A shell finite element formulation to analyze highly deformable rubber-like materials
Abstract: In this paper, a shell finite element formulation to analyze highly deformable shell structures composed of homogeneous rubber-like materials is presented. The element is a triangular shell of any-order with seven nodal parameters. The shell kinematics is based on geometrically exact Lagra...
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| Format: | Article |
| Language: | English |
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Marcílio Alves
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| Series: | Latin American Journal of Solids and Structures |
| Subjects: | |
| Online Access: | http://www.scielo.br/scielo.php?script=sci_arttext&pid=S1679-78252013000600006&lng=en&tlng=en |
| _version_ | 1818281913415106560 |
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| author | J. P. Pascon H. B. Coda |
| author_facet | J. P. Pascon H. B. Coda |
| author_sort | J. P. Pascon |
| collection | DOAJ |
| description | Abstract: In this paper, a shell finite element formulation to analyze highly deformable shell structures composed of homogeneous rubber-like materials is presented. The element is a triangular shell of any-order with seven nodal parameters. The shell kinematics is based on geometrically exact Lagrangian description and on the Reissner-Mindlin hypothesis. The finite element can represent thickness stretch and, due to the seventh nodal parameter, linear strain through the thickness direction, which avoids Poisson locking. Other types of locking are eliminated via high-order approximations and mesh refinement. To deal with high-order approximations, a numerical strategy is developed to automatically calculate the shape functions. In the present study, the positional version of the Finite Element Method (FEM) is employed. In this case, nodal positions and unconstrained vectors are the current kinematic variables, instead of displacements and rotations. To model near-incompressible materials under finite elastic strains, which is the case of rubber-like materials, three nonlinear and isotropic hyperelastic laws are adopted. In order to validate the proposed finite element formulation, some benchmark problems with materials under large deformations have been numerically analyzed, as the Cook's membrane, the spherical shell and the pinched cylinder. The results show that the mesh refinement increases the accuracy of solutions, high-order Lagrangian interpolation functions mitigate general locking problems, and the seventh nodal parameter must be used in bending-dominated problems in order to avoid Poisson locking. |
| first_indexed | 2024-12-13T00:12:40Z |
| format | Article |
| id | doaj.art-308eb64fc6284c47be2509ecd95f6821 |
| institution | Directory Open Access Journal |
| issn | 1679-7825 |
| language | English |
| last_indexed | 2024-12-13T00:12:40Z |
| publisher | Marcílio Alves |
| record_format | Article |
| series | Latin American Journal of Solids and Structures |
| spelling | doaj.art-308eb64fc6284c47be2509ecd95f68212022-12-22T00:05:53ZengMarcílio AlvesLatin American Journal of Solids and Structures1679-78251061177120910.1590/S1679-78252013000600006S1679-78252013000600006A shell finite element formulation to analyze highly deformable rubber-like materialsJ. P. Pascon0H. B. Coda1Universidade de São PauloUniversidade de São PauloAbstract: In this paper, a shell finite element formulation to analyze highly deformable shell structures composed of homogeneous rubber-like materials is presented. The element is a triangular shell of any-order with seven nodal parameters. The shell kinematics is based on geometrically exact Lagrangian description and on the Reissner-Mindlin hypothesis. The finite element can represent thickness stretch and, due to the seventh nodal parameter, linear strain through the thickness direction, which avoids Poisson locking. Other types of locking are eliminated via high-order approximations and mesh refinement. To deal with high-order approximations, a numerical strategy is developed to automatically calculate the shape functions. In the present study, the positional version of the Finite Element Method (FEM) is employed. In this case, nodal positions and unconstrained vectors are the current kinematic variables, instead of displacements and rotations. To model near-incompressible materials under finite elastic strains, which is the case of rubber-like materials, three nonlinear and isotropic hyperelastic laws are adopted. In order to validate the proposed finite element formulation, some benchmark problems with materials under large deformations have been numerically analyzed, as the Cook's membrane, the spherical shell and the pinched cylinder. The results show that the mesh refinement increases the accuracy of solutions, high-order Lagrangian interpolation functions mitigate general locking problems, and the seventh nodal parameter must be used in bending-dominated problems in order to avoid Poisson locking.http://www.scielo.br/scielo.php?script=sci_arttext&pid=S1679-78252013000600006&lng=en&tlng=enlarge deformation analysishomogeneous rubber-like materialsshell finite elements |
| spellingShingle | J. P. Pascon H. B. Coda A shell finite element formulation to analyze highly deformable rubber-like materials Latin American Journal of Solids and Structures large deformation analysis homogeneous rubber-like materials shell finite elements |
| title | A shell finite element formulation to analyze highly deformable rubber-like materials |
| title_full | A shell finite element formulation to analyze highly deformable rubber-like materials |
| title_fullStr | A shell finite element formulation to analyze highly deformable rubber-like materials |
| title_full_unstemmed | A shell finite element formulation to analyze highly deformable rubber-like materials |
| title_short | A shell finite element formulation to analyze highly deformable rubber-like materials |
| title_sort | shell finite element formulation to analyze highly deformable rubber like materials |
| topic | large deformation analysis homogeneous rubber-like materials shell finite elements |
| url | http://www.scielo.br/scielo.php?script=sci_arttext&pid=S1679-78252013000600006&lng=en&tlng=en |
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