A SPECTRAL METHOD FOR 3-DIMENSIONAL ELASTODYNAMIC FRACTURE PROBLEMS
A SPECTRAL METHOD FOR 3-DIMENSIONAL ELASTODYNAMIC FRACTURE PROBLEMS
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DOI：
10.1016/0022-5096(95)00043-i
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发表时间：
1995-11-01
影响因子：
5.3
通讯作者：
RICE, JR
中科院分区：
文献类型：
--
作者：
GEUBELLE, PH;RICE, JR
本文给出了平面裂纹和断层上三维弹性断裂动力学问题的数值计算公式。应力和位移分量在平行于断裂面的空间坐标系中以有限傅立叶级数的形式给出谱表示。该制剂是基于一个精确的表示，涉及卷积积分为每个傅立叶模式，弹性动力学之间的关系存在的时间依赖的傅立叶系数的牵引作用在断裂面和所产生的位移不连续。广泛的本构模型可用于将断裂面上的强度局部值与位移和速度历史联系起来。代码的效率是通过使用显式时间积分方案和通过FFT算法计算空间和频谱分布之间的转换来实现的。该方法特别适合在大规模并行计算机上实现;在这项工作中使用了CM-5。的稳定性和精度的制定进行了讨论拉伸（模式1）的情况下，在一个详细的模态分析，并与现有的三维弹性动力学解决方案的数值结果进行了比较。充分的方法来调查各种三维动态断裂问题，涉及非传播和传播拉伸裂纹的说明，包括裂纹扩展沿着一个平面的非均匀断裂韧性。
We present a numerical formulation for three-dimensional elastodynamic problems of fracture on planar cracks and faults. Stress and displacement components are given a spectral representation as finite Fourier series in space coordinates parallel to the fracture plane. The formulation is based on an exact representation, involving a convolution integral for each Fourier mode, of the elastodynamic relation existing between the time-dependent Fourier coefficients for the tractions acting on the fracture plane and for the resulting displacement discontinuities. A wide range of constitutive models can be used to relate the local value of the strength on the fracture plane with the displacement and velocity history. Efficiency of the code is achieved by using an explicit time integration scheme and by computing the conversion between the spatial and spectral distributions through a FFT algorithm. The method is particularly suited to implementation on massively parallel computers; a CM-5 was used in this work. The stability and precision of the formulation are discussed for tensile (mode 1) situations in a detailed modal analysis, and numerical results are compared with existing three-dimensional elastodynamic solutions. The adequacy of the method to investigate Various three-dimensional dynamic fracture problems involving non-propagating and propagating tensile cracks is illustrated, including crack growth along a plane of heterogeneous fracture toughness.