High-order NURBS elements based isogeometric formulation for swellable soft materials

Abstract This paper presents an isogeometric formulation and the corresponding algorithm to predict the mechanical behaviors of swellable soft materials by the high-order NURBS elements. To deal with the difficulties aroused from the growth and incompressibility of soft materials, a numerical scheme based on two multiplicative decompositions of deformation gradient is developed. For introducing the growth effect, the deformation gradient is decomposed into a growth tensor and an elastic deformation gradient. For circumventing the volumetric locking caused by incompressibility of soft materials, the elastic deformation gradient is further decomposed into its volume-preserving and volumetric-dilatational parts. Meanwhile, the volumetric-dilatational part is modified by a linear projection operator. Then, the incremental equations of the weak form are derived by an effective linearization method for this nonlinear problem. After introducing the discrete technique in isogeometric analysis, the formulations for numerical calculations, i.e., the stiffness matrices and the force vectors, are derived. The efficiency and accuracy of the proposed isogeometric method are demonstrated by several examples discretized by the high-order NURBS elements exactly, including conic sections and other complex geometries. The proposed method is also proved to have great potentials for analyzing the mechanical behaviors of swellable soft materials as well as bionic structures and designing the bionic devices.