High-performance unsymmetric 8-node hexahedral element for modeling growth-induced deformation of soft materials

Purpose This paper aims to extend the recent unsymmetric 8-node, 24-degree-of-freedom hexahedral solid element US-ATFH8 to simulate the compressible and nearly incompressible behaviors associated with growth-induced deformations in soft materials. Design/methodology/approach An effective total Lagrangian algorithm is designed to extend the element US-ATFH8 to the geometrically nonlinear analysis in which different test and analytical trial functions (ATFs) are employed. Then, the volumetric growth theory of biological tissue is embedded into the novel element US-ATFH8 to simulate the growth-induced deformations in soft materials. Findings The numerical examples, including cubes, cantilever beams, rods, tubes, petals and growth-induced deformations in skin and ventricles, fully prove that the element possesses high accuracy and a fast convergence rate in modeling growth behaviors. It can still perform well even when other conventional finite element methods cannot work. Originality/value It is again proved that the unsymmetric finite element with ATFs is still suitable for the constitutive model of growth-induced deformation.