice structures yog ib tus neeg sib tw uas muaj peev xwm raug suav hais tias yog cov txheej txheem tseem ceeb hauv cov qauv sib xyaw vim lawv lub zog nqus tau zoo dua thiab muaj zog-rau-qhov hnyav piv zog 1,2,3. Yav dhau los, kev siv zog zoo tau tsim los tsim cov qauv sib xyaw ua ke nrog concave lattices los txhim kho cov khoom siv kho tshuab. Piv txwv ntawm cov qauv tsim muaj xws li kev kub siab loads hauv nkoj hulls thiab shock absorbers hauv tsheb 4,5. Yog vim li cas vim li cas cov qauv concave lattice yog nrov heev, tshwj xeeb thiab haum rau kev tsim vaj huam sib luag sandwich yog nws lub peev xwm los kho nws tus kheej elastomechanical zog (xws li elastic stiffness thiab Poisson piv). Ib qho txiaj ntsig zoo li no yog tus cwj pwm auxetic (lossis tsis zoo Poisson tus piv), uas yog hais txog kev nthuav dav ntawm lub lattice qauv thaum ncab longitudinally. Qhov kev coj cwj pwm txawv txawv no muaj feem xyuam nrog kev tsim microstructural ntawm nws cov khoom siv hauv cov hlwb 7,8,9.
Txij li thaum Lakes 'kev tshawb fawb thawj zaug rau hauv kev tsim cov auxetic foams, kev siv zog tseem ceeb tau tsim los tsim cov qauv ntxeem tau nrog qhov tsis zoo Poisson tus piv 10,11. Ob peb lub geometries tau raug npaj kom ua tiav lub hom phiaj no, xws li chiral, semi-rigid, thiab rigid rotating unit cells, 12 tag nrho cov uas muaj kev coj cwj pwm auxetic. Lub advent ntawm additive manufacturing (AM, tseem hu ua 3D printing) technologies kuj tau yooj yim rau kev siv ntawm cov 2D los yog 3D auxetic structures13.
Tus cwj pwm auxetic muab cov khoom siv tshwj xeeb. Piv txwv li, Pas Dej thiab Elms14 tau pom tias cov auxetic foams muaj zog ntau dua, muaj peev xwm nqus tau ntau dua, thiab qis qis dua li cov pa npuas. Hais txog cov khoom siv hluav taws xob zoo ntawm cov auxetic foams, lawv pom tias muaj kev tiv thaiv ntau dua nyob rau hauv lub zog tawg thiab ntau dua elongation nyob rau hauv ntshiab tension15. Tsis tas li ntawd, kev siv cov auxetic fibers ua cov khoom siv ntxiv hauv cov khoom sib xyaw yuav txhim kho lawv cov khoom siv kho tshuab16 thiab tiv thaiv kev puas tsuaj los ntawm fiber ntau stretch17.
Kev tshawb fawb kuj tau qhia tias kev siv concave auxetic lug ua lub hauv paus ntawm cov qauv sib xyaw ua ke tuaj yeem txhim kho lawv qhov kev ua tau zoo ntawm lub dav hlau, suav nrog flexural txhav thiab lub zog18. Siv cov qauv txheej txheej, nws kuj tau pom tias cov tub ntxhais auxetic tuaj yeem ua rau kom tawg lub zog ntawm cov vaj huam sib luag sib xyaw19. Composites nrog auxetic fibers kuj tiv thaiv kev tawg tawg piv rau cov pa fibers20.
Zhang et al.21 tau ua qauv qhia txog kev sib tsoo zoo ntawm cov qauv ntawm tes rov qab. Lawv pom tias qhov hluav taws xob thiab lub zog nqus tau tuaj yeem txhim kho los ntawm kev ua kom lub kaum sab xis ntawm lub auxetic unit cell, ua rau lub grating nrog qhov tsis zoo Poisson tus piv. Lawv kuj tau hais tias xws li auxetic sandwich panels tuaj yeem siv los ua cov qauv kev tiv thaiv tiv thaiv kev cuam tshuam ntawm cov khoom hnyav. Imbalzano et al.22 kuj tau tshaj tawm tias auxetic composite sheets tuaj yeem cuam tshuam ntau lub zog (piv txwv li ob zaug ntau dua) los ntawm cov yas deformation thiab tuaj yeem txo qhov ceev ntawm sab nraub qaum los ntawm 70% piv rau ib daim ntawv ply.
