Şekil değiştirebilen cisimlerde kendiliğinden yapılanmanın hesaplamalı modellenmesi

Self-assembly is a process in which an irregular system transforms into a regular pattern or an organized structure through local interactions between the components of the material without any external influence. Therefore, self-assembly has great potential in the synthesis and manufacture of new materials. Although the main focus in the literature is mostly on self-assembly at the molecular level, there are many exciting applications of the self-assembling processes at larger scales. Space and time-varying patterns are described by various classes of spatio-temporal partial differential equations. The reaction-transport problems constitute one of these classes that employs the Cahn-Hilliard-type equation, also originally a fourth-order transport equation, for patterning. This study is concerned with the effect of mechanical stresses on the generated pattern in a self-assembling process. For mechanics, both finite elasticity and viscoelasticity are considered. To this end, the Cahn-Hilliard equations are solved together with the conservation equation of the linear momentum. The finite element method is used to solve the coupled partial differential equations. It is anticipated that the coupling with mechanics will open up possibilities for the design of new materials and lead to novel experiments for various kinds of self-assembly. Numerous representative numerical examples are presented to illustrate the characteristics and physics of the coupled and decoupled phase separation and self-assembly problems.