Data ya nyenzo¶
Katika FrontISTR, "material" ni kitengo chenye jina kinachosimamia kwa pamoja data ya material properties inayotolewa kwa elementi. Hii inajumuisha property values kama elastic modulus, density, na thermal conductivity, pamoja na constitutive-law parameters za elastoplasticity, viscoelasticity, creep, n.k., zote zikiwa chini ya jina moja. Ugawaji kwa element groups hufanywa kwa !SECTION, ambayo huunganisha aina ya elementi (solid, shell, interface, n.k.) na material name. Maudhui ya material yenyewe hufafanuliwa na !MATERIAL upande wa mesh data au ndani ya block ya !MATERIAL ya analysis control data.
Vizuizi vya material data huamuliwa na mambo matatu: aina ya uchanganuzi, aina ya elementi, na namna ya specification katika input files. Sehemu zifuatazo kwanza zinapanga material models zinazopatikana na ulinganifu wake na elementi/aina za uchanganuzi (Muhtasari wa vipengele), kisha zinaeleza jinsi ya kuchagua model (Jinsi ya kuchagua material model), na baadaye specification ya kila model (kuanzia Linear elasticity). Tazama keyword reference kwa syntax na default values za kila keyword.
Muhtasari wa vipengele¶
Material data inaweza kugawanywa kwa upana katika mechanical material models zinazotumika kwa structural analysis na thermal properties zinazotumika kwa heat-conduction na thermal-stress analyses. Kwa structural analysis, chagua linear elasticity, hyperelasticity, elastoplasticity, viscoelasticity, creep, au user-defined material kulingana na matumizi. Hizi ni constitutive laws huru; kwa elastoplasticity, viscoelasticity, na creep, linear elasticity pia hufafanuliwa ndani ya material hiyo kama elastic part (hyperelasticity hutumia strain-energy function yake na hairejelei stiffness ya linear elasticity). Kwa heat-conduction analysis, density, specific heat, na thermal conductivity hupewa elementi.
| Uainishaji | Matumizi makuu | Keywords kuu za input | Marejeo makuu |
|---|---|---|---|
| Linear elasticity | Small-deformation linear analysis, modal analysis, linear dynamic analysis, elastic part ya nonlinear materials | !ELASTIC, !MATERIAL ITEM=1 | !ELASTIC, !MATERIAL (mesh data) |
| Hyperelasticity | Large-deformation elastic response ya rubber-like materials, n.k. | !HYPERELASTIC | !HYPERELASTIC |
| Elastoplasticity | Permanent strain baada ya yield, metal plasticity, geomaterials | !PLASTIC | !PLASTIC |
| Viscoelasticity | Time-dependent response yenye relaxation na retardation | !VISCOELASTIC, !TRS | !VISCOELASTIC, !TRS |
| Creep | Deformation inayoendelea kwa muda chini ya stress | !CREEP | !CREEP |
| Thermal properties | Heat-conduction analysis, thermal-stress analysis | !MATERIAL ITEM=1–3, !EXPANSION_COEFF | !EXPANSION_COEFF |
| User-defined material | Constitutive law iliyotekelezwa na mtumiaji | !USER_MATERIAL, !ELASTIC TYPE=USER, !HYPERELASTIC TYPE=USER, !PLASTIC YIELD=USER | !USER_MATERIAL |
Katika structural analysis, material yenye jina lilelile ikifafanuliwa katika mesh data na analysis control data, definition ya analysis control data ina kipaumbele. Hata hivyo, material definition upande wa mesh data yenyewe ni lazima; ikiwa material yenye jina lilelile imefafanuliwa pia kwenye analysis control data, values za mesh data hazirejelewi na zinaweza kuwa dummy. Kwa heat-conduction analysis, material specification katika analysis control data haitumiki; values zilizowekwa katika mesh data hutumika moja kwa moja.
Ulinganifu kwa aina ya uchanganuzi unaweza kufupishwa hivi. Linear static analysis, modal analysis, na linear dynamic analysis hutumia linear elasticity. Nonlinear static na nonlinear dynamic analyses zenye 3D continuum solid elements zinaweza kutumia hyperelasticity, elastoplasticity, viscoelasticity, creep, na user-defined materials juu ya msingi wa linear elasticity. Heat-conduction analysis hutumia density, specific heat, na thermal conductivity badala ya structural material models. Tazama Aina za uchanganuzi kwa muhtasari.
