An extended finite element framework for slow‐rate frictional faulting with bulk plasticity and variable friction

Liu, Fushen; Borja, Ronaldo I.

doi:10.1002/nag.777

Cited by 42 publications

(11 citation statements)

References 61 publications

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“…They noted the superior rates of convergence for the penalty method compared to the LATIN method. The approach has been extended to problems with bulk plasticity (Khoei et al, 2006;Liu and Borja, 2009) and large sliding contact (Khoei and Mousavi, 2010;Liu and Borja, 2010a). It should be noted that these approaches still represent a regularization of a discrete formulation that is unstable, and involve a free penalty parameter.…”

Section: Introductionmentioning

confidence: 99%

An efficient finite element method for embedded interface problems

Dolbow

Harari

2008

Numerical Meth Engineering

219

223

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We focus on developing a computationally efficient finite element method for interface problems. Finite element methods are severely constrained in their ability to resolve interfaces. Many of these limitations stem from their inability in independently representing interface geometry from the underlying discretization. We propose an approach that facilitates such an independent representation by embedding interfaces in the underlying finite element mesh. This embedding, however, raises stability concerns for existing algorithms used to enforce interfacial kinematic constraints. To address these stability concerns, we develop robust methods to enforce interfacial kinematics over embedded interafces.We begin by examining embedded Dirichlet problems -a simpler class of embedded constraints. We develop both stable methods, based on Lagrange multipliers, and stabilized methods, based on Nitsche's approach, for enforcing Dirichlet constraints over three-dimensional embedded surfaces and compare and contrast their performance. We then extend these methods to enforce perfectly-tied kinematics for elastodynamics with explicit time integration. In particular, we examine the coupled aspects of spatial and temporal stability for Nitsche's approach. We address the incompatibility of Nitsche's method for explicit time integration by (a) proposing a modified weighted stress variational form, and (b) proposing a novel mass-lumping procedure.We revisit Nitsche's method and inspect the effect of this modified variational iv form on the interfacial quantities of interest. We establish that the performance of this method, with respect to recovery of interfacial quantities, is governed significantly by the choice for the various method parameters viz. stabilization and weighting. We establish a relationship between these parameters and propose an optimal choice for the weighting. We further extend this approach to handle non-linear, frictional sliding constraints at the interface. The naturally non-symmetric nature of these problems motivates us to omit the symmetry term arising in Nitsche's method.We contrast the performance of the proposed approach with the more commonly used penalty method. Through several numerical examples, we show that with the proposed choice of weighting and stabilization parameters, Nitsche's method achieves the right balance between accurate constraint enforcement and flux recovery -a balance hard to achieve with existing methods. Finally, we extend the proposed approach to intersecting interfaces and conduct numerical studies on problems with junctions and complex topologies.v To Amma (mom) and Nannagaru (dad), vi

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Section: Introductionmentioning

confidence: 99%

An efficient finite element method for embedded interface problems

Dolbow

Harari

2008

Numerical Meth Engineering

219

223

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“…Furthermore, the Galerkin finite element approach used in the current study may be replaced by any other domain-based model. For example, if we want to relax the constraint that the fault location is known apriori, a more flexible approach would be to adopt a discretization approach that readily accounts for discontinuities such as generalized finite element method (F. Liu & Borja, 2009), or discontinuous Galerkin methods (Pelties et al, 2012), or phase field model (Miehe et al, 2010), which would further enable arbitrary growth of fault surfaces, as well as nucleation and growth of new surfaces. Furthermore, the FEM may be replaced by a discrete element method (Herrmann et al, 1998) or smooth particle hydrodynamics formulation (Bui et al, 2008) to enable explicit incorporation of fault gouge dynamics.…”

Section: Discussionmentioning

confidence: 99%

A Novel Hybrid Finite Element-Spectral Boundary Integral Scheme for Modeling Earthquake Cycles: Application to Rate and State Faults with Low-Velocity Zones

Abdelmeguid¹,

Ma²,

Elbanna³

2019

Preprint

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We present a novel hybrid finite element (FE) - spectral boundary integral (SBI) scheme that enables efficient simulation of earthquake cycles. This combined FE-SBI approach captures the benefits of finite elements in modelling problems with nonlinearities, as well as the computational superiority of SBI. The domain truncation enabled by this scheme allows us to utilize high-resolution finite elements discretization to capture inhomogeneities or complexities that may exist in a narrow region surrounding the fault. Combined with an adaptive time stepping algorithm, this framework opens new opportunities for modeling earthquake cycles with high-resolution fault zone physics. In this initial study, we consider a two dimensional (2-D) anti-plane model with a vertical strike-slip fault governed by rate and state friction in the quasi-dynamic limit under the radiation damping approximation. The proposed approach is first verified using the benchmark problem BP-1 from the Southern California Earthquake Center (SCEC) sequence of earthquake and aseismic slip (SEAS) community verification effort. The computational framework is then utilized to model the earthquake sequence and aseismic slip of a fault embedded within a low-velocity fault zone (LVFZ) with different widths and compliance levels. Our results indicate that sufficiently compliant LVFZs contribute to the emergence of sub-surface events that fail to penetrate to the free surface and may experience earthquake clusters with nonuniform inter-seismic time. Furthermore, the LVFZ leads to slip rate amplification relative to the homogeneous elastic case. We discuss the implications of our results for understanding earthquake complexity as an interplay of fault friction and bulk heterogeneities.

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“…A new fault whose geometry is not a priori known is an important topic to study. One advantage of the proposed hybrid approach is that it can easily adopt volume based discretization techniques with embedded discontinuities such as XFEM() or explicit discontinuities such as Discontinuous Galerkin . These methods may replace the continuous Galerkin domain‐based method used in this current work.…”

Section: Discussionmentioning

confidence: 99%

A hybrid finite element‐spectral boundary integral approach: Applications to dynamic rupture modeling in unbounded domains

Hajarolasvadi

Albertini

et al. 2018

Num Anal Meth Geomechanics

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Summary The finite element method (FEM) and the spectral boundary integral method (SBI) have both been widely used in the study of dynamic rupture simulations along a weak interface. In this paper, we present a hybrid method that combines FEM and SBI through the consistent exchange of displacement and traction boundary conditions, thereby benefiting from the flexibility of FEM in handling problems with nonlinearities or small‐scale heterogeneities and from the superior performance and accuracy of SBI. We validate the hybrid method using a benchmark problem from the Southern California Earthquake Center's dynamic rupture simulation validation exercises.We further demonstrate the capability and computational efficiency of the hybrid scheme for resolving off‐fault heterogeneities by studying a 2D in‐plane shear crack in two different settings: one where the crack is embedded in a high‐velocity zone and another where it is embedded in a low‐velocity zone. Finally, we discuss the potential of the hybrid method for addressing a wide range of problems in geophysics and engineering.

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An extended finite element framework for slow‐rate frictional faulting with bulk plasticity and variable friction

Cited by 42 publications

References 61 publications

An efficient finite element method for embedded interface problems

An efficient finite element method for embedded interface problems

A Novel Hybrid Finite Element-Spectral Boundary Integral Scheme for Modeling Earthquake Cycles: Application to Rate and State Faults with Low-Velocity Zones

A hybrid finite element‐spectral boundary integral approach: Applications to dynamic rupture modeling in unbounded domains

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