MAT3

Bulk Data Entry Defines the material properties for linear, temperature-independent, and orthotropic materials used by the CTAXI, CTRIAX6, and CQAXI axisymmetric elements, and CTPSTN and CQPSTN plane strain elements.

Format

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
MAT3 MID EX ETH EZ NUXTH NUTHZ NUZX RHO  
      GZX AX ATH AZ TREF GE  

Example

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
MAT3 17 3.0+7 3.1+7 3.2+7 0.33 0.28 0.30 2.0e-5  
      7.0+6 1.1e-4 1.1e-4 1.2e-4 35.5 0.19  

Definitions

Field Contents SI Unit Example
MID Unique material identification.
Integer
Specifies an identification number for this material.
<String>
Specifies a user-defined string label for this material entry. 3

No default (Integer > 0 or <String>)

 
EX, ETH, EZ Young's moduli in the x, out-of-plane, and z directions, respectively.

No default (Real > 0.0)

 
NUXTH, NUTHZ, NUZX Poisson's ratios.
NUXTH
Poisson's ratio for strain in the out-of-plane direction, when stress is in the x direction.
NUTHZ
Poisson's ratio for strain in the z direction, when stress is in the out-of-plane direction.
NUZX
Poisson's ratio for strain in the x direction, when stress is in the z direction.

No default (Real)

 
RHO Mass density.

No default (Real)

 
GZX Shear modulus in the x-z plane.

No default (Real > 0.0)

 
AX, ATH, AZ Thermal expansion coefficient in the x, out-of-plane, and z directions, respectively.

No default (Real)

 
TREF Reference temperature for thermal loading.

Default = blank (Real or blank)

 
GE Structural element damping coefficient. 8

No default (Real)

 

Comments

  1. The indices of ‘z’ or ‘Z’ above represent (a) the in-plane z direction if the analysis is defined in x-z plane, or (b) the in-plane y direction if the analysis is defined in x-y plane. The out-of-plane index, ‘TH’ represents (a) the hoop direction θ in axisymmetric analysis, or (b) the direction of thickness in plane strain analyses, see Comment 7.
  2. The material identification number/string must be unique for all MAT1, MAT2, MAT8 and MAT9 entries.
  3. String based labels allow for easier visual identification of materials, including when being referenced by other cards. (example, the MID field of properties). For more details, refer to String Label Based Input File in the Bulk Data Input File.
  4. Values of all seven elastic constants, EX, ETH, EZ, NUXTH, NUTHZ, NUZX and GZX must be present.
  5. A warning is issued if absolute value of NUXTH or NUTHZ is greater than 1.0.
  6. The x, out-of-plane and z directions are principal material directions of the material coordinate system. The elements supported by MAT3 contains a THETA field to relate the principal material directions to the basic coordinate system.
  7. The strain-stress relations are defined as:
    1. axisymmetric analysis(1)
      { ε x ε y ε z γ z x } = [ 1 E X N U T H X E T H N U Z X E Z 0 N U X T H E X 1 E T H N U Z T H E Z 0 N U X Z E X N U T H Z E T H 1 E Z 0 0 0 0 1 G Z X ] { σ x σ θ σ z τ z x } + ( T T R E F ) { A X A T H A Z 0 } MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaiqaaeaada Gacaqaauaabeqaeeaaaaqaaiabew7aLnaaBaaaleaacaWG4baabeaa aOqaaiabew7aLnaaBaaaleaacaWG5baabeaaaOqaaiabew7aLnaaBa aaleaacaWG6baabeaaaOqaaiabeo7aNnaaBaaaleaacaWG6bGaamiE aaqabaaaaaGccaGL9baaaiaawUhaaiabg2da9maadmaabaqbaeqabq abaaaaaeaadaWcaaqaaiaaigdaaeaacaWGfbGaamiwaaaaaeaacqGH sisldaWcaaqaaiaad6eacaWGvbGaamivaiaadIeacaWGybaabaGaam yraiaadsfacaWGibaaaaqaaiabgkHiTmaalaaabaGaamOtaiaadwfa caWGAbGaamiwaaqaaiaadweacaWGAbaaaaqaaiaaicdaaeaacqGHsi sldaWcaaqaaiaad6eacaWGvbGaamiwaiaadsfacaWGibaabaGaamyr aiaadIfaaaaabaWaaSaaaeaacaaIXaaabaGaamyraiaadsfacaWGib aaaaqaaiabgkHiTmaalaaabaGaamOtaiaadwfacaWGAbGaamivaiaa dIeaaeaacaWGfbGaamOwaaaaaeaacaaIWaaabaGaeyOeI0YaaSaaae aacaWGobGaamyvaiaadIfacaWGAbaabaGaamyraiaadIfaaaaabaGa eyOeI0YaaSaaaeaacaWGobGaamyvaiaadsfacaWGibGaamOwaaqaai aadweacaWGubGaamisaaaaaeaadaWcaaqaaiaaigdaaeaacaWGfbGa amOwaaaaaeaacaaIWaaabaGaaGimaaqaaiaaicdaaeaacaaIWaaaba WaaSaaaeaacaaIXaaabaGaam4raiaadQfacaWGybaaaaaaaiaawUfa caGLDbaadaGabaqaamaaciaabaqbaeqabqqaaaaabaGaeq4Wdm3aaS baaSqaaiaadIhaaeqaaaGcbaGaeq4Wdm3aaSbaaSqaaiabeI7aXbqa baaakeaacqaHdpWCdaWgaaWcbaGaamOEaaqabaaakeaacqaHepaDda WgaaWcbaGaamOEaiaadIhaaeqaaaaaaOGaayzFaaaacaGL7baacqGH RaWkcaGGOaGaamivaiabgkHiTiaadsfacaWGsbGaamyraiaadAeaca GGPaWaaiqaaeaadaGacaqaauaabeqaeeaaaaqaaiaadgeacaWGybaa baGaamyqaiaadsfacaWGibaabaGaamyqaiaadQfaaeaacaaIWaaaaa GaayzFaaaacaGL7baaaaa@A06C@

