Calculated physical quantities in Stress analysis
For the stress analysis problems the QuickField postprocessor calculates the following set of local and integral physical quantities.
Local quantities:
- The absolute value of displacement \[ δ = \sqrt{δ_x^2 + δ_y^2} , \quad or \quad δ = \sqrt{δ_z^2 + δ_r^2} ;\]
- Maximum and minimum principal stresses in the plane of model σ1 and σ2;
- Normal and tangential stresses along coordinate axes σx, σy and τxy (σz, σr and τrz in axisymmetric case);
- Normal stress in out-of-plane direction (σz - for xy-plane, σθ - for rz-plane). For the plane stress problems this component vanishes by the definition;
- Von Mises criterion (stored energy of deformation): \[ σ_e = \sqrt{\frac{1}{2} \left [ (σ_1 - σ_2)^2 + (σ_2 - σ_3)^2 + (σ_3 - σ_1)^2 \right ]} , \] where σ1, σ2 and σ3 denote the principal stresses in descending order.
-
Tresca criterion (maximum shear):
σe = σ1 - σ3 -
Mohr-Coulomb criterion:
σe = σ1 - χ·σ3,
where χ = [σ+]/[σ-],
σ+ and σ- denote tensile and compressive allowable stress. - Drucker-Prager criterion: \[ σ_e = (1 + \sqrt{χ} )· σ_i - \frac{\sqrt{χ}+ χ}{1 + \sqrt{χ}}· \overline{σ} + \frac{1}{[σ_{-}]} · \left ( \frac{1 - \sqrt{χ}}{1 + \sqrt{χ}} · \overline{σ} \right )^2, \] where \[ σ_i = \sqrt{\frac{1}{2} \left [ (σ_1 - σ_2)^2 + (σ_2 - σ_3)^2 + (σ_3 - σ_1)^2 \right ]} , \] \[ \overline{σ} = \frac{σ_1 + σ_2 + σ_3}{3}. \]
-
Hill failure index for orthotropic materials:
\[ F.I. = \frac{σ_1^2}{Χ_1^2} - \frac{σ_1σ_2}{Χ_1^2} + \frac{σ_2^2}{Χ_2^2} + \frac{τ_{12}^2}{S_{12}^2} \]
where σ1, σ2 and τ12
are computed stresses in the material directions and,
Χ1 = Χ1T, if σ1>0; Χ1 = Χ1C, if σ1<0;
Χ2 = Χ2T, if σ2>0; Χ2 = Χ2C, if σ2<0;
S12 = S12+, if τ12>0; S12 = S12-, if τ12<0,where Χ1T, Χ2T, Χ1C, Χ1C, S12+ and S12- are tensile, compressive and shear allowable stresses.
Integral quantities:
See section Integral quantities in stress analysis.