Hashin Criterion

The Hashin criterion gives conditions to distinguish between matrix or fiber failure by tension or compression.

The implementation1is:
  • Fiber Tension σ 1 > 0 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaqGdpWdamaaBaaaleaapeGaaGymaaWdaeqaaOWdbiabg6da+iaa icdaaaa@3A4E@

    F f i b e r T = σ 1 X T 2 + τ 12 S 2 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaWGgbWdamaaDaaaleaapeGaamOzaiaadMgacaWGIbGaamyzaiaa dkhaa8aabaWdbiaadsfaaaGccqGH9aqpdaqadaWdaeaapeWaaSaaa8 aabaWdbiaabo8apaWaaSbaaSqaa8qacaaIXaaapaqabaaakeaapeGa amiwa8aadaWgaaWcbaWdbiaadsfaa8aabeaaaaaak8qacaGLOaGaay zkaaWdamaaCaaaleqabaWdbiaaikdaaaGccqGHRaWkdaqadaWdaeaa peWaaSaaa8aabaWdbiaabs8apaWaaSbaaSqaa8qacaaIXaGaaGOmaa WdaeqaaaGcbaWdbiaadofaaaaacaGLOaGaayzkaaWdamaaCaaaleqa baWdbiaaikdaaaaaaa@4D2D@

  • Fiber Compression σ 1 < 0 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacqaHdpWCpaWaaSbaaSqaa8qacaaIXaaapaqabaGcpeGaeyipaWJa aGimaaaa@3AC4@

    F f i b e r C = σ 1 X C MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaWGgbWdamaaDaaaleaapeGaamOzaiaadMgacaWGIbGaamyzaiaa dkhaa8aabaWdbiaadoeaaaGccqGH9aqpdaabdaWdaeaapeWaaSaaa8 aabaWdbiaabo8apaWaaSbaaSqaa8qacaaIXaaapaqabaaakeaapeGa amiwa8aadaWgaaWcbaWdbiaadoeaa8aabeaaaaaak8qacaGLhWUaay jcSdaaaa@45C4@

  • Matrix Tension σ 2 > 0 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacqaHdpWCpaWaaSbaaSqaa8qacaaIYaaapaqabaGcpeGaeyOpa4Ja aGimaaaa@3AC9@

    F m a t r i x T = σ 2 Y T 2 + τ 12 S 2 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaWGgbWdamaaDaaaleaapeGaamyBaiaadggacaWG0bGaamOCaiaa dMgacaWG4baapaqaa8qacaWGubaaaOGaeyypa0ZaaeWaa8aabaWdbm aalaaapaqaa8qacqaHdpWCpaWaaSbaaSqaa8qacaaIYaaapaqabaaa keaapeGaamywa8aadaWgaaWcbaWdbiaadsfaa8aabeaaaaaak8qaca GLOaGaayzkaaWdamaaCaaaleqabaWdbiaaikdaaaGccqGHRaWkdaqa daWdaeaapeWaaSaaa8aabaWdbiabes8a09aadaWgaaWcbaWdbiaaig dacaaIYaaapaqabaaakeaapeGaam4uaaaaaiaawIcacaGLPaaapaWa aWbaaSqabeaapeGaaGOmaaaaaaa@4F36@

  • Matrix Compression σ 2 < 0 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacqaHdpWCpaWaaSbaaSqaa8qacaaIYaaapaqabaGcpeGaeyipaWJa aGimaaaa@3AC5@

    F m a t r i x C = σ 2 2 S 2 + τ 12 S 2 + σ 2 2 S 2 1 σ 2 Y C MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaWGgbWdamaaDaaaleaapeGaamyBaiaadggacaWG0bGaamOCaiaa dMgacaWG4baapaqaa8qacaWGdbaaaOGaeyypa0ZaaeWaa8aabaWdbm aalaaapaqaa8qacaqGdpWdamaaBaaaleaapeGaaGOmaaWdaeqaaaGc baWdbiaaikdacaWGtbaaaaGaayjkaiaawMcaa8aadaahaaWcbeqaa8 qacaaIYaaaaOGaey4kaSYaaeWaa8aabaWdbmaalaaapaqaa8qacaqG epWdamaaBaaaleaapeGaaGymaiaaikdaa8aabeaaaOqaa8qacaWGtb aaaaGaayjkaiaawMcaa8aadaahaaWcbeqaa8qacaaIYaaaaOGaey4k aSYaamWaa8aabaWdbmaabmaapaqaa8qadaWcaaWdaeaapeGaae4Wd8 aadaWgaaWcbaWdbiaaikdaa8aabeaaaOqaa8qacaaIYaGaam4uaaaa aiaawIcacaGLPaaapaWaaWbaaSqabeaapeGaaGOmaaaakiabgkHiTi aaigdaaiaawUfacaGLDbaadaWcaaWdaeaapeGaae4Wd8aadaWgaaWc baWdbiaaikdaa8aabeaaaOqaa8qacaWGzbWdamaaBaaaleaapeGaam 4qaaWdaeqaaaaaaaa@5DDC@

Syntax

HashinFT(tensor,xt,xc,yt,yc,s,sets,plies,elems,parts,props,pool_name,layer_index,opt_str)

Arguments

tensor
Stress table
xt
Allowable tensile stress in ply material direction 1
xc
Allowable compressive stress in ply material direction 1
yt
Allowable tensile stress in ply material direction 2
yc
Allowable compressive stress in ply material direction 2
s
Allowable in-plane shear stress
sets
Set table (D=NULL)
plies
Ply table (D=NULL)
elems
Element table (D)
parts
Part table (D)
props
Property table (D)
pool_name
Pool name (D=@current_pool)
layer_index
Layer index (D=@current_slice_index)
opt_str
This is an optional argument specifying failure mode. Option can be Fiber or Matrix.

If opt_str is not passed, the resultant failure index is reported as:

F index =max F fiber , F matrix MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaWGgbWdamaaBaaaleaapeGaamyAaiaad6gacaWGKbGaamyzaiaa dIhaa8aabeaak8qacqGH9aqpciGGTbGaaiyyaiaacIhadaWadaWdae aapeGaamOra8aadaWgaaWcbaWdbiaadAgacaWGPbGaamOyaiaadwga caWGYbaapaqabaGcpeGaaiilaiaadAeapaWaaSbaaSqaa8qacaWGTb GaamyyaiaadshacaWGYbGaamyAaiaadIhaa8aabeaaaOWdbiaawUfa caGLDbaaaaa@4F71@

1 Formula implemented in HyperView core are reported.