On the enhanced strain technique for elasticity problems

Lovadina, Carlo; Auricchio, Ferdinando

doi:10.1016/s0045-7949(02)00412-1

Cited by 31 publications

(20 citation statements)

References 20 publications

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“…Several different strategies have been proposed to improve this lack of performance, and mainly can be summed up as follows: mixed-enhanced elements that use additional strain fields to augment the compatible strain fields from the simplex interpolations [1][2][3]; pressure stabilization that aims to stabilize the interpolated pressure fields by adding additional stabilization terms [4][5][6]; and average nodal pressures/strains that computes average volumetric strains or strains at nodes based on surrounding triangles or tetrahedrals [7,8]. Of course this list of references is by no means exhaustive.…”

Section: Introductionmentioning

confidence: 99%

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: Introductionmentioning

confidence: 99%

Linear tetrahedral element for problems of plastic deformation

2015

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“…Mixed-enhanced elements: Using additional strain fields to augment the compatible strain fields from the simplex interpolations along with a linearly interpolated pressure field to avoid volumetric locking in References [3][4][5].…”

Section: Introductionmentioning

confidence: 99%

A stabilized nodally integrated tetrahedral

Puso

Solberg

2006

Numerical Meth Engineering

186

201

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SUMMARYA stabilized, nodally integrated linear tetrahedral is formulated and analysed. It is well known that linear tetrahedral elements perform poorly in problems with plasticity, nearly incompressible materials, and acute bending. For a variety of reasons, low-order tetrahedral elements are preferable to quadratic tetrahedral elements; particularly for nonlinear problems. But the severe locking problems of tetrahedrals have forced analysts to employ hexahedral formulations for most nonlinear problems. On the other hand, automatic mesh generation is often not feasible for building many 3D hexahedral meshes. A stabilized, nodally integrated linear tetrahedral is developed and shown to perform very well in problems with plasticity, nearly incompressible materials and acute bending. The formulation is analytically and numerically shown to be stable and optimally convergent for the compressible case provided sufficient smoothness of the exact solution u ∈ C 2 ∩ (H 1 ) 3 . Future work may extend the formulation to the incompressible regime and relax the regularity requirements; nonetheless, the results demonstrate that the method is not susceptible to locking and performs quite well in several standard linear and nonlinear benchmarks. Published in

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“…In the literature, the poor performance of simplicial tessellations in large deformation analysis of nearlyincompressible solids has been improved through various techniques such as mixed-enhanced elements [6][7][8], pressure stabilization [9][10][11], composite pressure fields [12][13][14], and average nodal pressure/strains [15][16][17][18][19][20]. The last two approaches are broadly based on the idea of reducing pressure (dilatational) constraints to alleviate volumetric locking.…”

Section: Introductionmentioning

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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On the enhanced strain technique for elasticity problems

Cited by 31 publications

References 20 publications

Linear tetrahedral element for problems of plastic deformation

Linear tetrahedral element for problems of plastic deformation

A stabilized nodally integrated tetrahedral

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

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