Gradient smoothing in finite elasticity: near-incompressibility

This thesis presents the extension of the gradient smoothing technique for finite element approximation (so-called Smoothed Finite Element Method (S-FEM)) and its bubble-enhanced version for non-linear problems involving large deformations in nearly-incompressible and incompressible hyperelastic materials. Finite Element Method (FEM) presents numerous challenges for soft matter applications, such as incompressibility, complex geometries and mesh distortion from large deformation. S-FEM was introduced to overcome the challenges mentioned of FEM. The smoothed strains and the smoothed deformation gradients are evaluated on the smoothing domain selected by either edge information, nodal information or face information. This thesis aims the extension of S-FEM in finite elasticity as a means of alleviating locking and avoiding mesh distortion. S-FEM employs a “cubic” bubble enhancement of the element shape functions with edge-based and face-based S-FEMs, adding a linear displacement field at the centre of the element. Thereby bubble-enhanced S-FEM affords a simple and efficient implementation. This thesis reports the properties and performance of the proposed method for quasi-incompressible hyperelastic materials. Benchmark tests show that the method is well suited to soft matter simulation, overcoming deleterious locking phenomenon and maintaining the accuracy with distorted meshes