Nyob rau hauv xyoo tas los no, ntau qhov kev saib xyuas tau raug them rau cov lej thiab kev sim ntawm cov qauv sandwich nrog auxetic muab tub lim. Cov kev tshawb fawb no qhia txog txoj hauv kev los txhim kho cov khoom siv dag zog ntawm cov qauv sandwich. Piv txwv li, xav txog cov txheej auxetic tuab txaus raws li lub hauv paus ntawm lub vaj huam sib luag sandwich tuaj yeem ua rau muaj txiaj ntsig zoo dua Young's modulus dua li cov txheej txheem nruj tshaj plaws23. Tsis tas li ntawd, kev khoov tus cwj pwm ntawm laminated beams 24 lossis auxetic core tubes 25 tuaj yeem txhim kho nrog kev ua kom zoo dua qub. Muaj lwm cov kev tshawb fawb txog kev ntsuas kev ntsuas ntawm cov tub ntxhais kawm tiav cov txheej txheem sandwich nyob rau hauv ntau txoj kev thauj khoom. Piv txwv li, kev sim compression ntawm cov pob zeb sib xyaw nrog auxetic aggregates, sandwich panels nyob rau hauv explosive loads27, bending tests28 thiab low-velocity impact tests29, as well as analysis of non-linear bending of sandwich panels with functionally differentiated auxetic aggregates30.
Vim hais tias lub computer simulations thiab kev soj ntsuam kev soj ntsuam ntawm cov qauv no feem ntau siv sij hawm thiab kim, yuav tsum tau tsim theoretical txoj kev uas yuav ua tau zoo thiab raug muab cov ntaub ntawv xav tau los tsim multilayer auxetic core qauv nyob rau hauv arbitrary loading tej yam kev mob. lub sijhawm tsim nyog. Txawm li cas los xij, cov kev ntsuas niaj hnub no muaj ntau qhov kev txwv. Tshwj xeeb, cov kev xav no tsis yog qhov tseeb txaus los kwv yees tus cwj pwm ntawm cov ntaub ntawv sib xyaw tuab thiab txheeb xyuas cov khoom sib xyaw ua ke ntawm ntau cov ntaub ntawv uas muaj qhov sib txawv ntawm elasticity.
Txij li cov qauv kev ntsuas no nyob ntawm kev siv cov khoom thauj thiab ciam teb, ntawm no peb yuav tsom mus rau kev coj tus cwj pwm ntawm auxetic core sandwich panels. Qhov sib npaug ib txheej txoj kev xav siv rau cov kev ntsuam xyuas zoo li no tsis tuaj yeem kwv yees kev txiav thiab axial stresses hauv cov laminates uas tsis sib xws hauv cov tuab tuab tuab. Tsis tas li ntawd, nyob rau hauv qee qhov kev xav (piv txwv li, hauv cov txheej txheem txheej txheem), tus naj npawb ntawm cov kinematic variables (piv txwv li, hloov chaw, tshaj tawm, thiab lwm yam) muaj zog nyob ntawm cov txheej txheem. Qhov no txhais tau hais tias thaj tsam ntawm kev txav ntawm txhua txheej tuaj yeem piav qhia ntawm nws tus kheej, thaum txaus siab rau qee qhov kev txwv ntawm lub cev. Yog li ntawd, qhov no coj mus rau hauv tus account ib tug loj tus naj npawb ntawm variables nyob rau hauv cov qauv, uas ua rau qhov no txoj kev xam tau tias kim kim. Txhawm rau kov yeej cov kev txwv no, peb nthuav tawm txoj hauv kev raws li zigzag txoj kev xav, ib qho kev qhia tshwj xeeb ntawm ntau txoj kev xav. Txoj kev xav muab kev txuas ntxiv ntawm kev ntxhov siab thoob plaws lub thickness ntawm lub laminate, piv txwv li ib tug zigzag qauv ntawm nyob rau hauv-dav hlau hloov. Yog li, lub zigzag txoj kev xav muab tib tus naj npawb ntawm kinematic variables tsis hais tus naj npawb ntawm cov txheej hauv laminate.
