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首页> 外文期刊>Advances in Mechanical Engineering >A Finite Element Procedure with Poisson Iteration Method Adopting Pattern Approach Technique for Near-Incompressible Rubber Problems
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A Finite Element Procedure with Poisson Iteration Method Adopting Pattern Approach Technique for Near-Incompressible Rubber Problems

机译：近似不可压缩橡胶问题的采用泊松迭代法的有限元程序采用模式法

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摘要

A finite element procedure is presented for the analysis of rubber-like hyperelastic materials. The volumetric incompressibility condition of rubber deformation is included in the formulation using the penalty method, while the principle of virtual work is used to derive a nonlinear finite element equation for the large displacement problem that is presented in a total-Lagrangian description. The behavior of rubber deformation is represented by hyperelastic constitutive relations based on a generalized Mooney-Rivlin model. The proposed finite element procedure using analytic differentiation exhibited results that matched very well with those from the well-known commercial packages NISA II and ABAQUS. Furthermore, the convergence of equilibrium iteration is quite slow or frequently fails in the case of near-incompressible rubber. To prevent such phenomenon even for the case that Poisson's ratio is very close to 0.5, Poisson's ratio of 0.49000 is used, first, to get an approximate solution without any difficulty; then the applied load is maintained and Poisson's ratio is increased to 0.49999 following a proposed pattern and adopting a technique of relaxation by monitoring the convergence rate. For a given Poisson ratio near 0.5, with this approach, we could reduce the number of substeps considerably.
机译：提出了一种有限元程序，用于分析橡胶状超弹性材料。使用罚分法将橡胶变形的体积不可压缩条件包括在配方中，而虚拟工作原理则用于导出针对大位移问题的非线性有限元方程，该方程在总拉格朗日描述中给出。橡胶变形的行为由基于广义Mooney-Rivlin模型的超弹性本构关系表示。拟议的使用有限差分法的有限元程序显示出的结果与著名的商业软件包NISA II和ABAQUS的结果非常匹配。此外，在橡胶几乎不可压缩的情况下，平衡迭代的收敛非常慢，或者经常失败。为了即使在泊松比非常接近0.5的情况下也能防止这种现象，首先使用泊松比0.49000，以获得没有任何困难的近似解。然后按照建议的模式并通过监控收敛速度采用松弛技术，保持施加的载荷并将泊松比增加到0.49999。对于给定的泊松比接近0.5的情况，使用这种方法，我们可以大大减少子步骤的数量。

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