Benchmarking on bifurcation and localization in J2 plasticity for plane stress and plane strain conditions

Cervera, Miguel; Chiumenti, Michele; Capua, D. Di

doi:10.1016/j.cma.2012.06.002

Cited by 24 publications

(51 citation statements)

References 33 publications

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“…The dimensions of the cylinder are: length h = 1.95 m, external radius r = 0.50 m and thickness t = 0.05 m; the cylinder has a small square perforation in its midplane where stresses concentrate and one or more plastic strain localization helicoidal bands are initiated. For this geometry of the problem and for the actions considered, the stress state is plane; therefore, the localization angles are those in Table 1 ( [11,15,50]). Because of symmetry, only the top half of the cylinder needs to be discretized.…”

Section: Cook's Membrane Compressible and Quasi-incompressible Elastmentioning

confidence: 99%

“…For this loading, the stress state in the walls of the cylinder is of pure shear, with principal stresses of the same value but opposite signs acting at ±45 o with the horizontal plane. According to the analytical results in Table 1 ( [11,15,50]), shear band must form at ±22.5 o with the direction of minor principal stress, that is, at 22.5 o and 67.5 o with the horizontal plane. Both alternative solutions are shown in Figures 25 and 26, respectively.…”

Section: Cook's Membrane Compressible and Quasi-incompressible Elastmentioning

confidence: 99%

“…Differently, Cervera et al [11,15,50] propose an alternative methodology to find analytical solutions for the band orientation. This procedure states the conditions for boundedness of stresses and full decohesion, which combined, are more stringent necessary conditions for the formation of the shear band.…”

Section: Orientation Of the Localization Bandmentioning

confidence: 99%

“…Figure 24 shows three different views of the shear bands formed. The solution consists of two symmetrical helicoidal bands that start at the perforation and progress towards the free end of the cylinder ±45 o with the horizontal plane, which is the direction of the minor principal stress ( [11,15,50]). The numerical solution coincides exactly with the analytical prediction.…”

Section: Cook's Membrane Compressible and Quasi-incompressible Elastmentioning

confidence: 99%

“…The proferred schemes go from the introduction of localization limiters, regularized and non-local constitutive models to the more recent phase-field simulations. In references [8,9,11,25] mixed pressure-displacement u − p finite element (FE) formulations, free from volumetric locking, were shown to tackle problems involving isochoric J2 plasticity with strain softening and localization, obtaining non spuriously mesh dependent results. In these works, deviatoric strains are calculated by differentiation of the displacement field; hence, the rate of convergence for the angular distortions is the same as in the irreducible formulation.…”

Section: Introductionmentioning

confidence: 99%

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Explicit mixed strain–displacement finite elements for compressible and quasi-incompressible elasticity and plasticity

et al. 2016

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K: explicit mixed finite elements, stabilization, incompressibility, plasticity, strain softening, strain localization, mesh independence. AbstractThis paper presents an explicit mixed finite element formulation to address compressible and quasi-incompressible problems in elasticity and plasticity. This implies that the numerical solution only involves diagonal systems of equations. The formulation uses independent and equal interpolation of displacements and strains, stabilized by variational subscales (VMS). A displacement sub-scale is introduced in order to stabilize the mean-stress field. Compared to the standard irreducible formulation, the proposed mixed formulation yields improved strain and stress fields. The paper investigates the effect of this enhancement on the accuracy in problems involving strain softening and localization leading to failure, using low order finite elements with linear continuous strain and displacement fields (P 1P 1 triangles in 2D and tetrahedra in 3D) in conjunction with associative frictional Mohr-Coulomb and Drucker-Prager plastic models. The performance of the strain/displacement formulation under compressible and nearly incompressible deformation patterns is assessed and compared to analytical solutions for plane stress and plane strain situations. 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: Cook's Membrane Compressible and Quasi-incompressible Elastmentioning

confidence: 99%

Section: Cook's Membrane Compressible and Quasi-incompressible Elastmentioning

confidence: 99%

Section: Orientation Of the Localization Bandmentioning

confidence: 99%

Section: Cook's Membrane Compressible and Quasi-incompressible Elastmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Explicit mixed strain–displacement finite elements for compressible and quasi-incompressible elasticity and plasticity

et al. 2016

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Particle swarm optimization for numerical bifurcation analysis in computational inelasticity

Lai

Chen

2016

Num Anal Meth Geomechanics

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Summary An efficient and robust algorithm to numerically detect material instability or bifurcation is of great importance to the understanding and simulation of material failure in computational and applied mechanics. In this work, an intelligence optimizer, termed the particle swarm optimization, is introduced to the numerical solution of material bifurcation problem consisting of finding the bifurcation time as well as the corresponding bifurcation directions. The detection of material bifurcation is approached as a constrained minimization problem where the determinant of the acoustic tensor is minimized. The performance of the particle swarm optimization method is tested through numerical bifurcation analysis on both small and finite deformation material models in computational inelasticity with increasing complexity. Compared with conventional numerical approaches to detect material bifurcation, the proposed method demonstrates superior performance in terms of both computational efficiency and robustness. Copyright © 2016 John Wiley & Sons, Ltd.

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Three stress-based triangular elements

Rezaiee‐Pajand

Karimipour

2019

Engineering with Computers

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Benchmarking on bifurcation and localization in J2 plasticity for plane stress and plane strain conditions

Cited by 24 publications

References 33 publications

Explicit mixed strain–displacement finite elements for compressible and quasi-incompressible elasticity and plasticity

Explicit mixed strain–displacement finite elements for compressible and quasi-incompressible elasticity and plasticity

Particle swarm optimization for numerical bifurcation analysis in computational inelasticity

Three stress-based triangular elements

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