Dear Wolfram team:
I am just asking what to do if you take the divergence of a scalar. For example, thermal stresses are the result of changes in temperature, a scalar field.
I am guessing that this "divergence" is actually a gradient, but I am not sure. Now I give the details of my example:
EXAMPLE: Thermal elastic stresses.
Note: before using the equations, the following quantities are defined:
coordinates:
X={x1,x2,x3}; vars=Flatten[{t,X}];
fields: stress S, displacement U, gravity G, temperature TK;
S=Apply[s,vars];U=Apply[u,vars]; G=Apply[g,X]; TK=Apply[T,vars];
Then the equations:
Equation of motion:
D[Div[S,X]+rho*D[U,{t,2}]==rho*G
constitutive equation: c and alpha are constants of elasticity and thermal expansion, respectively, and T0 is the (constant) reference temperature
S=c*alpha*(TK-T0)
After plugging definition (2) into equation (1) , I get into trouble as said before, because the temperature is a scalar!
In many references I saw that a symbol called "KroneckerDelta" is used to turn scalars into tensors and vectors, among other things, but I have no idea how to use that symbol in the Wolfram Language... anyway, that symbol should be an array of constants (actually many "1"s and "0"s).
Your help would be greatly appreciated.
Merry Christhmas and keep the hope that 2022 would be better than 2020 and 2021!