Finite and Virtual Element Formulations for Large Strain Anisotropic Material with Inextensive Fibers

被引:9
作者
Wriggers, P. [1 ]
Hudobivnik, B. [1 ]
Schroeder, J. [2 ]
机构
[1] Leibniz Univ Hannover, Hannover, Germany
[2] Univ Duisburg Essen, Duisburg, Germany
来源
MULTISCALE MODELING OF HETEROGENEOUS STRUCTURES | 2018年 / 86卷
关键词
Anisotropic material; Finite element analysis; Virtual element schemes; Mixed methods; Constraints; ENERGY-SAMPLING STABILIZATION; ELASTICITY PROBLEMS; 8-NODE HEXAHEDRON; NONLINEAR ELASTICITY; INCOMPATIBLE MODES; HOURGLASS CONTROL; COSSERAT POINT; BRICK ELEMENT; PLANE-STRAIN; DEFORMATION;
D O I
10.1007/978-3-319-65463-8_11
中图分类号
TH [机械、仪表工业];
学科分类号
0802 ;
摘要
Anisotropic material with inextensive or nearly inextensible fibers introduce constraints in the mathematical formulations of the underlying differential equations from mechanics. This is always the case when fibers with high stiffness in a certain direction are present and a relatively weak matrix material is supporting these fibers. In numerical solution schemes like the finite element method or the virtual element method the presence of constraints-in this case associated to a possible fiber inextensibility compared to a matrix-lead to so called locking-phenomena. This can be overcome by special interpolation schemes as has been discussed extensively for volume constraints like incompressibility as well as contact constraints. For anisotropic material behaviour the most severe case is related to inextensible fibers. In this paper a mixed method is developed for finite elements and virtual elements that can handle anisotropic materials with inextensive and nearly inextensive fibers. For this purpose a classical ansatz, known from the modeling of volume constraint is adopted leading stable elements that can be used in the finite strain regime.
引用
收藏
页码:205 / 231
页数:27
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