Txhawm rau ua kom pom lub zog ntawm peb cov txheej txheem hauv kev kwv yees tus cwj pwm ntawm sandwich panels nrog concave cores nyob rau hauv khoov loads, peb muab piv peb cov txiaj ntsig nrog classical theories (piv txwv li peb txoj hauv kev nrog cov qauv kev suav (xws li cov ntsiab lus finite) thiab cov ntaub ntawv sim (piv txwv li peb-point dabtsi yog khoov ntawm 3D luam ntawv sandwich panels).Rau qhov kawg no, peb thawj zaug muab cov kev sib raug zoo hloov chaw raws li lub zigzag txoj kev xav, thiab tom qab ntawd tau txais cov kev sib npaug sib npaug siv Hamilton txoj cai thiab daws lawv siv txoj kev Galerkin.Cov txiaj ntsig tau txais yog cov cuab yeej muaj zog rau kev tsim qauv sib xws. geometric parameters ntawm sandwich panels nrog auxetic fillers, yooj yim rau kev tshawb nrhiav cov qauv nrog cov khoom siv kho kom zoo dua qub.
Xav txog peb txheej sandwich vaj huam sib luag (Fig. 1). Geometric tsim tsis: sab saum toj txheej \({h}_{t}\), nruab nrab txheej \({h}_{c}\) thiab hauv qab txheej \({h}_{b }\) thickness. Peb xav hais tias cov txheej txheem core muaj ib tug pitted lattice qauv. Cov qauv tsim muaj cov hlwb theem pib uas nyob ib sab ntawm ib leeg hauv kev txiav txim. Los ntawm kev hloov cov geometric tsis ntawm cov qauv concave, nws muaj peev xwm hloov nws cov khoom siv kho tshuab (piv txwv li, qhov tseem ceeb ntawm Poisson tus piv thiab elastic stiffness). Geometrical parameters ntawm lub hauv paus cell yog qhia nyob rau hauv daim duab. 1 suav nrog lub kaum sab xis (θ), ntev (h), qhov siab (L) thiab kab tuab (t).
Lub zigzag txoj kev xav muab kev kwv yees qhov tseeb ntawm kev ntxhov siab thiab kev coj cwj pwm ntawm cov txheej txheem sib xyaw ntawm cov tuab tuab. Kev hloov pauv ntawm cov qauv hauv lub zigzag txoj kev xav muaj ob feem. Thawj ntu qhia txog tus cwj pwm ntawm lub vaj huam sib luag sandwich tag nrho, thaum qhov thib ob saib tus cwj pwm ntawm cov khaubncaws sab nraud povtseg kom ntseeg tau tias kev ntxhov siab txuas ntxiv (los yog hu ua zigzag function). Tsis tas li ntawd, cov ntsiab lus zigzag ploj mus rau sab nrauv ntawm lub laminate, thiab tsis nyob hauv txheej no. Yog li, lub zigzag muaj nuj nqi ua kom ntseeg tau tias txhua txheej ua rau tag nrho cov hla ntu deformation. Qhov sib txawv tseem ceeb no muab qhov kev faib tawm ntawm lub cev ntau dua ntawm zigzag muaj nuj nqi piv rau lwm cov haujlwm zigzag. Tus qauv hloov kho zigzag tam sim no tsis muab kev sib hloov shear kev nyuaj siab txuas ntxiv raws li txheej nruab nrab. Yog li ntawd, qhov chaw hloov chaw raws li qhov kev xav zigzag tuaj yeem sau tau raws li hauv qab no31.
hauv kev sib npaug. (1), k = b, c thiab t sawv cev rau hauv qab, nruab nrab thiab sab saum toj txheej, feem. Qhov chaw xaav ntawm lub dav hlau nruab nrab raws Cartesian axis (x, y, z) yog (u, v, w), thiab khoov kev sib hloov hauv lub dav hlau txog (x, y) axis yog \({\uptheta} _ {x}\) and \ ({\uptheta}_{y}\). \({\psi}_{x}\) and \({\psi}_{y}\) are spatial quantities of zigzag rotation, and \({\phi}_{x}^{k}\left ( z \right)\) and \({\phi}_{y}^{k}\left(z\right)\) yog zigzag functions.
