Contact mechanics model of wrinkling instability of dielectric elastomer membranes for anti-biofouling

Existing experimental studies have shown that the dynamic morphology of dielectric elastomer (DE) membranes can effectively, and reproducibly remove biofouling, but a convincing theory to quantitatively explain anti-biofouling performance is lacking. In this study, a two-dimensional (2D) contact mechanics model is developed to quantify the effect of the wrinkling instability of DE membranes for anti-biofouling. We characterize the anti-biofouling effect by the pull-off force between the wrinkled DE membrane and biofouling. An electromechanical coupling finite element model is established, and post-buckling analysis is performed to predict the wrinkling instability morphology of the DE membrane caused by the Maxwell stress. The dimensionless pull-off force expressions for single-, double-, and multi-point attachments are derived. We define a dominant dimensionless parameter, the ratio of the wrinkle amplitude to wavelength (A/λ), revealing that it is linearly related to the dimensionless voltage after the critical drive voltage is exceeded. The influence of crucial parameters such as pre-stretch ratio, driving voltage, different DE materials, and Young's modulus on the pull-off force is systematically investigated. Results indicate that pre-stretch is necessary for resistance to biofouling and that approximately 1.5 is a preferred option. The wrinkled morphology of the DE membrane can be controlled by adjusting the drive voltage, which enables real-time regulation of the pull-off force. It is found that among the commercial DE materials investigated, VHB9473 is the preferred choice for single-point attachment, while VHB4910 is recommended for double- and multi-point attachments. The developed theoretical model opens a new path for quantitative research on the green, environmentally friendly, and sustainable anti-biofouling using intelligent materials.