F‐bar‐based linear triangles and tetrahedra for finite strain analysis of nearly incompressible solids. Part I: formulation and benchmarking
F‐bar‐based linear triangles and tetrahedra for finite strain analysis of nearly incompressible solids. Part I: formulation and benchmarking
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DOI：
10.1002/nme.1187
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发表时间：
2005-01
影响因子：
2.9
通讯作者：
E. A. S. Neto;F. Pires;D. Owen
中科院分区：
文献类型：
--
作者：
E. A. S. Neto;F. Pires;D. Owen
本文提出了一种新技术，允许在几乎不可压缩固体的大应变分析中使用单纯形有限元（2D 中的线性三角形和 3D 中的线性四面体）。这项新技术扩展了 de Souza Neto 等人提出的 F-bar 方法。 （Int. J. Solids and Struct. 1996; 33: 3277–3296）并且在概念上非常简单：它依赖于在一片单纯形元素上执行（近）不可压缩性（而不是传统的基于位移的有限元的逐点执行）。在 F-bar 方法的框架内，这是通过假设网格的每个元素都有一个修改后的（F-bar）变形梯度来实现的，其体积分量定义为预定义元素块的体积变化率。由此产生的约束松弛有效地克服了体积锁定，并允许在接近不可压缩的有限应变下成功使用单纯形单元。作为原始的 F 杆程序，本方法保留了有限元方程的基于位移的结构以及用于路径相关本构方程数值积分的标准算法的应变驱动格式，并且无论采用何种本构模型都可以使用。新元素是在隐式准静态环境中实现的。在这种情况下，导出了新单元的精确切向刚度的闭合形式表达式。这允许使用完整的牛顿-拉夫森方案进行平衡迭代。所提出的元件的性能通过一组全面的基准二维和三维数值示例进行评估。版权所有 © 2005 约翰·威利父子有限公司
This paper proposes a new technique which allows the use of simplex finite elements (linear triangles in 2D and linear tetrahedra in 3D) in the large strain analysis of nearly incompressible solids. The new technique extends the F‐bar method proposed by de Souza Neto et al. (Int. J. Solids and Struct. 1996; 33: 3277–3296) and is conceptually very simple: It relies on the enforcement of (near‐) incompressibility over a patch of simplex elements (rather than the point‐wise enforcement of conventional displacement‐based finite elements). Within the framework of the F‐bar method, this is achieved by assuming, for each element of a mesh, a modified (F‐bar) deformation gradient whose volumetric component is defined as the volume change ratio of a pre‐defined patch of elements. The resulting constraint relaxation effectively overcomes volumetric locking and allows the successful use of simplex elements under finite strain near‐incompressibility. As the original F‐bar procedure, the present methodology preserves the displacement‐based structure of the finite element equations as well as the strain‐driven format of standard algorithms for numerical integration of path‐dependent constitutive equations and can be used regardless of the constitutive model adopted. The new elements are implemented within an implicit quasi‐static environment. In this context, a closed form expression for the exact tangent stiffness of the new elements is derived. This allows the use of the full Newton–Raphson scheme for equilibrium iterations. The performance of the proposed elements is assessed by means of a comprehensive set of benchmarking two‐ and three‐dimensional numerical examples. Copyright © 2005 John Wiley & Sons, Ltd.