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• invariant measure
• Porous Materials
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Clear All  References  ABRAMOFF M.D., MAGALHAES P.J., RAM S.J., Image Processing with ImageJ, Biophotonics International, 2004, 11 (7), 36-42.  GLINICKI M.A., LITOROWICZ A., Diagnostyka rys w kompozytach o matrycy cementowej metodą komputerowej analizy obrazu, Drogi i Mosty, 2007, 3, 45-77.  HUANG H., YE G., QIAN C., SCHLANGEN E., Self-healing in cementitious materials: Materials, methods and service conditions, Materials and Design, 2016, 92, 499-511.  LOWE D.G., Distinctive image features from scale-invariant keypoints, International Journal of Computer Vision

, $${{\sigma }_{1}}=p+q,$$ (8) σ 2 = p − a q , $${{\sigma }_{2}}=p-aq,$$ (9) σ 3 = p − q , $${{\sigma }_{3}}=p-q,$$ (10) where: a = 2 b − 1 ∈ 〈 − 1 , 1 〉 $$a=2b-1\in \left\langle -1,1 \right\rangle$$ (11) is an equivalent measure of principal stress ratio. Introducing equations (8) - (10) into the definitions of invariants the following relations are obtained: I 1 = 3 p − a q , $${{I}_{1}}=3p-aq,$$ (12) J 2 = q 2 3 ( a 2 + 3 ) , $${{J}_{2}}=\frac{{{q}^{2}}}{3}\left( {{a}^{2}}+3 \right),$$ (13) J 3 = 2 a 27 q 3 ( − a 3 + 9 ) .  {{J}_{3}}=\frac{2a}{27}{{q}^{3}}\left

describing volumetric and deviatoric deformations of granular soil as a function of invariants: mean effective stress and deviator stress. The invariant form of the equations makes it possible to extend the model to 3D conditions, see [ 31 , 35 , 36 ]. A verification of this model based on plane strain tests is presented in [ 38 , 42 ]. Although the original model gives good predictions for many complex triaxial tests, its authors suggested the algorithmisation of the model and a clear definition of only one form of equations. In the latest version of the Sawicki and  