ESPCI web site
Sanjay Govindjee (Berkley)
Liquid-crystal elastomers : Physics and models
Liquid crystal elastomers (LCEs) present an interesting class of materials that display soft and semi-soft elastic behavior as well as a somewhat less explored viscoelastic behavior. These materials, comprised of liquid crystal molecules together with polymerizing agents to form a final solid, behave as an elastomeric solid would, as well as like a liquid crystal would. The interaction of these two features provides for a wide and complex range of macroscopically observed phenomena, including for example optical actuation, extreme softness, pattern formation, and high damping to name a few.
In this talk, I will present a general introduction to the physics of these unique materials at a microscopic as well as macroscopic scale. This will lead to presentation of the long-standing well-established models that are used to understand their elastic behavior. Consideration will also be given to models that can account for time-dependent, i.e. viscoelastic, behavior – an aspect that is not well examined in the literature.
In the presentation, I will mainly consider so-called mono-domain liquid crystal elastomers that possess both a viscous director response as well as a viscoelastic elastomeric network response. The modeling framework will be built from the continuum scale, utilizing the formal principles of invariance of expended power to develop the governing balance laws for such materials accounting for loads that can impose twist directly at the continuum level. This framework is combined with free-energy dissipation arguments to generate restrictions on the possible constitutive relations for LCEs based upon hypothesized functional dependencies of the free-energy function. This mathematical framework leads to natural choices for evolution laws governing the viscous kinematics that have an appealing and intuitive nature. We demonstrate the utility of the model by considering its capabilities in comparison to a set of previously published experiments on homogenous deformations.
As a next step towards engineering, we consider the issues related to the solution of boundary value problems. Here one needs to at once grapple with the issues of whether the models are quasi-convex, as well as consider the details of the unique functional dependencies seen in LCE models. In this regard, we present a finite element formulation that admits models of the LCE type and discuss its extension to accommodate viscous LCE response.