Linear tetrahedral element for problems of plastic deformation

Castellazzi, Giovanni; Artioli, Edoardo; Krysl, Petr

doi:10.1007/s11012-015-0185-1

Cited by 4 publications

(6 citation statements)

References 35 publications

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“…9 and agrees with the data reported in Ref. [16]. The data also corresponds to the original problem by Zienkiewicz, Vallippan and King [52], who show results for the plastic region in the perfectly-plastic case.…”

Section: Drilled Plate Under Tensionsupporting

confidence: 91%

“…We now consider an elastic perfectly-plastic benchmark which was employed by Castellazzi, Artioli and Krysl [16] to validate their nodally integrated (element patch-based) NICE-T4 element. This is especially relevant, since their nodally integrated elements entail fewer degreesof-freedom than the present element but produce denser Jacobian matrices.…”

Section: Drilled Plate Under Tensionmentioning

confidence: 99%

“…2 in Ref. [16]. Krysl's group elements exhibit high performance in demanding problems, such as incompressible and bending-dominated problems.…”

Section: Drilled Plate Under Tensionmentioning

confidence: 99%

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A continuous-stress tetrahedron for finite strain problems

Areias

Rabczuk

Carapau

et al. 2019

Finite Elements in Analysis and Design

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A finite-strain tetrahedron with continuous stresses is proposed and analyzed. The complete stress tensor is now a nodal tensor degree-of-freedom, in addition to displacement. Specifically, stress conjugate to the relative Green-Lagrange strain is used within the framework of the Hellinger-Reissner variational principle. This is an extension of the Dunham and Pister element to arbitrary constitutive laws and finite strain. To avoid the excessive continuity shortcoming, outer faces can have null stress vectors. The resulting formulation is related to the nonlocal approaches popularized as smoothed finite element formulations. In contrast with smoothed formulations, the interpolation and integration domain is retained. Sparsity is also identical to the classical mixed formulations. When compared with variational multiscale methods, there are no parameters. Very high accuracy is obtained for four-node tetrahedra with incompressibility and bending benchmarks being successfully solved. Although the ad-hoc factor is removed and performance is highly competitive, computational cost is high, as each tetrahedron has 36 degrees-of-freedom. Besides the inf-sup test, four benchmark examples are adopted, with exceptional results in bending and compression with finite strains.

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Section: Drilled Plate Under Tensionsupporting

confidence: 91%

Section: Drilled Plate Under Tensionmentioning

confidence: 99%

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A continuous-stress tetrahedron for finite strain problems

Areias

Rabczuk

Carapau

et al. 2019

Finite Elements in Analysis and Design

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“…In the selection of this element type, studies in the literature that presents the suitability of the use of these elements for meshing complex geometries and plastic analysis were considered. 21,22 At the sternum-closure material contact surfaces, the mesh is refined to improve accuracy of computations. The mesh quality was checked considering the ''skewness'' parameter which determines how close to ideal (i.e.…”

Section: Methodsmentioning

confidence: 99%

Evaluation of sternum closure methods by means of a nonlinear finite element analysis

Orhan

Ozyazicioglu

2019

Proc Inst Mech Eng H

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The main purpose of this study is to develop a validated three-dimensional finite element model of sternum closure techniques. For this aim, the finite element method analysis results of three closure methods were compared with experimental test results. Also, three more closure techniques are simulated numerically to study the effect of the number of wires used in the manubrium and xiphoid regions. A three-dimensional model of polyurethane sternum foam was created based on computed tomography images. Six different closure techniques using steel wire, steel bands and ZipFix bands were modeled on the sternum and transferred into a three-dimensional finite element model. The sternum was modeled as an isotropic bilinear-elasto-plastic material, and nonlinear contact conditions were applied. The models were analyzed under lateral distraction loading, and load-displacement curves were obtained from displacements at the incision line. Allowable loads and stiffness values of the methods were evaluated from these curves. The results showed the importance of the including material as well as geometric nonlinearities in the simulations to obtain realistic results from the numerical analyses. Also, the analyses showed that closures that include steel or ZipFix bands are superior to conventional wiring, and addition of a single wire at the manubrium and xiphoid regions significantly improved the efficiency of the closure techniques.

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“…In their approach, the strain tensor was defined, at each node, as the average of the strain tensors in the various elements containing it (nodal averaging technique). Several authors developed similar approaches for dynamic problems in a large strain with an explicit algorithm [13], and quasistatic elastoplastic problems [14]. Other types of elements were also considered [15,16].…”

Section: Introdutionmentioning

confidence: 99%

A New Nodal-Integration-Based Finite Element Method for the Numerical Simulation of Welding Processes

Jia

Bergheau

Leblond

et al. 2020

Metals

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This paper aims at introducing a new nodal-integration-based finite element method for the numerical calculation of residual stresses induced by welding processes. The main advantage of the proposed method is to be based on first-order tetrahedral meshes, thus greatly facilitating the meshing of complex geometries using currently available meshing tools. In addition, the formulation of the problem avoids any locking phenomena arising from the plastic incompressibility associated with von Mises plasticity and currently encountered with standard 4-node tetrahedral elements. The numerical results generated by the nodal approach are compared to those obtained with more classical simulations using finite elements based on mixed displacement–pressure formulations: 8-node Q1P0 hexahedra (linear displacement, constant pressure) and 4-node P1P1 tetrahedra (linear displacement, linear pressure). The comparisons evidence the efficiency of the nodal approach for the simulation of complex thermal–elastic–plastic problems.

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Linear tetrahedral element for problems of plastic deformation

Cited by 4 publications

References 35 publications

A continuous-stress tetrahedron for finite strain problems

A continuous-stress tetrahedron for finite strain problems

Evaluation of sternum closure methods by means of a nonlinear finite element analysis

A New Nodal-Integration-Based Finite Element Method for the Numerical Simulation of Welding Processes

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