Three-dimensional growth simulation of swellable soft materials based on CS-FEM

In this paper, a three-dimensional numerical framework for modeling growth of swellable soft materials at large deformation is established based on the cell-based smooth finite element method, and the multiplicative decomposition scheme of deformation gradient is given. The second P-K stress and Green's strain tensor are selected as work conjugate pairs, and the corresponding mathematical expressions of stiffness matrix and geometric stiffness matrix are derived. The numerical method is implemented based on Matlab platform, and the isotropic and anisotropic growth behaviors of swellable soft materials are simulated respectively. The results show that anisotropic growth will inhibit the deformation of expandable soft materials compared with isotropic growth. The simulation results are compared with the calculation results in the existing literature. The comparison results show that the characteristics and the morphological mode are in good agreement, which proves the effectiveness of the numerical framework in simulating the growth behavior of expandable soft materials at large deformation, and is able to reveal the mechanical mechanism of the plant growth phenomenon in nature.