Lub amplitude ntawm lub zigzag yog ib tug vector muaj nuj nqi ntawm cov lus teb tiag tiag ntawm lub phaj rau cov ntaub ntawv load. Lawv muab qhov tsim nyog scaling ntawm lub zigzag muaj nuj nqi, yog li tswj tag nrho cov kev pab cuam ntawm zigzag mus rau qhov chaw nyob rau hauv lub dav hlau. Shear strain hla lub phaj thickness muaj ob yam. Qhov thib ib yog lub kaum sab xis shear, niaj hnub hla lub thickness ntawm lub laminate, thiab qhov thib ob yog ib qho kev ua haujlwm tas mus li, niaj hnub hla lub thickness ntawm txhua tus neeg txheej. Raws li cov haujlwm tas li no, zigzag muaj nuj nqi ntawm txhua txheej tuaj yeem sau ua:
hauv kev sib npaug. (2), \({c}_{11}^{k}\) thiab \({c}_{22}^{k}\) yog cov elasticity tas li ntawm txhua txheej, thiab h yog tag nrho cov tuab ntawm lub disc. Ntxiv rau, \({G}_{x}\) thiab \({G}_{y}\) yog qhov hnyav nruab nrab shear stiffness coefficients, qhia raws li 31:
Ob lub zigzag amplitude functions (Equation (3)) thiab qhov seem tsib kinematic variables (Equation (2)) ntawm thawj qhov kev txiav txim shear deformation txoj kev xav ua ib pawg ntawm xya kinematics txuam nrog qhov hloov kho zigzag phaj txoj kev xav txawv txav. Piv txwv li ib tug linear dependence ntawm deformation thiab coj mus rau hauv tus account lub zigzag txoj kev xav, lub deformation teb nyob rau hauv lub Cartesian coordinate system yuav muab tau raws li:
qhov twg \({\varepsilon}_{yy}\) and \({\varepsilon}_{xx}\) yog ib txwm deformations, thiab \({\gamma}_{yz},{\gamma}_{xz} \ ) and \({\gamma}_{xy}\) yog shear deformations.
Siv Hooke txoj cai thiab coj mus rau hauv tus account lub zigzag txoj kev xav, kev sib raug zoo ntawm kev ntxhov siab thiab strain ntawm ib lub phaj orthotropic nrog ib tug concave lattice qauv tuaj yeem tau los ntawm kev sib npaug (1). (5) 32 qhov twg \({c}_{ij}\) yog qhov elastic tas li ntawm qhov kev ntxhov siab-txoj kev matrix.
where \({G}_{ij}^{k}\), \({E}_{ij}^{k}\) and \({v}_{ij}^{k}\) raug txiav quab yuam yog lub modulus nyob rau hauv ntau cov lus qhia, Young's modulus thiab Poisson tus piv. Cov coefficients no sib npaug hauv txhua qhov kev qhia rau txheej isotopic. Tsis tas li ntawd, rau qhov rov qab nuclei ntawm lub lattice, raws li qhia hauv daim duab 1, cov khoom no tuaj yeem rov sau dua li 33.
Daim ntawv thov ntawm Hamilton lub hauv paus ntsiab lus rau qhov sib npaug ntawm cov lus tsa suab ntawm ib lub phaj multilayer nrog lub concave lattice core muab cov kev sib npaug yooj yim rau kev tsim. Hamilton lub hauv paus ntsiab lus tuaj yeem sau ua:
Ntawm lawv, δ sawv cev rau tus neeg teb xov tooj sib txawv, U sawv cev rau lub zog muaj peev xwm, thiab W sawv cev rau kev ua haujlwm los ntawm lub zog sab nraud. Tag nrho cov peev xwm strain zog yog tau los ntawm kev sib npaug. (9), qhov twg A yog thaj tsam ntawm lub dav hlau nruab nrab.
