TY - JOUR
T1 - A spectral method for three-dimensional elastodynamic fracture problems
AU - Geubelle, Philippe H.
AU - Rice, James R.
N1 - Funding Information:
Our study was funded by the ONR Mechanics Program under grant NOOO14-90-J-1379I.n addition, P. H. Geubelle had a partial support of a NATO Postdoctoral Fellowship. Access to the NCSA CM-5 has been provided through the NSF grant EAR940004N. Computations were also performed on the SCOUT CM-5 which is part of a joint MIT-Harvard University-Boston University-Thinking Machine Corporation Project sponsored by ARPA. We are grateful to our co-workers Y. Ben-Zion, J. Kysar, J. Morrissey and G. Zheng for helpful discussions.
PY - 1995/11
Y1 - 1995/11
N2 - 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.
AB - 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.
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U2 - 10.1016/0022-5096(95)00043-I
DO - 10.1016/0022-5096(95)00043-I
M3 - Article
AN - SCOPUS:0029405381
SN - 0022-5096
VL - 43
SP - 1791
EP - 1824
JO - Journal of the Mechanics and Physics of Solids
JF - Journal of the Mechanics and Physics of Solids
IS - 11
ER -