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A smoothed finite element method for three-dimensional dynamic impactcontact problem based on penalty function method
Chao Sun

Last modified: 2020-08-04


Boundary value problems represented by contact problem are of great importance in engineering and biomechanics applications[1]. However, due to the strong nonlinearities and possible large deformation, caused by non-smoothed contact interfaces and uncertain contact region, special techniques are needed for efficient treatment of such difficulties[2]. Therefore, a scheme that combines smoothed finite method (S-FEM) with penalty method is developed for contact/impact problems with hyperelastic materials and large geometric deformations[3]. The S-FEM models including edge-based FEM(ES-FEM), face-based FEM(FS-FEM), selective face-based/node-based S-FEM(FS/NS-FEM), and selective edge-based/node-based S-FEM (ES/NS-FEM) are developed based on tetrahedral elements[4][5]. Both dynamic selective smoothed S-FEM models are free of nearly incompressible locking by splitting the strain energy into individual parts and applying different integration rules separately. For enforcing contact constraints, the penalty method is chosen to enforce the non-penetration condition, because it could avoid additional variables by introducing a user-defined penalty factor. A contact point-pairs method constructed using a node to surface (NTS) algorithm are utilized to discretize the equations for interface discretization. Eventually, several 3D dynamic numerical results are employed to evaluate the accuracy and robustness of the S-FEM  penalty scheme.

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