On the advantages of mixed formulation and higher-order elements for computational morphoelasticity

In this paper, we present a mixed displacement–pressure finite element formulation that can successively model compressible as well truly incompressible behaviour in growth-induced deformations significantly observed soft materials. Inf–sup stable elements of various shapes based on quadratic Bézier are employed for spatial discretisation. At first, the capability proposed framework to accurately finite-strain is illustrated using several examples plate models which numerical results directly compared with analytical solutions. The also classical Q1/P0 has been used extensively simulating deformation materials quasi-incompressibility assumption. comparisons clearly demonstrate superior capabilities framework. Later, effect hyperelastic constitute and compressibility studied example bilayered strip three dimensions. Finally, potential simulate complex three-dimensional problems flower petals, morphoelastic rods, thin cylindrical tubes.