applied to the function g= l, we get which applied to our tetrahedron gives 0=△Sn-△S1 If we take the scalar product of this equation with ei, we obtain AS(n:e)=△S S;=△S can then be replaced in equation 3 to obtain t2)+(n:e3)t③) The factor in parenthesis is the definition of the Cauchy stress tensor o elt/+e2t+est Note it is a tensorial expression (independent of the vector and tensor com- ponenents in a particular coordinate system). To obtain the tensorial com- ponenents in our rectangular system we replace the expressions of to from Eqn. 2 (6) Replacing in Eqn. 4: n0ie,e;=0i(n-;=(0igniej ti okit� � � � � applied to the function φ = 1, we get 0 = S ndS which applied to our tetrahedron gives: 0 = ΔSn − ΔS1e1 − ΔS2e2 − ΔS3e3 If we take the scalar product of this equation with ei, we obtain: ΔS(n · ei) = ΔSi or ΔSi = ΔSni can then be replaced in equation 3 to obtain: ΔS � t(n) − (n · e1)t(1) + (n · e2)t(2) + (n · e3)t(3)� = 0 or � � t(n) = n · e1t(1) + e2t(2) + e3t(3) (4) The factor in parenthesis is the definition of the Cauchy stress tensor σ: σ = e1t(1) + e2t(2) + e3t(3) = eit(i) (5) Note it is a tensorial expression (independent of the vector and tensor com￾ponenents in a particular coordinate system). To obtain the tensorial com￾ponenents in our rectangular system we replace the expressions of t(i) from Eqn.2 σ = eiσijej (6) Replacing in Eqn.4: t(n) = n · σ (7) or: t(n) = n · σijeiej = σij n · ei ej = σijni ej (8) ti = σkink (9) 4