期刊
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
卷 121, 期 16, 页码 3702-3721出版社
WILEY
DOI: 10.1002/nme.6378
关键词
analytical trial functions (ATFs); finite deformation; hyperelastic; incompressible; mesh distortion; unsymmetric finite element methods
资金
- China Scholarships Council fellowship [201806210280]
- National Natural Science Foundation of China [11872229]
A recent unsymmetric 4-node, 8-DOF plane finite element US-ATFQ4 is generalized to hyperelastic finite deformation analysis. Since the trial functions of US-ATFQ4 contain the homogenous closed analytical solutions of governing equations for linear elasticity, the key of the proposed strategy is how to deal with these linear analytical trial functions (ATFs) during the hyperelastic finite deformation analysis. Assuming that the ATFs can properly work in each increment, an algorithm for updating the deformation gradient interpolated by ATFs is designed. Furthermore, the update of the corresponding ATFs referred to current configuration is discussed with regard to the hyperelastic material model, and a specified model, neo-Hookean model, is employed to verify the present formulation of US-ATFQ4 for hyperelastic finite deformation analysis. Various examples show that the present formulation not only remain the high accuracy and mesh distortion tolerance in the geometrically nonlinear problems, but also possess excellent performance in the compressible or quasi-incompressible hyperelastic finite deformation problems where the strain is large.
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