A physically and geometrically nonlinear scaled‐boundary‐based finite element formulation for fracture in elastomers
A physically and geometrically nonlinear scaled‐boundary‐based finite element formulation for fracture in elastomers
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DOI：
10.1002/nme.4714
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发表时间：
2014-09
影响因子：
2.9
通讯作者：
R. Behnke;M. Mundil;Carolin Birk;M. Kaliske
中科院分区：
文献类型：
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作者：
R. Behnke;M. Mundil;Carolin Birk;M. Kaliske
本文研究了一种初厚度为常数的平面比例边界元，它可以处理材料的物理和几何非线性问题。通过使用标准比例边界有限元法的解析位移解推导出特殊的二维单元形函数，该方法最初基于线性材料行为和小应变。这些2D形状函数可以针对任意数量的单元节点来构造，并且允许捕获奇点（例如，在一个平面裂纹尖端）分析，没有广泛的网格细化。映射这些建议的2D形状函数的3D情况下，一个配方，是兼容的标准有限元。由此产生的物理和几何非线性比例边界有限元制定实施到有界平面域和无几何奇点的有限元方法的框架。数值实现的细节。为了描述弹性体试件的物理和几何非线性材料和结构行为，采用了扩展管模型和Yeoh模型。数值研究的收敛行为和标准Q1P0有限元的比较证明了正确的实施和发展的比例边界有限元的优点。版权所有© 2014约翰威利父子有限公司.
This paper is devoted to the formulation of a plane scaled boundary finite element with initially constant thickness for physically and geometrically nonlinear material behavior. Special two‐dimensional element shape functions are derived by using the analytical displacement solution of the standard scaled boundary finite element method, which is originally based on linear material behavior and small strains. These 2D shape functions can be constructed for an arbitrary number of element nodes and allow to capture singularities (e.g., at a plane crack tip) analytically, without extensive mesh refinement. Mapping these proposed 2D shape functions to the 3D case, a formulation that is compatible with standard finite elements is obtained. The resulting physically and geometrically nonlinear scaled boundary finite element formulation is implemented into the framework of the finite element method for bounded plane domains with and without geometrical singularities. The numerical realization is shown in detail. To represent the physically and geometrically nonlinear material and structural behavior of elastomer specimens, the extended tube model and the Yeoh model are used. Numerical studies on the convergence behavior and comparisons with standard Q1P0 finite elements demonstrate the correct implementation and the advantages of the developed scaled boundary finite element. Copyright © 2014 John Wiley & Sons, Ltd.