# 3d plot of young's modulus for anisotropic material

can anyone can help me in plotting 3d plot of young's modulus for anisotropic material. For input i have 6*6 stiffness tensor matrix and hydrostatic pressure value.

I am trying with the following script, but its not helping. The code is for cubic system for which system is symmetric. But in my case I have triclinic system, in which every element of tensor matrix is non zero. So how should i incorporate this thing for my system.

(*tensile direction*)
n = {Cos[phi]*Sin[theta], Sin[phi]*Sin[theta], Cos[theta]};
(*Basic tensors*)
I2 = IdentityMatrix@3;
IdI = TensorProduct[I2, I2];
I4 = TensorTranspose[IdI, {1, 3, 2, 4}];
IS = (I4 + TensorTranspose[I4, {1, 2, 4, 3}])/2;
(*Projectors of cubic materials*)
Pc1 = 1/3*IdI;
Dc = ConstantArray[0, {3, 3, 3, 3}];
Dc[[1, 1, 1, 1]] = 1;
Dc[[2, 2, 2, 2]] = 1;
Dc[[3, 3, 3, 3]] = 1;
Pc2 = Dc - Pc1;
Pc3 = IS - Pc1 - Pc2;
(*Spectral represention of cubic compliance*)
comp = 1/l1*Pc1 + 1/l2*Pc2 + 1/l3*Pc3;
l1 = 10;
l2 = 3;
l3 = 8;
(*Young's modulues*)
Y = (Total[comp*TensorProduct[n, n, n, n], Infinity])^(-1) //
Simplify;
(*Plot*)
SphericalPlot3D[Y, {theta, 0, Pi}, {phi, 0, 2 Pi}]

• The code, by itself, works and produces a plot. It is unclear what you are specifically after and where do you encounter problems. Please clarify. – corey979 Feb 12 at 9:40
• @corey979 the code is for cubic system for which system is symmetric. but in my case i have triclinic system, in which every element of tensor matrix is non zero. So how should i incorporate this thing for my system. – Tanay Sahu Feb 13 at 5:49