Assumed strain nodally integrated hexahedral finite element formulation for elastoplastic applications

Artioli, Edoardo; Castellazzi, Giovanni; Krysl, Petr

doi:10.1002/nme.4723

Cited by 13 publications

(16 citation statements)

References 42 publications

(88 reference statements)

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“…Without going into too much detail on the numerical procedure here adopted (for which purpose the interested reader may refer to [16,31]) the double-step midpoint methods divides the current time interval ½t n ; t nþ1 in two intervals ½t n ; t nþa and ½t nþa ; t nþ1 , or sub-steps, being t nþa 2 ½t n ; t nþ1 the midpoint instant, such that:…”

Section: Elastic-plastic Constitutive Model and Integration Algorithmmentioning

confidence: 99%

“…(29). The elasto-plastic material tangent stiffness D consistent with the algorithm is computed in closed form [16,31]; details are here omitted for conciseness.…”

Section: Elastic-plastic Constitutive Model and Integration Algorithmmentioning

confidence: 99%

“…The element stems from the Nodally Integrated Continuum Element (NICE) formulation [8] and its further extensions [14,15], in particular from the analogous linear hexahedral NICE-H8 formulation which was presented and validated for plasticity problems in [16]. We introduce a de Veubeke straindisplacement functional by eliminating the Lagrange multipliers from the general Hu-Washizu functional.…”

Section: Introductionmentioning

confidence: 99%

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Linear tetrahedral element for problems of plastic deformation

2015

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Linear tetrahedra perform poorly in problems with plasticity, nearly incompressible materials, and in bending. While higher-order tetrahedra can cure or alleviate some of these weaknesses, in many situations low-order tetrahedral elements would be preferable to quadratic tetrahedral elements: e.g. for contact problems or fluid-structure interaction simulations. Therefore, a low-order tetrahedron that would look on the outside as a regular four-node tetrahedron, but that would possess superior accuracy is desirable. An assumed-strain, nodally integrated, four-node tetrahedral element is presented (NICE-T4). Several numerical benchmarks are provided showing its robust performance in conjunction with material nonlinearity in the form of von Mises plasticity. In addition we compare the computational cost of the nodally integrated NICE-T4 with the isoparametric quadratic tetrahedron. Because of the reduced number of quadrature points, the NICE-T4 element is competitive in nonlinear analyses with complex material models.

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Section: Elastic-plastic Constitutive Model and Integration Algorithmmentioning

confidence: 99%

“…(29). The elasto-plastic material tangent stiffness D consistent with the algorithm is computed in closed form [16,31]; details are here omitted for conciseness.…”

Section: Elastic-plastic Constitutive Model and Integration Algorithmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Linear tetrahedral element for problems of plastic deformation

2015

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“…[20] (see (16) therein) and the assumed strain nodal matrix of Ref. [51] (see (18) therein). As can be inferred from (30), the nodal operator applied to J gives its nodal representation as…”

Section: Volume-averaged Nodal Projection Methodsmentioning

confidence: 99%

Improved robustness for nearly-incompressible large deformation meshfree simulations on Delaunay tessellations

Ortiz-Bernardin¹,

Puso²,

Sukumar³

2015

Computer Methods in Applied Mechanics and Engineering

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Artículo de publicación ISIA displacement-based Galerkin meshfree method for large deformation analysis of nearly-incompressible elastic solids is presented. Nodal discretization of the domain is defined by a Delaunay tessellation (three-node triangles and four-node tetrahedra), which is used to form the meshfree basis functions and to numerically integrate the weak form integrals. In the proposed approach for nearly-incompressible solids, a volume-averaged nodal projection operator is constructed to average the dilatational constraint at a node from the displacement field of surrounding nodes. The nodal dilatational constraint is then projected onto the linear approximation space. The displacement field is constructed on the linear space and enriched with bubble-like meshfree basis functions for stability. The new procedure leads to a displacement-based formulation that is similar to F-bar methodologies in finite elements and isogeometric analysis. We adopt maximum-entropy meshfree basis functions, and the performance of the meshfree method is demonstrated on benchmark problems using structured and unstructured background meshes in two and three dimensions. The nonlinear simulations reveal that the proposed methodology provides improved robustness for nearlyincompressible large deformation analysis on Delaunay meshes.Chilean National Fund for Scientific and Technological Development (Fondecyt) 11110389 U.S. National Science Foundation CMMI-133478

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“…The loading was F = 100 N , and the geometry is shown in Figure A. Such a problem has been solved by many authors (see the works of Simo and Rifai and Kasper and Taylor for details) and recently by Hughes et al through a B‐bar or F‐bar projection, by Hauret et al via diamond elements, and by Artioli et al employing assumed strain nodally integrated continuum element formulation for elastoplastic applications. Navas et al presented this problem with the first implementation of the B‐bar method with LME shape functions .…”

Section: Model Validationmentioning

confidence: 99%

Optimal transportation meshfree method in geotechnical engineering problems under large deformation regime

Navas

López‐Querol

et al. 2018

Numerical Meth Engineering

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Summary Meshfree methods have been demonstrated as suitable and strong alternatives to the more standard numerical schemes such as finite elements or finite differences. Moreover, when formulated in a Lagrangian approach, they are appropriate for capturing soil behavior under high‐strain levels. In this paper, the optimal transportation meshfree method has been applied for the first time to geotechnical problems undergoing large deformations. All the features employed in the current methodology (ie, F‐bar, explicit viscoplastic integration, and master‐slave contact) are described and validated separately. Finally, the model is applied to the particular case of shallow foundations by using von Mises and Drucker‐Prager yield criteria to find the load at failure in the. The presented methodology is demonstrated to be robust and accurate when solving this type of problems.

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Assumed strain nodally integrated hexahedral finite element formulation for elastoplastic applications

Cited by 13 publications

References 42 publications

Linear tetrahedral element for problems of plastic deformation

Linear tetrahedral element for problems of plastic deformation

Improved robustness for nearly-incompressible large deformation meshfree simulations on Delaunay tessellations

Optimal transportation meshfree method in geotechnical engineering problems under large deformation regime

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