Pia kuna vizuizi kwa aina ya elementi. 3D continuum solid elements zinaweza kutumia nonlinear material models za structural analysis. Plane-stress, plane-strain, na axisymmetric elements hutumia linear elasticity kama msingi; 2D elements hizi hazitumii elastoplasticity, hyperelasticity, viscoelasticity, au creep. Shell elements hutumia linear elasticity na zinaweza kuwa single-layer au laminated, isotropic au anisotropic; hazitumii nonlinear material models hizo. Interface elements hutumika kwa gap heat transfer na radiation katika heat-conduction analysis; gap parameters huwekwa katika data rows za !SECTION, si material data. Kwa mapping ya element groups na mifano ya laminated input, tazama pia Maktaba ya elementi.
Jedwali lifuatalo linaonyesha upatikanaji wa material models kwa kila aina ya elementi.
| Aina ya elementi | Linear elasticity (isotropic) | Linear elasticity (orthotropic/laminated) | Hyperelasticity | Elastoplasticity | Viscoelasticity | Creep | Thermal properties |
|---|---|---|---|---|---|---|---|
| 3D solid | ○ | ○ | ○ | ○ | ○ | ○ | ○ |
| Plane stress / plane strain / axisymmetric | ○ | — | — | — | — | — | ○ |
| Shell (single-layer/laminated) | ○ | ○ | — | — | — | — | — |
| Beam / truss | ○ | — | — | — | — | — | — |
| Interface | — | — | — | — | — | — | ○ |
(Alama: ○ inapatikana / — haitumiki). Kwa interface elements, thermal properties za gap heat transfer na radiation huwekwa kwa !SECTION.
Kuna njia mbili za kufafanua material. Katika mesh data, !SECTION huunganisha element group na material name, na !MATERIAL pamoja na !ITEM hufafanua properties. Katika analysis control data, ndani ya block ya !MATERIAL, material model hufafanuliwa kwa kuweka !ELASTIC, !HYPERELASTIC, !PLASTIC, n.k. Ikiwa !MATERIAL imefafanuliwa katika analysis control data, definition hiyo hutumika badala ya material yenye jina lilelile katika mesh data. Kwa maelezo ya !SECTION na !MATERIAL upande wa mesh data, tazama !SECTION (mesh data) na !MATERIAL (mesh data). Kwa material block ya analysis control data, tazama !MATERIAL (analysis control data).
Jinsi ya kuchagua material model¶
Wakati wa kuchagua material model, kwanza amua kama linear elasticity inatosha. Tumia linear elasticity ikiwa deformation ni ndogo, stress haivuki yield point, na time-dependent relaxation au creep hazihitajiki. Tumia hyperelasticity kwa large-deformation elastic response, elastoplasticity kwa plastic strain baada ya yield, viscoelasticity kwa material yenye relaxation time, na creep kwa deformation inayoendelea chini ya load ya muda mrefu.
| Sifa ya tatizo | Material model inayofaa | Mwongozo wa uamuzi |
|---|---|---|
| Small deformation na linear stress–strain relation | Linear elasticity | Ikiweza kuwakilishwa na Young's modulus na Poisson's ratio |
| Hurudi kwenye umbo la awali baada ya unloading hata kwa large deformation | Hyperelasticity | Rubber-like material au nonlinear elastic potential inahitajika |
| Permanent strain hubaki baada ya kuvuka yield point | Elastoplasticity | Yield function na hardening law lazima zichaguliwe |
| Stress relaxation au retardation hutokea wakati load inashikiliwa | Viscoelasticity | Ikiweza kuwakilishwa na relaxation coefficients na relaxation times |
| Strain hujikusanya chini ya long-term load | Creep | Ikiwa Norton law inaweza kukadiria behavior |
| Built-in models hazitoshi | User-defined material | Constitutive law hutekelezwa kwa external subroutine |
Kwa temperature dependence, thibitisha support ya kila material model. Linear elasticity, creep, na thermal expansion coefficient zinasaidia temperature-dependent tables. Viscoelasticity haitumii temperature interpolation ya Prony coefficients zenyewe; hutumia temperature shift kupitia !TRS. Kwa elastoplasticity, temperature-dependent tables zinapatikana kwa multilinear hardening ya Mises yield. Mohr-Coulomb na Drucker-Prager hazitumii temperature dependence.
Kwa anisotropy au lamination, zingatia pia aina ya elementi. Solid elements zinasaidia orthotropic linear elasticity. Ndani ya linear-elastic range, shell elements zinaauni isotropic single-layer, anisotropic single-layer, isotropic laminated, na anisotropic laminated materials. Nonlinear material models haziwezi kutumika kwa shell elements.