Piv txwv li ib daim ntawv thov ntawm lub load (p) nyob rau hauv lub z kev taw qhia, kev ua hauj lwm ntawm sab nraud quab yuam tuaj yeem tau los ntawm cov qauv hauv qab no:
Hloov cov kab zauv sib npaug (4) thiab (5) (9) thiab hloov qhov sib npaug. (9) thiab (10) (8) thiab kev sib xyaw ua ke ntawm cov phaj tuab, qhov sib npaug: (8) tuaj yeem sau dua tshiab raws li:
Lub index \(\phi\) sawv cev rau zigzag muaj nuj nqi, \({N}_{ij}\) thiab \({Q}_{iz}\) yog rog nyob rau hauv thiab tawm ntawm lub dav hlau, \({M} _{ij }\) sawv cev rau lub sijhawm khoov, thiab cov qauv kev suav yog raws li hauv qab no:
Siv kev sib xyaw ua ke los ntawm qhov chaw rau qhov sib npaug. Hloov mus rau hauv cov mis (12) thiab xam cov coefficient ntawm variation, lub defining sib npaug ntawm lub sandwich vaj huam sib luag yuav muab tau nyob rau hauv daim ntawv ntawm cov mis (12). (13).
Qhov sib txawv tswj sib npaug rau kev txhawb nqa peb-txheej daim hlau yog daws los ntawm txoj kev Galerkin. Raws li qhov kev xav ntawm quasi-static tej yam kev mob, qhov tsis paub muaj nuj nqi yog xam raws li ib qho kev sib npaug: (14).
\({u}_{m,n}\), \({v}_{m,n}\), \({w}_{m,n}\),\({\uptheta}_ {\mathrm {x}}}_{\mathrm {m} \text{,n}\),\({{\uptheta }_{\mathrm {y}}}_{\mathrm {m} \text {,n}}\), \({{\uppsi}_{\mathrm{x}}}_{\mathrm{m}\text{,n}}\) and \({{\uppsi}_{ \mathrm{y}}}_{\mathrm{m}\text{,n}}\) yog cov tsis paub tas li uas tuaj yeem tau txais los ntawm kev txo qhov yuam kev. \(\overline{\overline{u}} \left({x\text{,y}} \right)\), \(\overline{\overline{v}} \left({x\text {,y}}} \right)\), \(\overline{\overline{w}} \left( {x\text{,y}} \right)\), \(\overline{w}} {{{\uptheta}_{x}}} \left( {x{\text{,y}} \right)\), \(\overline{{{\uptheta}_{y}) }}} \left( {x{\text{,y}}} \right)\), \(\overline{{\psi_{x}}} \left( {x{\text{, y}}} \right)\) and \(\overline{\overline{{ \psi_{y} }}} \left( {x{\text{,y}}} \right)\) yog test functions, uas yuav tsum tau raws li qhov tsawg kawg nkaus tsim nyog ciam teb tej yam kev mob. Rau qhov kev txhawb nqa ciam teb xwb, qhov kev xeem muaj nuj nqi tuaj yeem suav rov qab raws li:
Hloov cov kev sib npaug muab algebraic equations. (14) rau cov kev sib npaug tswj, uas tuaj yeem ua rau kom tau txais cov coefficients tsis paub hauv kab zauv (14). (14).
Peb siv finite element modeling (FEM) rau lub computer-simulate lub dabtsi yog khoov ntawm ib tug dawb kev txhawb nqa sandwich vaj huam sib luag nrog ib tug concave lattice qauv raws li cov tub ntxhais. Kev tsom xam tau ua nyob rau hauv kev lag luam finite caij code (piv txwv li, Abaqus version 6.12.1). 3D hexahedral cov khoom (C3D8R) nrog kev sib koom ua ke yooj yim tau siv los ua qauv rau saum thiab hauv qab cov khaubncaws sab nraud povtseg, thiab linear tetrahedral ntsiab (C3D4) tau siv los ua qauv nruab nrab (concave) lattice qauv. Peb tau ua ib qho kev ntsuam xyuas mesh rhiab heev los ntsuas qhov sib koom ua ke ntawm cov mesh thiab xaus lus tias qhov kev hloov pauv tau sib koom ua ke ntawm qhov tsawg tshaj plaws feature loj ntawm peb txheej. Lub sandwich phaj yog loaded siv lub sinusoidal load muaj nuj nqi, coj mus rau hauv tus account lub dawb kev txhawb ciam nyob rau hauv lub plaub ntug. Tus cwj pwm linear elastic mechanical yog suav tias yog cov qauv khoom siv rau txhua txheej. Tsis muaj kev sib cuag tshwj xeeb ntawm cov khaubncaws sab nraud povtseg, lawv muaj kev sib tshuam.
