Unified finite element formulation for computational solid mechanics

Dear iMechanica members,

I have recently proposed a novel finite element framework for computational solid mechanics. I hope you find it interesting. I appreciate any feedback.

Towards addressing some long-standing issues in performing explicit elastodynamic simulations of incompressible hyperelastic and elastoplastic material models, finite element formulations based on Bézier elements are developed. The formulations are based on quadratic Bézier triangular and tetrahedral elements. You can download the papers from the following links.

SmallStrain SmallStrainRG

FiniteStrain FiniteStrainRG

Small strain regime:

For problems in the small-strain regime, B-bar formulation is extended to quadratic triangular/tetrahedral elements. This extension is a novel aspect.

Finite strain regime:

For problems in the finite strain regime, new mixed displacement-pressure elements BT2/BT0 and BT2/BT1 are introduced. (BT refers to Bézier Triangle or Bézier Tetrahedron). These elements are equally valid for small strain problems.

Important characteristics:

1.) Versatility: A single formulation for elastostatics, implicit elastodynamics and explicit elastodynamics.

2.) Simplicity: No additional variables in the B-bar formulation and significantly fewer pressure DOFs in the mixed formulations.

3.) Effectiveness: The formulation deals with both volumetric and shear locking very efficiently; also, no issues in modelling bending.

4.) Efficiency: Accurate results using coarse meshes. This feature is extremely beneficial for explicit dynamic simulations in which the critical time step is directly proportional to the smallest element size.

5.) Robustness: The formulation does not involve any ad-hoc parameters that control stability and accuracy.

6.) Ease of mesh generation: The formulation is based on unstructured triangular/tetrahedral meshes that can be generated using existing mesh generators. So, it is applicable for complex engineering problems.

Snapshots of some examples are shown in the attached figure.