Kwa material karibu incompressible, usiweke Poisson's ratio kuwa 0.5. FrontISTR haitumii specification ya perfectly incompressible material. Kwa large-deformation problems zenye incompressibility kubwa, uchaguzi wa element formulation pia ni muhimu; angalia formulation options katika Maktaba ya elementi.
Linear elasticity¶
Linear elasticity ndiyo material model ya msingi zaidi katika structural analysis ya FrontISTR. Linear static analysis, modal analysis, na linear dynamic analysis hutumia linear elasticity. Hata unapotumia elastoplasticity, viscoelasticity, au creep, linear elasticity hufafanuliwa ndani ya material hiyo kama elastic part. → Tazama !ELASTIC kwa maelezo.
Kwa isotropic linear elasticity, Young's modulus na Poisson's ratio hutajwa. Kwa temperature dependence, Young's modulus na Poisson's ratio zinaweza kutolewa kama tables za temperature. Kwa orthotropic elasticity, constants huru tisa hutajwa: Young's moduli tatu, Poisson's ratios tatu, na shear moduli tatu. Kwa kuwa orthotropy inahitaji material coordinate system, local coordinate system hutajwa kwenye !SECTION inayolingana.
Kwa linear elasticity upande wa mesh data, unganisha !SECTION na !MATERIAL. Mfano ufuatao unaassign solid element group ALL kwa material M1, na hufafanua Young's modulus na Poisson's ratio kwa ITEM=1, mass density kwa ITEM=2, na linear expansion coefficient kwa ITEM=3.
!SECTION, TYPE=SOLID, EGRP=ALL, MATERIAL=M1
!MATERIAL, NAME=M1, ITEM=3
!ITEM=1, SUBITEM=2
4000., 0.3
!ITEM=2
8.0102E-10
!ITEM=3
1.0E-5
Kwa shell elements, single-layer na laminated definitions zinaweza kutumika ndani ya linear elasticity. Tumia SUBITEM=4 kwa isotropic single-layer material na SUBITEM=9 kwa anisotropic single-layer material. Kwa laminate, material constants na layer weights za kila layer huorodheshwa ndani ya !ITEM ileile. Layer weights hunormalizwa kwa jumla yake na hutumika kama weights za through-thickness integration. Physical thickness ya shell nzima hutajwa kama thickness ya !SECTION, TYPE=SHELL.
Mfano wa isotropic single-layer shell unaonyeshwa hapa chini.
Mfano wa isotropic two-layer laminated shell unaonyeshwa hapa chini.
Mfano wa anisotropic single-layer shell unaonyeshwa hapa chini. Anisotropy angle hutajwa kwa degrees.
!MATERIAL, NAME=M1, ITEM=1
!ITEM=1, SUBITEM=9
1, 28600., 0.15, 32.3, 28600., 12434., 12434., 12434., 0.0
Mfano wa anisotropic two-layer laminated shell unaonyeshwa hapa chini.
!MATERIAL, NAME=M1, ITEM=1
!ITEM=1, SUBITEM=17
1, 28600., 0.15, 32.3, 28600., 12434., 12434., 12434., 0.0,
28600., 0.15, 32.3, 28600., 12434., 12434., 12434., 0.0
Hyperelasticity¶
Hyperelasticity ni nonlinear elastic material ambayo stress hufafanuliwa kutoka strain-energy function. Hutumika kwa rubber-like materials zinazopitia large deformation lakini hurudi kwenye hali ya awali baada ya unloading. Kwenye input, ndani ya block ya !MATERIAL, weka !HYPERELASTIC. → Tazama !HYPERELASTIC kwa maelezo.
FrontISTR inasaidia hyperelastic models zifuatazo. OGDEN model haitumiki.
| Model | Aina ya input | Coefficients kuu | Sifa |
|---|---|---|---|
| Neo-Hookean | NEOHOOKE | \(C_{10}\), \(D\) | Simple isotropic hyperelastic model inayolingana na Mooney-Rivlin yenye \(C_{01}=0\) |
| Mooney-Rivlin | MOONEY-RIVLIN | \(C_{10}\), \(C_{01}\), \(D\) | Isotropic hyperelastic model inayotumia reduced invariants mbili |
| Arruda-Boyce | ARRUDA-BOYCE | \(\mu\), \(\lambda_m\), \(D\) | Rubber-like material model inayotegemea molecular-chain network |
| Anisotropic Mooney-Rivlin | MOONEY-RIVLIN-ANISO | Input husoma coefficients 10, lakini current constitutive law hutumia tano za kwanza | Model ya hyperelastic response yenye anisotropy kama fiber direction |
| User-defined hyperelasticity | USER | User constants | Model inayotekeleza hyperelastic constitutive law kwa external subroutine |
Kwa hyperelasticity, coefficient \(D\) inayohusiana na volume change hutumika kuwakilisha compressibility. Perfect incompressibility haitumiki, hivyo specification inayolingana na Poisson's ratio \(\nu=0.5\) isitumike. Kwa nearly incompressible materials, chagua si coefficients za hyperelastic model pekee bali pia element formulation inayofaa.
