Response of a nonlinear elastic general Cosserat brick element in simulations typically exhibiting locking and hourglassing
Response of a nonlinear elastic general Cosserat brick element in simulations typically exhibiting locking and hourglassing
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DOI：
10.1007/s00466-005-0662-9
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发表时间：
2005-05
影响因子：
4.1
通讯作者：
S. Loehnert;E. Boerner;M. Rubin;P. Wriggers
中科院分区：
文献类型：
--
作者：
S. Loehnert;E. Boerner;M. Rubin;P. Wriggers
本文将最近发展的Cosserat砖单元（见[9]）与文献中已知的其它标准单元作了比较。Cosserat砖元素使用基于Cosserat点理论的指向矢公式。将超弹性单元的应变能叠加分解为均匀变形和非均匀变形两部分。由于不均匀变形引起的动力学响应使用由长方体弯曲、扭转和沙漏变形模式的解析解确定的本构常数。执行标准测试，这些测试通常表现出许多其他有限元的沙漏或锁定。这些测试包括梁和板弯曲，壳体结构和几乎不可压缩的材料，以及在高压载荷下的屈曲问题。对于所有这些关键测试，Cosserat砖元件都表现出坚固性和可靠性。此外，它不依赖于用户调整的稳定参数。因此，它显示了作为一个真正的用户友好的元素在非线性弹性问题的承诺。
A comparison between the recently developed Cosserat brick element (see [9]) and other standard elements known from the literature is presented in this paper. The Cosserat brick element uses a director vector formulation based on the theory of a Cosserat point. The strain energy for a hyperelastic element is split additively into parts for homogeneous and inhomogeneous deformations respectively. The kinetic response due to inhomogeneous deformations uses constitutive constants that are determined by analytical solutions of a rectangular parallelepiped to the deformation modes of bending, torsion and hourglassing. Standard tests are performed which typically exhibit hourglassing or locking for many other finite elements. These tests include problems for beam and plate bending, shell structures and nearly incompressible materials, as well as for buckling under high pressure loads. For all these critical tests the Cosserat brick element exhibits robustness and reliability. Moreover, it does not depend on user-tuned stabilization parameters. Thus, it shows promise of being a truly user-friendly element for problems in nonlinear elasticity.