Chen Xuan

Research

We predicted instability with peristaltic patterns triggered by surface tension in thin cylindrical soft solids. We found two cases where finite wavelength instability requires minimum critical surface tension, which has not been reportedever. By using the photoisomerization model proposed by [D. Corbett and M. Warner, PRL. (2006)] and the opto-mechanical bending model of thin strips, we have analyzed the polarization dependence of the opto-mechanical behavior of monodomain photochromic liquid crystal polymer samples under polarized light illumination with suitable wavelength. We’ve extended the monodomain analysis to polydomain. We propose a simple yet seems telling homogenization method commonly seen in micromechanics in dealing with the polydomain strain, in an attempt to give a plausible explanation of the cylindrical shape, without visible anticlastic, bending observed in the experiment [Y. Yu, M. Nakano, T. Ikeda. Nature, (2003).]. We solve the Ginzburg Landau Equation to describe the LC domain switching coupled with large deformation of the biaxial LCE. We consider the bulk free energy involving the biaxial Landau free energy and gradient free energy in the Q tensor form, together with the incompressible soft elastic energy in trace formula. The uniaxial stretching perpendicular to the LC director is simulated. We are aimed at solving three problems simultaneously in one general theory: the puzzles of the many constitutive models for LCE elasticity; how LC domains are switched; time effect taking into account viscosity. We make use of the Lagrange Equation method in the framework of continuum mechanics, adding a Rayleigh dissipation function due to viscosity. By energy equilibrium and the variational principle, we have derived governing equations for both the viscoelastic elastomer and the LC orientation. A general representation theory of the free energy and Rayleigh dissipation function is obtained by means of the tensor representation theory. The LC Frank energy, (semi) soft elastic energy are exact limits in our general theory. Our next plan is to simplify our theory to the largest extent insofar as it remains revealing in explaining some phenomena observed. We consider the martensitic transformation in certain shape memory alloys. The punchline is a double well potential energy, where two energy minimizers exist, used to depict transitions between and coexistence of two phases. That’s an analogue of LCEs in that multiple states of LC orientations may coexist in monodomain-polydomain transformations. The energy and stress instability occurs both in the martensitic transformation in shape memory alloys and monodomain-polydomain transformations in LCEs. We solve the Euler-Lagrange Equation of the variation of the functional and get solutions by a specific technique called Homotopy Analysis Method.