Hyperelasticity hushughulikiwa kwa default katika Total Lagrange framework. Tazama Hyperelasticity (theory) kwa definitions za strain-energy function, stress, na tangent stiffness.
Elastoplasticity¶
Elastoplasticity ni material model inayotenganisha elastic na plastic regions kwa yield function na kueleza post-yield response kwa hardening law. Kwenye input, ndani ya block ileile ya !MATERIAL, unganisha !ELASTIC na !PLASTIC. → Tazama !PLASTIC kwa maelezo.
FrontISTR hufafanua elastoplastic model kwa kuunganisha yield function na hardening law. Support ni kama ifuatavyo.
| Yield function | Aina ya input | Hardening laws zinazosaidiwa | Matumizi makuu |
|---|---|---|---|
| Mises | MISES | BILINEAR, MULTILINEAR, SWIFT, RAMBERG-OSGOOD, KINEMATIC, COMBINED | Isotropic yielding ya metals, n.k. |
| Mohr-Coulomb | MOHR-COULOMB | BILINEAR, MULTILINEAR | Soil na rock materials zinazoelezwa kwa friction angle na cohesion |
| Drucker-Prager | DRUCKER-PRAGER | BILINEAR, MULTILINEAR | Pressure-dependent yield inayokadiria Mohr-Coulomb kwa smooth form |
| User-defined yield | USER | User-defined | Wakati tangent stiffness na return mapping zinatekelezwa kwa external subroutine |
Multilinear hardening ya Mises yield inasaidia temperature-dependent tables. Bilinear hardening, Swift hardening, Ramberg-Osgood hardening, kinematic hardening, na combined hardening za Mises hutathminiwa kama constant expressions. Mohr-Coulomb na Drucker-Prager hazitumii temperature dependence. Kwa multilinear hardening, input lazima iwe na plastic strain isiyo hasi na plastic strain ya kwanza lazima iwe 0.
Shell, plane-stress, plane-strain, na axisymmetric elements hazitumii elastoplasticity. Tumia 3D continuum solid elements kwa elastoplastic material.
Elastoplasticity hushughulikiwa kwa default katika Updated Lagrange framework. Katika !PLASTIC, ukiweka INFINITESIMAL, hutendewa kama small-deformation constitutive law. Stress update hutumia integration inayotegemea return mapping; tazama Elastoplasticity (theory) kwa algorithm.
Viscoelasticity¶
Viscoelasticity ni material model inayoongeza time-dependent relaxation kwenye elastic response. FrontISTR huingiza generalized Maxwell model kama Prony series. Ndani ya block ileile ya !MATERIAL, fafanua !ELASTIC na !VISCOELASTIC. → Tazama !VISCOELASTIC kwa maelezo.
Katika Prony series, jozi za relaxation coefficient na relaxation time hutajwa katika mistari mingi. Relaxation time haiwezi kuwa 0. Kwa temperature dependence, weka !TRS baada ya !VISCOELASTIC na utaje temperature shift factor. → Tazama !TRS kwa maelezo.
Temperature shift inaweza kuwa WLF au Arrhenius; zote hutoa shift factor \(A\) kama function ya analysis temperature \(\theta\) na reference temperature \(\theta_0\). Kwenye input, material constants mbili (C1, C2) na reference temperature hutolewa kwa zote, lakini maana yake hutegemea shift model iliyochaguliwa (coefficients mbili za Williams-Landel-Ferry kwa WLF, au coefficients mbili zinazohusiana na activation energy kwa Arrhenius). Tazama theory manual Viscoelasticity kwa function forms na derivation ya shift factor.
Creep¶
Creep ni material model ya deformation inayoendelea kwa muda chini ya constant load au constant stress. !CREEP ya FrontISTR inasaidia Norton law. Ndani ya block ileile ya !MATERIAL, fafanua !ELASTIC na !CREEP. → Tazama !CREEP kwa maelezo.
Norton law huwakilisha creep strain rate kwa power-law form ya equivalent stress, time, na material constants \(A\), \(n\), \(m\) (tazama theory manual Creep kwa function form). Material constants zinaweza kuwa temperature-dependent tables, hivyo values zinaweza kutolewa kwa kila temperature.
