Cosserat point element \((CPE)\) for finite deformation of orthotropic elastic materials. (English) Zbl 1398.74341
Summary: An eight node brick Cosserat point element \((CPE)\) has been developed for the numerical solution of three-dimensional problems of hyperelastic nonlinear orthotropic elastic materials. In the Cosserat approach, a strain energy function for the \(CPE\) is proposed which satisfies restrictions due to a nonlinear form of the patch test. Part of the strain energy of the \(CPE\) is characterized by a three-dimensional strain energy function that depends on physically based nonlinear orthotropic invariants. Special attention has been focused on developing closed form expressions for constitutive coefficients in another part of the strain energy that characterizes the response to inhomogeneous deformations appropriate for orthotropic material response. A number of example problems are presented which demonstrate that the \(CPE\) is a robust user friendly element for finite deformations of orthotropic elastic materials, which does not exhibit unphysical locking or hourglassing for thin structures or nearly
incompressible materials.
MSC:
| 74S05 | Finite element methods applied to problems in solid mechanics |
| 74B20 | Nonlinear elasticity |
| 74K10 | Rods (beams, columns, shafts, arches, rings, etc.) |
| 74S30 | Other numerical methods in solid mechanics (MSC2010) |
| 74C99 | Plastic materials, materials of stress-rate and internal-variable type |
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