Peb siv cov txheej txheem luam ntawv 3D los tsim peb tus qauv (xws li triple luam tawm auxetic core sandwich vaj huam sib luag) thiab sib haum rau kev sim teeb tsa los siv cov xwm txheej zoo sib xws (cov ris tsho load p raws z-kev taw qhia) thiab ciam teb cov xwm txheej (xws li kev txhawb nqa xwb). assumed nyob rau hauv peb analytical mus kom ze (Fig. 1).
Lub vaj huam sib luag luam tawm ntawm lub tshuab luam ntawv 3D muaj ob daim tawv nqaij (sab sauv thiab sab qis) thiab cov tub ntxhais concave lattice, qhov ntev ntawm cov uas tau qhia hauv Table 1, thiab tau tsim los ntawm Ultimaker 3 3D tshuab luam ntawv (Ltalis) siv txoj kev tso nyiaj ( FDM). technology yog siv nyob rau hauv nws cov txheej txheem. Peb 3D luam tawm lub hauv paus phaj thiab lub ntsiab auxetic lattice qauv ua ke, thiab luam tawm sab saum toj txheej nyias. Qhov no yuav pab kom tsis txhob muaj teeb meem thaum lub sijhawm kev txhawb nqa tshem tawm yog tias tag nrho cov qauv tsim yuav tsum tau luam tawm ib zaug. Tom qab 3D luam ntawv, ob qhov sib cais yog glued ua ke siv superglue. Peb luam tawm cov khoom siv no siv polylactic acid (PLA) ntawm qhov siab tshaj plaws infill ntom (piv txwv li 100%) los tiv thaiv ib qho chaw luam ntawv tsis xws luag.
Kev cai clamping system ua raws li tib yam kev txhawb nqa yooj yooj yim ciam teb tau txais los ntawm peb cov qauv ntsuas. Qhov no txhais tau hais tias lub kaw lus tuav tiv thaiv lub rooj tsavxwm los ntawm kev txav ntawm nws cov npoo hauv x thiab y cov lus qhia, tso cai rau cov npoo no tig ywj siab nyob ib ncig ntawm x thiab y axes. Qhov no yog ua los ntawm kev txiav txim siab fillets nrog lub vojvoog r = h / 2 ntawm plaub ntug ntawm lub kaw lus (Fig. 2). Lub kaw lus clamping no tseem ua kom ntseeg tau tias cov khoom siv tau raug xa mus los ntawm lub tshuab kuaj mus rau lub vaj huam sib luag thiab ua raws li cov kab nruab nrab ntawm lub vaj huam sib luag (daim duab 2). Peb tau siv ntau lub dav hlau 3D luam ntawv thev naus laus zis (ObjetJ735 Connex3, Stratasys® Ltd., USA) thiab cov khoom lag luam tawv tawv (xws li Vero series) los luam cov tuav.
Schematic daim duab ntawm 3D luam tawm kev cai gripping system thiab nws los ua ke nrog 3D luam ntawv sandwich vaj huam sib luag nrog ib tug auxetic core.
Peb ua cov kev soj ntsuam quasi-static compression uas siv lub tshuab ntsuas lub rooj ntev zaum (Lloyd LR, load cell = 100 N) thiab sau cov tshuab quab yuam thiab kev txav ntawm qhov piv txwv ntawm 20 Hz.
Tshooj lus no nthuav qhia txog kev tshawb fawb txog tus lej ntawm cov txheej txheem sandwich npaj. Peb xav tias cov khaubncaws sab saum toj thiab hauv qab yog ua los ntawm cov pa roj carbon epoxy resin, thiab cov lattice qauv ntawm cov tub ntxhais concave yog ua los ntawm polymer. Cov khoom siv hluav taws xob ntawm cov khoom siv hauv qhov kev tshawb fawb no tau pom nyob rau hauv Table 2. Tsis tas li ntawd, qhov tsis muaj qhov sib piv ntawm cov txiaj ntsig kev hloov pauv thiab cov kev ntxhov siab yog qhia hauv Table 3.