!CREEP haitumii TYPE=USER. Tumia user-defined material ikiwa unahitaji constitutive law maalumu yenye creep.
Material properties za heat-conduction analysis¶
Katika heat-conduction analysis, fafanua density, specific heat, na thermal conductivity badala ya elastic/plastic materials za structural analysis. Kwa link, plane, solid, na shell elements, katika !MATERIAL upande wa mesh data tumia ITEM=1–3. Thermal properties zinaweza kutolewa kama temperature-dependent tables.
Mfano ufuatao hufafanua density, specific heat, na thermal conductivity kwa material M1 kama functions za temperature. Kwa SECTION, assign solid element group ALL kwa material M1; kisha katika !MATERIAL, toa density kwa ITEM=1, specific heat kwa ITEM=2, na thermal conductivity kwa ITEM=3, kila moja kama jozi na temperature.
!SECTION, TYPE=SOLID, EGRP=ALL, MATERIAL=M1
!MATERIAL, NAME=M1, ITEM=3
!ITEM=1, SUBITEM=1
7850., 300.
7790., 500.
7700., 800.
!ITEM=2
0.465, 300.
0.528, 500.
0.622, 800.
!ITEM=3
43., 300.
38.6, 500.
27.7, 800.
Kwa interface elements, material data haitumiki; gap width, gap heat-transfer coefficient, na radiation coefficient hutajwa katika data row ya !SECTION, TYPE=INTERFACE.
Katika heat-conduction analysis ya shell elements, thermal properties huwekwa katika material !MATERIAL sawa na solid elements. Shell thickness na idadi ya through-thickness integration points huwekwa upande wa !SECTION.
Katika thermal-stress analysis, linear expansion coefficient hufafanuliwa ili kuhesabu thermal strain kutoka temperature field. Isotropic na orthotropic thermal-expansion coefficients zinasaidiwa, pamoja na temperature dependence. → Tazama !EXPANSION_COEFF. Kwa mass density upande wa analysis control data unaotumika kwa structural/dynamic analysis, tazama !DENSITY. Density ya heat-conduction analysis hutajwa kwa !MATERIAL ITEM=1 upande wa mesh data kama ilivyoelezwa hapa.
User-defined material¶
User-defined material ni entry point ya kutekeleza kwa external subroutine constitutive law isiyoweza kuwakilishwa na built-in material models za FrontISTR. Kwenye input, !USER_MATERIAL hutoa idadi ya state variables na user constants. → Tazama !USER_MATERIAL kwa maelezo.
!USER_MATERIAL hushughulikiwa kwa default kama Updated Lagrange constitutive law na hubadilishwa kuwa Total Lagrange kwa KIRCHHOFF. Idadi ya state variables huwekwa kwa NSTATUS. Hadi user constants 100 zinaweza kupitishwa katika data rows. Constants hizi na state variables hutumika kama internal variables za constitutive law upande wa user subroutine.
Kwa !USER_MATERIAL, constitutive law body hutekelezwa katika uMatlMatrix na uUpdate: uMatlMatrix hurudisha material tangent stiffness, na uUpdate husasisha stress na state variables. Kwa user elasticity ya small deformation tumia !ELASTIC, TYPE=USER; kwa user hyperelastic model tumia !HYPERELASTIC, TYPE=USER; elastic response hutekelezwa kwa uElasticMatrix na uElasticUpdate. Kwa user-defined yield function, tumia !PLASTIC, YIELD=USER na utekeleze elastoplastic tangent stiffness na return mapping.
Mada zinazohusiana¶
- Aina za uchanganuzi — Aina za uchanganuzi zinazoweza kutumia material models
- Maktaba ya elementi — Aina za elementi na formulations ambazo materials hupewa
- Constitutive laws (theory) — Constitutive equations na stress update za material models
- !MATERIAL (mesh data) — Material-property tables upande wa mesh data
- !SECTION (mesh data) — Mapping kati ya element groups na material names
- !MATERIAL (analysis control data) — Material block upande wa analysis control data
- !ELASTIC — Linear elastic material
- !HYPERELASTIC — Hyperelastic material
- !PLASTIC — Elastoplastic material
- !VISCOELASTIC — Viscoelastic material
- !TRS — Temperature shift ya viscoelasticity
- !CREEP — Creep material
- !DENSITY — Mass density inayotumika kwa structural na dynamic analyses
- !EXPANSION_COEFF — Linear expansion coefficient
- !USER_MATERIAL — User-defined material