Patch based recovery in finite element elastoplastic analysis

Daghia, Fédérica; Miranda, Stefano de; Ubertini, Francesco

doi:10.1007/s00466-013-0847-6

Cited by 9 publications

(8 citation statements)

References 26 publications

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“…This paper presents an approach consisting in using 3D computations with a reduced number (namely, one) of elements through the thickness and a layerwise integration rule, which is then post-processed in order to obtain an accurate 3D stress state. The post-processing relies on the integration of the equilibrium equations (such as in the recovery techniques proposed in [16,20,21,22,23,24,25]) to compute the stresses through the thickness from the in-plane ones. This allows to drastically reduce the computational time compared to the 3D layerwise approach as the number of degrees of freedom is significantly decreased.…”

Section: Introductionmentioning

confidence: 99%

A cost-effective isogeometric approach for composite plates based on a stress recovery procedure

Dufour

Antolín

Sangalli

et al. 2018

Composites Part B: Engineering

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This paper introduces a cost-effective strategy to simulate the behavior of laminated plates by means of isogeometric 3D solid elements. Exploiting the high continuity of spline functions and their properties, a proper out-ofplane stress state is recovered from a coarse displacement solution using a post-processing step based on the enforcement of equilibrium in strong form.Appealing results are obtained and the method is shown to be particularly effective on slender composite stacks with a large number of layers.

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Section: Introductionmentioning

confidence: 99%

A cost-effective isogeometric approach for composite plates based on a stress recovery procedure

Dufour

Antolín

Sangalli

et al. 2018

Composites Part B: Engineering

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“…Additionally, although the procedure has been developed and presented for two‐dimensional elasticity problems, thanks to its simple and clear variational background, it can be easily adopted to three‐dimensional cases as well as inelastic problems …”

Section: Recovery By Compatibility In Patchesmentioning

confidence: 99%

An equilibrium‐based stress recovery procedure for the VEM

Artioli

Miranda

Lovadina

et al. 2018

Numerical Meth Engineering

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Summary Within the framework of the displacement‐based virtual element method (VEM), namely, for plane elasticity, an important topic is the development of optimal techniques for the evaluation of the stress field. In fact, in the classical VEM formulation, the same projection operator used to approximate the strain field (and then evaluate the stiffness matrix) is employed to recover, via constitutive law, the stress field. Considering a first‐order formulation, strains are locally mapped onto constant functions, and stresses are piecewise constant. However, the virtual displacements might engender more complex strain fields for polygons, which are not triangles. This leads to an undesirable loss of information with respect to the underlying virtual stress field. The recovery by compatibility in patches, originally proposed for finite element schemes, is here extended to VEM, aiming at mitigating such an effect. Stresses are recovered by minimizing the complementary energy of patches of elements over an assumed set of equilibrated stress modes. The procedure is simple, efficient, and can be readily implemented in existing codes. Numerical tests confirm the good performance of the proposed technique in terms of accuracy and indicate an increase of convergence rate with respect to the classical approach in many cases.

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“…A perforated strip in uniaxial tension under plane stress condition is considered. This problem is a popular benchmark used to assess the precision and the effectiveness of the numerical technique . The perforated plate is assumed to have the following material properties: Young's modulus, E = 7000 Kg/mm 2 , Poisson's ratio, ν = 0.2; and yield stress, σ y = 24.3 Kg/mm 2 .…”

Section: Numerical Examplesmentioning

confidence: 99%

“…If the trial solution(40) is plastically admissible, such that † TR nC˛ 6 y;0 C H iso TR nC˛, the state variables at t nC˛a re updated with the trial ones . 1 D 0/, otherwise, a plastic correction .…”

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confidence: 99%

Assumed strain nodally integrated hexahedral finite element formulation for elastoplastic applications

Artioli

Castellazzi

Krysl

2014

Numerical Meth Engineering

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In this work, a linear hexahedral element based on an assumed strain finite element technique is presented for the solution of plasticity problems. The element stems from the Nodally Integrated Continuum Element (NICE) formulation and its extensions. Assumed gradient operators are derived via nodal integration from the kinematic-weighted residual; the degrees of freedom are only the displacements at the nodes. The adopted constitutive model is the classical associative von Mises plasticity model with isotropic and kinematic hardening; in particular, a double-step midpoint integration algorithm is adopted for the integration and solution of the relevant nonlinear evolution equations. Efficiency of the proposed method is assessed through simple benchmark problems and comparison with reference solutions

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Patch based recovery in finite element elastoplastic analysis

Cited by 9 publications

References 26 publications

A cost-effective isogeometric approach for composite plates based on a stress recovery procedure

A cost-effective isogeometric approach for composite plates based on a stress recovery procedure

An equilibrium‐based stress recovery procedure for the VEM

Assumed strain nodally integrated hexahedral finite element formulation for elastoplastic applications

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