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As far as I understood from your answers to comments you like KronekerDelta in the stiffness tensor, but not in the stress tensor. You can do as follows: stiff[i_, j_, k_, l_] := L KroneckerDelta[i, j] KroneckerDelta[k, l] + \[Mu] (KroneckerDelta[i, k] KroneckerDelta[j, l] + KroneckerDelta[i, l] KroneckerDelta[j, k]) vg = Array[v, {3, 3}]; vg //...

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I use subscripted variables extensively in analysis of summations etc (e.g. derivation of Cramer-Rao lower bounds for cases with large numbers of variables). As a very simple example, find the value of m that minimises the following sum. sum = Sum[(Subscript[x, i] - m)^2, {i, 1, n}] eqn1 = D[sum, m] == 0 eqn2 = eqn1 /. u_Sum :> (u /. Subscript[x, i] -&...

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This is very late to the party, but someone might still be interested. You can do what you want by solving the conditions of the material symmetry group. My answer is organized in 1) Background information 2) Mathematica code 1) Background information First, some background information for those who are not engineers but want to understand better the ...

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One can still speed up your code a lot rp3[A_, B_] := Module[{a,c}, a = Transpose[A]; c = B; Do[c = Transpose[c.a, {2, 3, 4, 1}], {i, 4}]; c ] Now timing subroutine: test[n_] := Module[{t0, t1, nrm, A, B,c0,c1}, A = RandomInteger[{-10, 10}, {n, n}]; B = RandomInteger[{-10, 10}, {n, n, n, n}]; t0 = Timing[c0 = rp2[A, B];] // First; t1 = ...

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This kept me busy for a while. This answer is organized in 1) Results 2) Explanations 3) Examples From the beginning, if you only need the results, under "1) Results" you'll find the index transpositions for the different tensor orders $n$ (also referred to as degree or rank). A Mathematica notebook with all programs and text files with index ...

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