A numerical framework for the simulation of coupled electromechanical growth

Electro-mechanical response exists in growing materials such as biological tissues and hydrogels, influencing the growth process, pattern formation and geometry remodelling. To gain a better understanding of the mechanism of the coupled effects of growth and electric fields on the deformation behaviour, a finite element framework for coupled electro-elastic growth is established. Based on the extended volume growth theory, the governing equations of the growing electro-elastic solid are obtained. A coupled three-field mixed displacement-pressure-potential finite element formulation using inf–sup stable combinations is adapted. The finite element formulation is implemented in ABAQUS via a user element subroutine. The implementation is validated first by comparing the deformation and stress components of a growing tubular structure under axial strain and radial voltage. Using the example of a bi-layer beam actuator, it is illustrated that growth parameters and the external voltage can precisely control the bending angle. The framework is then applied to simulate pattern formation and transition behaviour, such as doubling and tripling of wrinkles, by specifying growth parameters and external voltage in a 3D stiff film/soft substrate structure. Furthermore, the suppression of wrinkles by applying external voltage is demonstrated. It is observed that the electric field plays a significant role in stress redistribution and guiding growth, resulting in the promotion or suppression of wrinkles, which is demonstrated by the numerical simulation of a long tubular structure. The proposed finite element scheme provides an accurate, efficient and stable tool for numerical simulation of electro-elastic solids incorporating growth effect, which can be used for understanding coupled growth phenomenon in biological soft matter and developing smart devices for medical treatment