Qhov siab tshaj plaws ntsug dimensionless hloov chaw ntawm ib tug uniformly loaded dawb txhawb phaj yog muab piv nrog cov txiaj ntsig tau los ntawm ntau txoj kev (Table 4). Muaj kev pom zoo zoo ntawm qhov kev xav tau, cov txheej txheem finite element thiab cov kev sim ua pov thawj.
Peb muab piv rau txoj kev hloov ntsug ntawm kev hloov kho zigzag txoj kev xav (RZT) nrog 3D elasticity txoj kev xav (Pagano), thawj qhov kev txiav txim shear deformation theory (FSDT), thiab FEM cov txiaj ntsig (saib daim duab 3). Thawj qhov kev txiav txim shear txoj kev xav, raws li cov duab xaav ntawm cov phaj tuab tuab, sib txawv feem ntau ntawm cov tshuaj elastic. Txawm li cas los xij, qhov hloov kho zigzag txoj kev kwv yees kwv yees tau qhov tseeb heev. Tsis tas li ntawd, peb kuj tau muab piv rau qhov tawm ntawm lub dav hlau shear kev nyuaj siab thiab nyob rau hauv lub dav hlau ib txwm muaj kev ntxhov siab ntawm ntau yam kev xav, ntawm cov kev tshawb xav zigzag tau txais txiaj ntsig zoo dua li FSDT (Fig. 4).
Kev sib piv ntawm normalized ntsug strain xam siv cov kev xav sib txawv ntawm y = b/2.
Hloov hauv kev ntxhov siab shear (a) thiab kev ntxhov siab ib txwm (b) hla lub thickness ntawm lub vaj huam sib luag sandwich, suav nrog ntau yam kev xav.
Tom ntej no, peb txheeb xyuas qhov cuam tshuam ntawm geometric tsis ntawm chav tsev cell nrog lub concave core ntawm tag nrho cov khoom siv ntawm lub vaj huam sib luag sandwich. Lub kaum sab xis ntawm tes yog qhov tseem ceeb tshaj plaws geometric parameter nyob rau hauv kev tsim ntawm reentrant lattice structures34,35,36. Yog li ntawd, peb xam qhov cuam tshuam ntawm lub kaum sab xis ntawm tes, nrog rau cov tuab sab nraud ntawm cov tub ntxhais, ntawm tag nrho cov deflection ntawm lub phaj (Fig. 5). Raws li lub thickness ntawm nruab nrab txheej nce, qhov siab tshaj plaws dimensionless deflection txo. Tus txheeb ze dabtsi yog khoov lub zog nce rau thicker core txheej thiab thaum \(\frac{{h}_{c}}{h}=1\) (ie, thaum muaj ib tug concave txheej). Sandwich panels nrog ib qho auxetic unit cell (ie \(\theta = 70^\circ\)) muaj qhov tsawg tshaj plaws hloov chaw (Fig. 5). Qhov no qhia tau hais tias lub zog dabtsi yog khoov ntawm auxetic core yog siab dua li ntawm cov pa auxetic core, tab sis tsis tshua muaj txiaj ntsig thiab muaj qhov zoo ntawm Poisson tus piv.
Normalized siab tshaj deflection ntawm ib tug concave lattice pas nrig nrog txawv chav tsev cell ces kaum thiab tawm-ntawm-plane thickness.
Lub thickness ntawm cov tub ntxhais ntawm lub auxetic grating thiab nam piv (ie \(\theta = 70^\circ\)) cuam tshuam rau qhov siab tshaj plaws ntawm lub sandwich phaj (Daim duab 6). Nws tuaj yeem pom tias qhov siab tshaj plaws deflection ntawm phaj nce nrog nce h / l. Tsis tas li ntawd, nce lub thickness ntawm lub auxetic core txo qhov porosity ntawm concave qauv, yog li ua rau lub zog khoov ntawm cov qauv.
Qhov siab tshaj plaws deflection ntawm sandwich panels tshwm sim los ntawm cov txheej txheem lattice nrog ib tug auxetic core ntawm ntau thicknesses thiab lengths.
