HR: 0800h
AN: T41B-0587    [Abstracts]
TI: Localization of Deformation in Elastic-Plastic Analysis of Dynamic Shear Rupture Propagation
AU: * Templeton, E L
EM: templet@fas.harvard.edu
AF: Sch. Engin. Appl. Sci., Harvard Univ., Cambridge, MA 02138,
AU: Rice, J R
EM: rice@deas.harvard.edu
AF: Dept. Earth Planet. Sci. and Sch. Engin. Appl. Sci., Harvard Univ., Cambridge, MA 02138,
AB: Recent studies have allowed for off-fault elastic-plastic deformation in analyses of dynamic earthquake rupture propagation on slip-weakening faults [Andrews, 2005; Shi and Ben-Zion, 2006; Templeton et al., 2006; Viesca et al., 2006]. These studies used Mohr Coulomb (MC) or Drucker-Prager (DP) type pressure-dependent yield criteria for describing the onset of plastic deformation in granulated or cracked rocks. In plane strain finite element analyses of such dynamically propagating ruptures, for a DP material, we found features in the strain field that indicate localization into shear-band-like structures. Bifurcation analyses for states of spatially homogeneous quasistatic deformation have shown that instabilities in the constitutive description for certain classes of elastic-plastic materials can lead to such localizations [Hill, 1952; Thomas, 1961; Rudnicki and Rice, 1975; Rice, 1976]. Localization conditions coincide with those for a vanishing propagation speed of elastic- plastic body waves [Hadamard,1903; Hill, 1962; Mandel, 1963]. Rudnicki and Rice found that localization can occur even for positive values of the plastic strain-hardening modulus, h, in materials with pressure-dependent yield and non-associated plastic flow. They determined a critical value, h_cr, such that localization will occur only for h ≤ h_cr. For 2D stress fields with the out of plane principal stress equal to the average of the in plane values, the MC and DP criteria coincide, and h_cr>0. Elastic-plastic analyses of rupture dynamics typically use a plane strain, non-hardening model, h=0; that means hcr usually, so that localization conditions are met and one must expect an inherent grid dependence in numerical solutions. Our refined-grid numerical solutions with h=0 show notable variations of plastic strain at the scale of grid spacing, precluding point-wise convergence with increasing refinement. Such features signal that no continuum solution exists for the adopted model, and some localization limiting procedure [Bazant; de Borst; Needleman] based on non-locality or strain gradient effects would need to be added to the constitutive description to allow one. Implementation of those procedures is computationally challenging for rupture propagation, and it is sometimes suggested that inertial effects can, in any event, ameliorate strong localization. In our dynamic analyses, we observed shear-band-like structures at the scale of grid spacing, for grid spacings of 10 to 20 elements within a static slip-weakening zone length, R₀. We investigated the localization features to understand how their shape, spacing, and extent change with grid refinement and element shape. We expected that with increased refinement, the size and spacing of the localization features would remain at the scale of grid spacing. Instead we see a transition in the spacing of the longest shear localization zones for extremely refined grids, having 80 elements within R₀. Those long shear features recur aperiodically along the rupture path, with a characteristic spacing that appears to be roughly on the order of R, the dynamic slip-weakening zone length. We show, at least for some range of rupture propagation, that although the localization features are strongly mesh dependent, overall sizes and shapes of off-fault plastic regions, and also the dynamics of rupture propagation (e.g., rupture length vs. time), seem to be little different from what is obtained when we increase the assumed plastic hardening modulus h above h_cr and obtain a locally smooth and presumably point-wise convergent numerical solution.
DE: 4400 NONLINEAR GEOPHYSICS (3200, 6944, 7839)
DE: 7209 Earthquake dynamics (1242)
DE: 8100 TECTONOPHYSICS
SC: Tectonophysics [T]
MN: 2007 Fall Meeting