Finite element simulation of strain localization with large deformation: capturing strong discontinuity using a Petrov–Galerkin multiscale formulation

Borja, Ronaldo I.

doi:10.1016/s0045-7825(02)00218-9

Cited by 53 publications

(46 citation statements)

References 37 publications

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“…For the purposes of this paper, we will use small strain assumptions. Strong discontinuity kinematics in a finite deformation setting are described in more detail in [22,38].…”

Section: Kinematicsmentioning

confidence: 99%

“…The formulation in this paper follows the strong discontinuity formulation of Simo and co-workers [20,21], and more closely the reformulation of Borja and Regueiro [33][34][35][36][37][38], which is described in more detail in Section 3. Other sub-classes of this element type have been described and differ primarily in the way the extra degrees of freedom are condensed; see [30,39] for reviews of the various types of these elements.…”

Section: Introductionmentioning

confidence: 99%

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Embedded strong discontinuity finite elements for fractured geomaterials with variable friction

Foster

Borja

Regueiro

2007

Numerical Meth Engineering

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SUMMARYThe strong discontinuity approach to modelling strain localization, combined with an enhanced strain element, has been used for more than a decade to model strain localization in materials including geomaterials. Most implementations of enhanced strain elements in the post-localization regime use very simple constitutive formulations along the discontinuity, such as linear softening or a constant friction coefficient. However, the softening relations can be much more complex for geomaterials. For rocks this softening is induced by micro-fractures coalescing into macroscopic cracks during a narrow time interval called 'slip weakening.' During this interval the cohesive resistance on the nucleating crack decays to zero while the frictional resistance increases. Furthermore, research has shown that the coefficient of friction for these materials is not constant, but in fact is a function both of the slip speed and the state of the material, including wear, temperature, and other factors. In this paper we augment the modelling capabilities of an enhanced strain element by incorporating a cohesive softening law and a popular rateand state-dependent friction model commonly used for describing the constitutive properties of rocks and rock-like materials sliding along the fractured surface.

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“…For the purposes of this paper, we will use small strain assumptions. Strong discontinuity kinematics in a finite deformation setting are described in more detail in [22,38].…”

Section: Kinematicsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Embedded strong discontinuity finite elements for fractured geomaterials with variable friction

Foster

Borja

Regueiro

2007

Numerical Meth Engineering

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“…The displacement field u(X) in the current configuration is conventionally decomposed as [43][44][45] …”

Section: Problem Statementmentioning

confidence: 99%

Finite deformation formulation for embedded frictional crack with the extended finite element method

Liu¹,

Borja²

2009

Numerical Meth Engineering

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SUMMARYWe reformulate an extended finite element (FE) framework for embedded frictional cracks in elastoplastic solids to accommodate finite deformation, including finite stretching and rotation. For the FE representation, we consider a Galerkin approximation in which both the trial and weighting functions adapt to the current contact configuration. Contact and frictional constraints employ two Kuhn-Tucker conditions, a contact/separation constraint nesting over a stick/slip constraint for the case when the crack faces are in frictional sliding mode. We integrate finite deformation bulk plasticity into the formulation using the multiplicative decomposition technique of nonlinear continuum mechanics. We then present plane strain simulations demonstrating various aspects of the extended FE solutions. The mechanisms considered include combined opening and frictional sliding in initially straight, curved, and S-shaped cracks, with and without bulk plasticity. To gain further insight into the extended FE solutions, we perform mesh convergence studies focusing on both the global and the local responses of structures with cracks, including the distribution of the normal component of traction on the crack faces.

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“…In the context of finite element (FE) analysis, there are many alternative approaches that one can possibly pursue to model thrust faulting, including: (a) the embedded discontinuity approach [9,11,15,16]; (b) the extended finite element approach, or XFEM [29,40,57]; and (c) the contact mechanics technique [5,20,31,44,58,73,93]. All of these approaches entail some form of regularization to characterize the thickness of the fault.…”

Section: Introductionmentioning

confidence: 99%

“…As the layers fold their geometry changes and the directions of the principal stress axes rotate. Faults are structural features that translate and rotate with the deforming domain; their motions are also tracked by the Lagrangian formulation [10,11]. Compared to kilometer-scale folding the fault thickness is very small, so in this paper we assume that the fault thickness is zero [2,13].…”

Section: Introductionmentioning

confidence: 99%

Mechanical aspects of thrust faulting driven by far-field compression and their implications for fold geometry

2007

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In this paper we present a mechanical model that intends to captures the kinematical aspects of thrust fault related folds induced by regional-scale far-field contraction. Fold shapes may be the only surface evidence of the geometry of underlying faults, so complex fault interactions are assessed in terms of how they influence fold geometry. We use the finite element method to model the fold and finite deformation frictional contact to model the activation and evolution of slip throughout preexisting faults. From several simulated 2D fault patterns we infer how one may form an anticline similar to that observed at Sheep Mountain Anticline, Wyoming.

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Finite element simulation of strain localization with large deformation: capturing strong discontinuity using a Petrov–Galerkin multiscale formulation

Cited by 53 publications

References 37 publications

Embedded strong discontinuity finite elements for fractured geomaterials with variable friction

Embedded strong discontinuity finite elements for fractured geomaterials with variable friction

Finite deformation formulation for embedded frictional crack with the extended finite element method

Mechanical aspects of thrust faulting driven by far-field compression and their implications for fold geometry

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