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Thermal expansion is a normal concept everyday. There are 2 explanations:

1, thermal expansion result in stress, then result in deformation

2, thermal expansion result in deformation, then result in stress

I am confused about it. Could you explain the thermal expansion?

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    $\begingroup$ Thermal expansion is caused by atomic and molecular movement. It does not have to lead to thermal stress, though, that only happens when different materials with different expansion coefficients are being joint improperly. Proper engineering can relieve thermal stress in mechanical designs very efficiently. $\endgroup$ – CuriousOne Dec 24 '14 at 10:04
  • $\begingroup$ If I fix two ends of cantilever, it will lead to thermal stress, right? In this kind of condition, what's the mechanism of expansion? $\endgroup$ – Chad Meng Dec 24 '14 at 11:21
  • $\begingroup$ Atomic and molecular movement. $\endgroup$ – CuriousOne Dec 24 '14 at 11:23
  • $\begingroup$ I know it is from atomic movement. I mean the stress or deformation, which comes first? $\endgroup$ – Chad Meng Dec 24 '14 at 12:01
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    $\begingroup$ You are confounding expansion and stress. Does not need to lead to the other. Could you clarify your question? $\endgroup$ – Floris Dec 24 '14 at 14:45
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Roughly speaking solid matter is on a lattice form,

lattice

A three-dimensional lattice filled with two molecules A and B, here shown as black and white spheres.

The molecules fit like LEGO , the forces tying them together are mainly the spill over electric field forces , attractive and repulsive forming the patterns of the lattice.

In a single crystal one quantum mechanical solution applies and the atomic distances are at their lowest/ground energy state, which has vibrational and rotational degrees of freedom of the molecules and atoms.

Thermal input increases the energy transferred to the lattice and this means that the atoms/molecules transit to higher energy levels by absorbing thermal photons. Higher energy levels for each atom mean higher average distance in the solution of the potential well for each of them. This necessarily means expansion, which will be transferred by electromagnetic interactions, from atom/molecule to atom/molecule. This will induce stress macroscopically, the addition of the impulses will have macroscopic consequences, expansion.

Correspondingly in cooling the atoms/molecules return to the ground state emitting thermal photons and that is the noise heard as the lattice contracts.

So it is the change in energy levels at the microscopic framework, leading to change in average distances which will manifest as stress.

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Thermal expansion from an atomistic perspective:

The energetic potential between two atoms can be approximated by two exponential functions, one for the attractive force between the atoms, one for the repulsive force. The superposition of these two force fields has a minimum at a certain distance. Examples for such empirical potentials are Stillinger-Weber, Lennard-Jones or the Abel-Tersoff potential. This corresponds to the bond length in the ground state (at minimum energy) and can be measured macroscopically as length of a bulk solid.

If now the energy is increased (e.g. due to higher temperature), the atoms can move freely within the bounds of the potential function, where the mean value moves towards larger bond lengths and therefore causes thermal expansion. Check the figures at Thermal expansion modelling (MIT web page)

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