An analysis of strong discontinuities induced by strain-softening in rate-independent inelastic solids

Simo, J. C.; Oliver, J.; Armero, F.

doi:10.1007/bf00372173

Cited by 757 publications

(588 citation statements)

References 29 publications

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“…The discontinuity then has to be captured in the interiors of the finite elements. Early approaches include the work of Dvorkin et al (1990) and the general framework for finite elements with embedded strong discontinuities presented in Simo et al (1993), Garikipati (1995, 1996), Oliver (1996a,b), and Larsson et al (1998), to just mention some early publications. Other approaches not sharing this element-based enhancement rely on nodally-based enrichments, like the so-called extended finite element method and its variations as presented in Belytschko and Black (1999), Moës et al (1999), Dolbow et al (2000), Wells and Sluys (2001), Wells et al (2002), or Hansbo and Hansbo (2004), among others.…”

Section: Introductionmentioning

confidence: 99%

Numerical simulation of dynamic fracture using finite elements with embedded discontinuities

2009

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This paper presents the extension of some finite elements with embedded strong discontinuities to the fully transient range with the focus on dynamic fracture. Cracks and shear bands are modeled in this setting as discontinuities of the displacement field, the so-called strong discontinuities, propagating through the continuum. These discontinuities are embedded into the finite elements through the proper enhancement of the discrete strain field of the element. General elements, like displacement or assumed strain based elements, can be considered in this framework, capturing sharply the kinematics of the discontinuity for all these cases. The local character of the enhancement (local in the sense of defined at the element level, independently for each element) allows the static condensation of the different local parameters considered in the definition of the displacement jumps. All these features lead to an efficient formulation for the modeling of fracture in solids, very easily incorporated in an existing general finite element code due to its modularity. We investigate in this paper the use of this finite element formulation for the special challenges that the dynamic range leads to. Specifically, we consider the modeling of failure mode transitions in ductile materials and crack branching in brittle solids. To illustrate the performance of the proposed formulation, we present a series of numerical simulations of these cases with detailed comparisons with experimental and other numerical results reported in the literature. We conclude that these finite element methods handle well these dynamic problems, still maintaining the aforementioned features of computational efficiency and modularity.

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Section: Introductionmentioning

confidence: 99%

Numerical simulation of dynamic fracture using finite elements with embedded discontinuities

2009

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“…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%

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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“…Local enrichment functions have been used to embed discontinuous strains [6,7], curvatures [8] and displacements [9,10]. Variational Multiscale Method (VMS) [11] fall into this category of methods.…”

Section: Introductionmentioning

confidence: 99%

Multiscale enrichment based on partition of unity

Fish¹,

Yuan²

2004

Numerical Meth Engineering

139

110

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A new Multiscale Enrichment method based on the Partition of Unity (MEPU) method is presented. It is a synthesis of mathematical homogenization theory and the Partition of Unity method. Its primary objective is to extend the range of applicability of mathematical homogenization theory to problems where scale separation may not be possible. MEPU is perfectly suited for enriching the coarse scale continuum descriptions (PDEs) with fine scale features and the quasi-continuum formulations with relevant atomistic data. Numerical results show that it provides a considerable improvement over classical mathematical homogenization theory and quasi-continuum formulations.

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An analysis of strong discontinuities induced by strain-softening in rate-independent inelastic solids

Cited by 757 publications

References 29 publications

Numerical simulation of dynamic fracture using finite elements with embedded discontinuities

Numerical simulation of dynamic fracture using finite elements with embedded discontinuities

Embedded strong discontinuity finite elements for fractured geomaterials with variable friction

Multiscale enrichment based on partition of unity

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