      with N U X T H E X = N U T H X E T H , N U X Z E X = N U Z X E Z MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaca WGobGaamyvaiaadIfacaWGubGaamisaaqaaiaadweacaWGybaaaiab g2da9maalaaabaGaamOtaiaadwfacaWGubGaamisaiaadIfaaeaaca WGfbGaamivaiaadIeaaaGaaiilamaalaaabaGaamOtaiaadwfacaWG ybGaamOwaaqaaiaadweacaWGybaaaiabg2da9maalaaabaGaamOtai aadwfacaWGAbGaamiwaaqaaiaadweacaWGAbaaaaaa@4F8B@ and N U T H Z E T H = N U Z T H E Z MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaca WGobGaamyvaiaadsfacaWGibGaamOwaaqaaiaadweacaWGubGaamis aaaacqGH9aqpdaWcaaqaaiaad6eacaWGvbGaamOwaiaadsfacaWGib aabaGaamyraiaadQfaaaaaaa@4399@ .

    2. plain strain analysis(2)
      { ε x ε z γ z x } = [ 1 E X N U Z X E Z 0 N U X Z E X 1 E Z 0 0 0 1 G Z X ] { σ x σ z τ z x } + ( T T R E F ) { A X A Z 0 } MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaiWaaeaafa qabeWabaaabaGaeqyTdu2aaSbaaSqaaiaadIhaaeqaaaGcbaGaeqyT du2aaSbaaSqaaiaadQhaaeqaaaGcbaGaeq4SdC2aaSbaaSqaaiaadQ hacaWG4baabeaaaaaakiaawUhacaGL9baacqGH9aqpdaWadaqaauaa beqadmaaaeaadaWcaaqaaiaaigdaaeaacaWGfbGaamiwaaaaaeaacq GHsisldaWcaaqaaiaad6eacaWGvbGaamOwaiaadIfaaeaacaWGfbGa amOwaaaaaeaacaaIWaaabaGaeyOeI0YaaSaaaeaacaWGobGaamyvai aadIfacaWGAbaabaGaamyraiaadIfaaaaabaWaaSaaaeaacaaIXaaa baGaamyraiaadQfaaaaabaGaaGimaaqaaiaaicdaaeaacaaIWaaaba WaaSaaaeaacaaIXaaabaGaam4raiaadQfacaWGybaaaaaaaiaawUfa caGLDbaadaGadaqaauaabeqadeaaaeaacqaHdpWCdaWgaaWcbaGaam iEaaqabaaakeaacqaHdpWCdaWgaaWcbaGaamOEaaqabaaakeaacqaH epaDdaWgaaWcbaGaamOEaiaadIhaaeqaaaaaaOGaay5Eaiaaw2haai abgUcaRiaacIcacaWGubGaeyOeI0IaamivaiaadkfacaWGfbGaamOr aiaacMcadaGadaqaauaabeqadeaaaeaacaWGbbGaamiwaaqaaiaadg eacaWGAbaabaGaaGimaaaaaiaawUhacaGL9baaaaa@75BE@

      with N U X Z E X = N U Z X E Z MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaca WGobGaamyvaiaadIfacaWGAbaabaGaamyraiaadIfaaaGaeyypa0Za aSaaaeaacaWGobGaamyvaiaadQfacaWGybaabaGaamyraiaadQfaaa aaaa@413E@ .

    The material constants associated with ‘TH’ (i.e. E T H MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyraiaads facaWGibaaaa@3866@ , N U X T H MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOtaiaadw facaWGybGaamivaiaadIeaaaa@3A26@ , N U T H Z MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOtaiaadw facaWGybGaamivaiaadIeaaaa@3A26@ and A T H MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyraiaads facaWGibaaaa@3866@ ) are used to calculate the out-of-plane stress in plane strain analysis.(3)
    σ t h = E T H [ N U X T H E X σ x + N U Z T H E Z σ Z ( T T R E F ) A T H ] MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Wdm3aaS baaSqaaiaadshacaWGObaabeaakiabg2da9iaadweacaWGubGaamis amaadmaabaWaaSaaaeaacaWGobGaamyvaiaadIfacaWGubGaamisaa qaaiaadweacaWGybaaaiabeo8aZnaaBaaaleaacaWG4baabeaakiab gUcaRmaalaaabaGaamOtaiaadwfacaWGAbGaamivaiaadIeaaeaaca WGfbGaamOwaaaacqaHdpWCdaWgaaWcbaGaamOwaaqabaGccqGHsisl caGGOaGaamivaiabgkHiTiaadsfacaWGsbGaamyraiaadAeacaGGPa GaamyqaiaadsfacaWGibaacaGLBbGaayzxaaaaaa@5B7C@
    Note: The strain and stress here are both defined in the material coordinate system.
  8. To obtain the damping coefficient GE, multiply the critical damping ratio, C / C 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4qaiaac+ cacaWGdbWaaSbaaSqaaiaaicdaaeqaaaaa@391F@ by 2.0.
  9. This card is represented as a material in HyperMesh.