In my opinion, I would look at passing function handles into your function for X, Y, or Z. The workflow would look something like this:
X = @(x,y,z)(x.*y.*z);
Y = @(x,z)(6.*z + 3.*x);
Z = @(y,z)(y+z);
[F,R,U] = deformationgradients(X,Y,Z,x,y,z);
If you plan on handling vector data, note the ".*" (element-wise multiplication) inside each function. If you are planning on performing matrix-multiplication, remove the ".". Then inside your function, it could look something like:
function [F,R,U] = deformationgradients(X,Y,Z,x,y,z)
someVar1 = X(x,y,z);
someVar2 = X(x,y,z) + Y(x,z);
.
.
.
end
where X,|Y|,and Z are the function handles and x,|y|, and z are data.
Hope this is what you are looking for.
