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My research is on elastic instabilities. Soft elastic solids can undergo large deformations, which allow it to have many intersesting non-linear effects. Elastic instabilities, such as wrinklings and bucklings, allow the solids to form unusual patterns or shapes. Many of these instabilities are complicated because of their non-linearity. The shape formations from these instabilites could explain how biological shape, such as wrinkle on brains, can be formed.
My current project is investigating the pattern formation of two elastic layers growing on each other. This mimics growth of many biological tissues such as cerebrum and intestinal villi. For cerebrum, the outer layer grows faster than the inner layer, causing them to fold into complex labyrinth patterns. This allows me to understand how these tissues obtain their patterns and what other patterns these system could form and at which conditions. At small growth limits, it is possible to do analytic calculations. Here, there exist many patterns such as checker board and hexagonal patterns. I aim to calculate the energy associated with each pattern to find the optimum pattern that gives the lowest energy
In Plain English
When elastic solids, such as rubbers, are compressed, they can wrinkle and buckle. In some cases, complicated shapes or patterns can be formed. This applies to development of some biological tissues. For example, foldings in brains are caused by the outer tissue layer growing faster than the inner tissue layer.This causes them to fold into complicated brain patterns. I study these pattern formation for different systems that involve elastic solids.