Two mixed finite element formulations with area bubble functions for tetrahedral elements

Mahnken, Rolf; Caylak, Ismail; Laschet, Gottfried

doi:10.1016/j.cma.2007.10.007

Cited by 27 publications

(42 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Future work should be directed to applications of the algorithm to real structures, when experimental data are available. Furthermore, we will investigate the influence of low-order finite element formulations with stabilization recently developed in Mahnken and Caylak [57] and Mahnken et al [58]. Additionally, anisotropic effects, the consideration of a large strain theory and consideration of effective properties of functionally graded composites would be challenging aspects for future work.…”

Section: Discussionmentioning

confidence: 98%

Geometry update driven by material forces for simulation of brittle crack growth in functionally graded materials

Mahnken

2008

Numerical Meth Engineering

Self Cite

View full text Add to dashboard Cite

SUMMARYFunctionally graded materials (FGMs) are advanced materials that possess continuously graded properties, such that the growth of cracks is strongly dependent on the gradation of the material. In this work a thermodynamic consistent framework for crack propagation in FGMs is presented, by applying a dissipation inequality to a time-dependent migrating control volume. The direction of crack growth is obtained in terms of material forces as a result of the principle of maximum dissipation. In the numerical implementation a staggered algorithm-deformation update for fixed geometry followed by geometry update for fixed deformation-is employed within each time increment. The geometry update is a result of the incremental crack propagation, which is driven by material forces. The corresponding mesh is generated by combining Delaunay triangulation with local mesh refinement. Furthermore a Newton algorithm is proposed, taking into account mesh transfer of displacements for crack propagation in incremental elasticity. In two numerical examples brittle crack propagation in FGMs is investigated for various directions of strength gradation within the structures.

show abstract

Section: Discussionmentioning

confidence: 98%

Geometry update driven by material forces for simulation of brittle crack growth in functionally graded materials

Mahnken

2008

Numerical Meth Engineering

Self Cite

View full text Add to dashboard Cite

show abstract

“…Here, T 1P1 denotes a linear interpolation for displacements and pressure. The authors show in Mahnken and Caylak [12] and Mahnken et al [27] for element families based on the methods of incompatible modes or enhanced strains in combination with area and volume bubble functions not only the performance of the displacement approximation but also a resulting almost smooth stress field in the quasi-incompressible limit. The results for the clamped plate are depicted in Figure 13.…”

Section: Three-dimensional Clamped Platementioning

confidence: 98%

A modified least‐squares mixed finite element with improved momentum balance

Schwarz

Schröder

Starke

2009

Numerical Meth Engineering

View full text Add to dashboard Cite

SUMMARYThe main goal of this contribution is to provide an improved mixed finite element for quasi-incompressible linear elasticity. Based on a classical least-squares formulation, a modified weak form with displacements and stresses as process variables is derived. This weak form is the basis for a finite element with an advanced fulfillment of the momentum balance and therefore with a better performance. For the continuous approximation of stresses and displacements on the triangular and tetrahedral elements, lowest-order Raviart-Thomas and linear standard Lagrange interpolations can be used. It is shown that coercivity and continuity of the resulting asymmetric bilinear form could be established with respect to appropriate norms. Further on, details about the implementation of the least-squares mixed finite elements are given and some numerical examples are presented in order to demonstrate the performance of the proposed formulation.

show abstract

“…(7) is exploited for verification of the patch test. For specific explanation please see [18,19,32]. …”

Section: Area Bubble Functions For Triangular Elementsmentioning

confidence: 99%

“…Unnecessary repetitions, like the governing equations which do not differ from [18,19,32,31] are not presented here. In the representative examples Cook's membrane problem and a block under central pressure illustrate the performance of the presented approaches in comparison to existing finite element formulations for linear elastic, elasto-plastic and non-linear elastic materials.…”

Section: Introductionmentioning

confidence: 96%

“…A mixed-enhanced formulation using volume bubble functions for the enhanced part is developed in [15] for tetrahedral elements at small and large deformations and an optimization has been presented in [16]. Recent works which also consider volume bubble functions are [17][18][19]. Furthermore, bubble functions could be used for the method of incompatible modes introduced by Wilson et al [20] and is used in [14,21].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Stabilized mixed triangular elements with area bubble functions at small and large deformations

Caylak¹,

Mahnken²

2014

Computers & Structures

Self Cite

View full text Add to dashboard Cite

Two mixed finite element formulations with area bubble functions for tetrahedral elements

Cited by 27 publications

References 17 publications

Geometry update driven by material forces for simulation of brittle crack growth in functionally graded materials

Geometry update driven by material forces for simulation of brittle crack growth in functionally graded materials

A modified least‐squares mixed finite element with improved momentum balance

Stabilized mixed triangular elements with area bubble functions at small and large deformations

Contact Info

Product

Resources

About