Computational Analysis of the Deformation Behavior of 4d-Printed Liquid Crystal Elastomers Under Change of Temperature

This paper focuses on an FE simulation of Liquid Crystal Elastomers (LCE). For this purpose, a new method is proposed based on the combination ofnonlinear deformation analysis based on a St. Venant – Kirchhoff law, i.e., a physically linear but geometrically nonlinear stress-strain relationship.The deformation gradient is decomposed multiplicatively into elastic, (classical) thermal, and phase transformation parts. For the transformation part anovel representation is chosen based on an orientation parameter within a distribution function for the mesogens. This parameter can be linked to temperature.The stiffness tensor in the St. Venant – Kirchhoff law as well as the tensor of thermal expansion (for the thermal part of the deformation gradient)are obtained from Mori-Tanaka homogenization schemes. It is shown that classical thermal expansion with positive expansion coefficients and realistic values does not contribute much to the total large deformations. The mayor contribution comes from phase transformation. It is, therefore, misleading to model the deformation of LCEs during temperature change by classical thermal expansion, although exactly this is done in the literatureby a trick–namely, using negative anisotropic thermal expansion coefficients.