Txoj kev kawm ntawm cov kev ntxhov siab yog ib qho chaw nthuav dav uas tuaj yeem tshawb xyuas los ntawm kev hloov cov geometric parameters ntawm chav tsev cell los kawm cov hom kev ua tsis tiav (xws li delamination) ntawm cov txheej txheem multilayer. Poisson qhov piv tau muaj txiaj ntsig zoo dua rau thaj tsam ntawm kev tawm ntawm lub dav hlau shear stresses dua li ib txwm muaj kev ntxhov siab (saib daim duab 7). Tsis tas li ntawd, cov nyhuv no yog inhomogeneous nyob rau hauv cov lus qhia sib txawv vim yog cov khoom orthotropic ntawm cov khoom ntawm cov gratings. Lwm qhov kev ntsuas geometric, xws li thickness, qhov siab, thiab ntev ntawm cov qauv concave, muaj kev cuam tshuam me ntsis ntawm qhov kev ntxhov siab, yog li lawv tsis tau txheeb xyuas hauv qhov kev tshawb fawb no.
Hloov cov shear stress Cheebtsam nyob rau hauv sib txawv txheej ntawm ib tug sandwich vaj huam sib luag nrog ib tug lattice muab tub lim nrog txawv concavity kaum.
Ntawm no, lub zog dabtsi yog khoov ntawm ib qho kev txhawb nqa ywj pheej multilayer phaj nrog lub concave lattice core yog tshawb xyuas siv lub zigzag txoj kev xav. Cov txheej txheem npaj tau muab piv nrog rau lwm cov kev tshawb xav classical, suav nrog peb-dimensional elasticity txoj kev xav, thawj-txiav txiav deformation txoj kev xav, thiab FEM. Peb kuj siv tau peb txoj kev los ntawm kev sib piv peb cov txiaj ntsig nrog cov txiaj ntsig kev sim ntawm 3D luam ntawv sandwich qauv. Peb cov txiaj ntsig tau pom tias qhov kev xav zigzag muaj peev xwm kwv yees qhov deformation ntawm cov vaj huam sib luag ntawm cov tuab tuab nyob rau hauv kev khoov loads. Tsis tas li ntawd, qhov cuam tshuam ntawm geometric tsis ntawm concave lattice qauv ntawm kev khoov tus cwj pwm ntawm sandwich panels tau txheeb xyuas. Cov txiaj ntsig tau pom tias thaum qib auxetic nce ntxiv (piv txwv li, θ <90), lub zog khoov nce ntxiv. Tsis tas li ntawd, kev nce qhov sib piv thiab txo cov thickness ntawm cov tub ntxhais yuav txo tau lub zog dabtsi yog khoov ntawm lub vaj huam sib luag sandwich. Thaum kawg, cov txiaj ntsig ntawm Poisson qhov piv ntawm qhov kev ntxhov siab tawm ntawm lub dav hlau shear yog kawm, thiab nws tau lees paub tias Poisson tus piv muaj qhov cuam tshuam loj tshaj plaws ntawm kev ntxhov siab shear tsim los ntawm lub thickness ntawm lub phaj laminated. Cov qauv tsim thiab cov lus xaus tuaj yeem qhib txoj hauv kev rau kev tsim thiab kev ua kom zoo ntawm cov txheej txheem ntau txheej nrog concave lattice fillers nyob rau hauv ntau txoj kev thauj khoom uas tsim nyog rau kev tsim cov qauv thauj khoom hauv aerospace thiab biomedical technology.
Cov ntaub ntawv siv thiab / lossis tshuaj ntsuam hauv txoj kev tshawb fawb tam sim no muaj los ntawm cov kws sau ntawv raws li qhov kev thov tsim nyog.
Aktai L., Johnson AF thiab Kreplin B. Kh. Numerical simulation ntawm kev puas tsuaj yam ntxwv ntawm honeycomb cores. engineer. fractal. plaub. 75(9), 2616–2630 (2008).
Gibson LJ thiab Ashby MF Porous Solids: Structure thiab Properties (Cambridge University Press, 1999).


Post lub sij hawm: Aug-12-2023