I'm trying to learn continuum mechanics and thermo-mechanics.
As we know, heating an object increases the mean atomic distance $a_0$ of the atoms in a rigid body. Let's assume it is a linear elastic material and we're well below the melting point. The lattice is perfect (no defects). I'm interested in whether the topology of a body plays a role when it is heated up.
I think, the cross section of a torus (topologically different to convex bodies) changes like in the sketch below (A: circumference at initial temperature, B: circumference at higher temperature).
B still a circle or is it an ellipsoid?
Question 2 (main question):
Is there a non-uniform internal stress field in the torus? E.g. is there more stress on the inner rim? How does this compare to the thermal expansion of a convex body (e.g. sphere)?
What is the influence of the crystal structure (FCC, BCC, wurzite) to the internal stress of an thermally expanding body?
References are appreciated - especially good books on this subject.