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