权益分类	功能权益	普通用户	{{item.name}}会员
{{category.name}}	{{benefitItem.name}}

Explanation of fracture phenomena by crack extension analysis using extended finite element method

使用扩展有限元法通过裂纹扩展分析解释断裂现象

基本信息

批准号：
16360226
负责人：
YATOMI Chikayoshi
金额：
$ 3.78万
依托单位：
Kanazawa University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (B)
财政年份：
2004
资助国家：
日本
起止时间：
2004 至 2006
项目状态：
已结题

项目摘要

Extended finite element method (X-FEM) was first developed by Belytcheko et al. in 1996 for the linear elastic fracture mechanics to avoid awkward remeshing near a crack tip as the crack grows. The key idea of the extended finite element method is that the unknown variables of discontinuous displacement are added to the nodal continuous displacements so that the crack can extend across the element. The method was, however, restricted only to the cracks in the linear elastic material.With the aim of analyzing the fracture of geomaterials, we develop a new extended finite element method(X-FEM) available to an elastic-plastic material. We analyzes the stress distributions near a crack tip for the Drucker-Prager elastic-plastic material in a rectangular plate with a centered crack under two axial compressive loads. The elastic-plastic material is analyzed by the implicit return mapping algorithm, which gives a high accuracy and much reduces CPU time by using an incremental and iterative method of the Newton-Raphson method.Under the compressive loads there exist friction forces along the crack faces. In solving this contact problem, we introduce a new method which conform to the extended finite element method. The friction forces are assumed to follow the elastic-perfect plastic material with Coulomb law for the slip criterion. The friction problem is also analyzed in the context of an implicit return mapping algorithm.Thus the contact problem and the elastic-plastic material become a simultaneous combining incremental and iterative method of the same implicit scheme of the Newton-Raphson method. This makes the algorithm very simple.The stress distributions near the crack tip obtained by the simple X-FEM agree very well with the reliable solutions in the classical FEM solution for the elastic-plastic material. For the future, therefore, we anticipate a practical application of this new method such as a land slide.

扩展有限元法（X-FEM）首先由 Belytcheko 等人开发。 1996 年，用于线性弹性断裂力学，以避免随着裂纹扩展而在裂纹尖端附近进行笨拙的重新网格化。扩展有限元方法的关键思想是将不连续位移的未知变量添加到节点连续位移中，使得裂纹能够延伸穿过单元。然而，该方法仅限于线弹性材料中的裂纹。为了分析岩土材料的断裂，我们开发了一种新的适用于弹塑性材料的扩展有限元方法（X-FEM）。我们分析了具有中心裂纹的矩形板中 Drucker-Prager 弹塑性材料在两个轴向压缩载荷下裂纹尖端附近的应力分布。采用隐式返回映射算法对弹塑性材料进行分析，该算法使用牛顿-拉夫森法的增量迭代方法，精度高，大大减少了CPU时间。在压缩载荷作用下，沿裂纹面存在摩擦力。在解决这个接触问题时，我们引入了一种符合扩展有限元法的新方法。假定摩擦力遵循完美弹性塑料材料，并采用库仑定律作为滑动准则。摩擦问题也在隐式返回映射算法的背景下进行了分析。因此，接触问题和弹塑性材料成为牛顿-拉夫森方法相同隐式格式的同时结合增量和迭代的方法。这使得算法变得非常简单。通过简单的X-FEM获得的裂纹尖端附近的应力分布与弹塑性材料的经典FEM解中的可靠解非常吻合。因此，在未来，我们预计这种新方法将得到实际应用，例如滑坡。