Abaqus project

Project Description:

Deformation of thin plates (films) driven by eigenstrain. Different from conventional deformation driven by applied force, in this project, no external force is applied. For convenience, we only consider the eigenstrain caused by thermal expansion. Therefore, stress and strain throughout the field are all from the non-uniform thermal effect. One reason to consider thermal effect is that it is convenient to prescribe temperature field in Abaqus. Another is that the idea is universal since we can map thermal expansion to a wide range of other eigenstrains. 

Why is this problem interesting to me:

First, eigenstrains caused by thermal effect requires attention in industrial issues. Engineers would never casually neglect the thermal stress in MEMS. As we may all know, thermal stress is a big issue when it comes to packing CPUs and physical memories of computers. As these components work, heat always accompanies. If you have ever used a software to measure the temperature of CPU in summer before, you may find it is not unrare that the temperature reaches 55 degrees centigrade or even higher. Such a difference from the room temperature might arouse a harmful tension or compression inside the highly integrated chip. Therefore, how to eliminate or minimize the negative effect brought by thermal effect becomes a meaningful task. Of course, nowadays, people have brought the negative effect well under control for this kind of problem. I just want to use this project to build up some concrete impression about thermal eigenstrain.Another and maybe more important reason why I choose this project is that although I only consider the thermal strain here, it is really not restricted to the thermal strain. For example, liquid crystal elastomer can undertake large thermal deformation. The same magnitude can be obtained by exposing the sample to a proper polarized light, which means thermal eigenstrain can be mapped to light-induced eigenstrain. Similarly, as so much work has shown, the buckling effect in ribbon growth can be also understood by introducing growth rate eigenstrain. 

Plan for this project:

Basically I will consider an elliptical thin plate as a start in my project, by varying a and b, I can approximate several different geometries.  And then check that how different shapes influence the deformation mode. I also expect to see the result with different thicknesses. Eigenstrain will be mainly applied within the plane. If necessarily, that along the thickness direction will also be tried. 

References:

[1] Mansfield, Bending, buckling and curling of a heated thin plate, Proc. R. Soc. A, 268, 316-327, 1962

[2] Warner, M. and L. Mahadevan, Photo-induced deformation of beams, plates and films, Physical Review Letters, 92, 134302, 2004

[3] some work subjected to publication in our group