Strong discontinuities and continuum plasticity models: the strong discontinuity approach

Oliver, J.; Cervera, Miguel; Manzoli, Osvaldo L.

doi:10.1016/s0749-6419(98)00073-4

Cited by 217 publications

(186 citation statements)

References 24 publications

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“…Several authors [22,23,24,25,26,27,28] have found analytical and geometrical solutions for the orientation of the discontinuity bands resulting from elasto-plastic models using di¤erent strategies. All of them seek their solutions after the so-called localization condition, which implies the loss of material ellipticity of the constitutive relation and is shown to be a necessary condition for the appearance of weak discontinuities and localized failure to take place.…”

Section: Orientation Of the Shear Band Discontinuitiesmentioning

confidence: 99%

“…In fact, they can be shown to be necessary conditions for the occurrence of bifurcation and localization of the strain …eld, with bounded stresses and decohesion in the limit case along a localization band (or a regularized strong discontinuity). This is why the term strong discontinuity condition was used in reference [28] for it. However, it applies to localization bands (limited by weak discontinuities) and strong discontinuities alike.…”

Section: Orientation Of the Shear Band Discontinuitiesmentioning

confidence: 99%

See 1 more Smart Citation

Mixed stabilized finite element methods in nonlinear solid mechanics. Part III: Compressible and incompressible plasticity

Cervera

Chiumenti

Benedetti

et al. 2015

Computer Methods in Applied Mechanics and Engineering

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This paper presents the application of a stabilized mixed strain/displacement …nite element formulation for the solution of nonlinear solid mechanics problems involving compressible and incompressible plasticity. The variational multiscale stabilization introduced allows the use of equal order interpolations in a consistent way. Such formulation presents two advantages when compared to the standard, displacement based, irreducible formulation: (a) it provides enhanced rate of convergence for the strain (and stress) …eld and (b) it is able to deal with incompressible situations. The …rst advantage also applies to the comparison with the mixed pressure/displacement formulation. The paper investigates the e¤ect of the improved strain and stress …elds in problems involving strain softening and localization leading to failure, using low order …nite elements with continuous strain and displacement …elds (P 1P 1 triangles or tetrahedra and Q1Q1 quadrilaterals, hexahedra, and triangular prisms) in conjunction with an associative frictional Drucker-Prager plastic model. The performance of the strain/displacement formulation under compressible and nearly incompressible deformation patterns is assessed and compared to a previously proposed pressure/displacement formulation. Benchmark numerical examples show the capacity of the mixed formulation to predict correctly failure mechanisms with localized patterns of strain, virtually free from any dependence of the mesh directional bias. No auxiliary crack tracking technique is necessary.

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Section: Orientation Of the Shear Band Discontinuitiesmentioning

confidence: 99%

Section: Orientation Of the Shear Band Discontinuitiesmentioning

confidence: 99%

Mixed stabilized finite element methods in nonlinear solid mechanics. Part III: Compressible and incompressible plasticity

Cervera

Chiumenti

Benedetti

et al. 2015

Computer Methods in Applied Mechanics and Engineering

Self Cite

View full text Add to dashboard Cite

show abstract

“…A recently developed phenomenological model (Regueiro and Borja, 1999;Borja and Regueiro, 2001) extends the strong discontinuity approach developed by Simo and co-workers (Simo et al, 1993;Simo and Oliver, 1994;Armero andGarikipati, 1995, 1996;Oliver et al, 1999) to pressure sensitive, nonassociative plasticity models. The strong discontinuity approach yields mesh-independent ®nite element solutions without introducing a material length scale and without requiring special mesh alignment strategies.…”

Section: Introductionmentioning

confidence: 97%

Plane strain finite element analysis of pressure sensitive plasticity with strong discontinuity

Regueiro

Borja

2001

International Journal of Solids and Structures

117

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Numerical simulations of localized deformation in solids should capture the structural phenomenon of localization and associated loss of material body strength in a manner independent of spatial discretization. Many regularization techniques have been proposed to address the ill posedness associated with rate-independent softening plasticity that leads to mesh-dependent numerical simulations. One approach to alleviating mesh dependence is the strong discontinuity approach, which represents localized deformation as a slip surface within a plasticity model; a strong discontinuity is a discontinuous displacement ®eld. This approach is used in this paper to formulate a plane strain, pressure sensitive, nonassociative plasticity model with strong discontinuity and to implement the model, along with an enhanced bilinear quadrilateral element, via an assumed enhanced strain method. Numerical examples demonstrate mesh independence of the method for pressure sensitive materials. Ó

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“…More recently, the XFEM [26,27] was introduced as an enrichment of finite elements through the notion of partition of unity. Finally, the strong discontinuity approach [28,29] provides an element formulation that embed the displacement jump in its interior. The implementation of such enrichments requires the use of auxiliary tracking techniques in 2D and 3D.…”

Section: Introductionmentioning

confidence: 99%

3D numerical modelling of twisting cracks under bending and torsion of skew notched beams

Benedetti

Cervera

Chiumenti

2017

Engineering Fracture Mechanics

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The testing of mode III and mixed mode failure is every so often encountered in the dedicated literature of mechanical characterization of brittle and quasi-brittle materials. In this work, the application of the mixed strain displacement ε − u finite element formulation to three examples involving skew notched beams is presented. The use of this FE technology is effective in problems involving localization of strains in softening materials.The objectives of the paper are: (i) to test the mixed formulation in mode III and mixed mode failure and (ii) to present an enhancement in terms of computational time given by the kinematic compatibility between irreducible displacement-based and the mixed strain-displacement elements.Three tests of skew-notched beams are presented: firstly, a three point bending test of a PolyMethyl MethaAcrylate beam; secondly, a torsion test of a plain concrete prismatic beam with square base; finally, a torsion test of a cylindrical beam made of plain concrete as well. To describe the mechanical behavior of the material in the inelastic range, Rankine and Drucker-Prager failure criteria are used in both plasticity and isotropic continuum damage formats.The proposed mixed formulation is capable of yielding results close to the experimental ones in terms of fracture surface, peak load and global loss of carrying capability. In addition, the symmetric secant formulation and the compatibility condition between the standard irreducible method and the strain-displacement one is exploited, resulting in a significant speedup of the computational procedure.

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Strong discontinuities and continuum plasticity models: the strong discontinuity approach

Cited by 217 publications

References 24 publications

Mixed stabilized finite element methods in nonlinear solid mechanics. Part III: Compressible and incompressible plasticity

Mixed stabilized finite element methods in nonlinear solid mechanics. Part III: Compressible and incompressible plasticity

Plane strain finite element analysis of pressure sensitive plasticity with strong discontinuity

3D numerical modelling of twisting cracks under bending and torsion of skew notched beams

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