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A new efficient explicit formulation for linear tetrahedral elements non-sensitive to volumetric locking for infinitesimal elasticity and inelasticity. (English) Zbl 1171.74458

Summary: We introduce an innovative formulation for simple linear tetrahedral elements non-sensitive to volumetric locking. Tetrahedral meshes enable to deal with high deformation by using efficient and robust adaptive meshers - while standard explicit formulations based on linear hexahedral elements with reduced integration and hourglassing stabilization cannot be coupled with efficient remeshing procedures. The principle of this anti-locking modification is to impose the volumetric constraints at each node instead of at each integration point, as been done in the averaged nodal pressure formulation proposed by Bonet in 1998. However, the modification made here is material independent: the strain tensor is directly modified before any stress or pressure calculus. The formulation is extended to incompressible elasticity and von Mises incompressible isotropic inelasticity (elastic-visco-plasticity). An infinitesimal strain formulation has been chosen in order to obtain a very simple and thus computational time saving algorithm. This choice can be easily justified taking into account the value of the critical time step in explicit simulations, especially for metal-forming processes. Standard elastic and inelastic benchmarks issued from the literature validate qualitatively and quantitatively this promising formulation for quasi-incompressible deformations cases.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
74B05 Classical linear elasticity
74C05 Small-strain, rate-independent theories of plasticity (including rigid-plastic and elasto-plastic materials)
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[1] Teodorescu, A partly explicit finite element formulation for the forging process, International Journal of Computational Engineering Science 2 (3) pp 425– (2001)
[2] Zienkiewicz, A general algorithm for compressible and incompressible flow-Part I. The split, characteristic-based scheme, International Journal for Numerical Methods in Fluids 20 pp 869– (1995) · Zbl 0837.76043
[3] Zienkiewicz, Triangles and tetrahedra in explicit dynamic codes for solid, International Journal for Numerical Methods in Engineering 43 pp 565– (1998) · Zbl 0939.74073
[4] Rojek, Advances in FE explicit formulation for simulation of metal forming processes, Journal of Materials Processing Technology 119 (1-3) pp 41– (2001)
[5] Rojek, CBS-based stabilization in explicit solid dynamic, International Journal for Numerical Methods in Engineering 66 pp 1547– (2006) · Zbl 1110.74856
[6] Irving, Volume conserving finite element simulations of deformable models, ACM Transactions on Graphics 26 (3) pp 13.1– (2007)
[7] Marti, Mixed discretization procedure for accurate modelling of plastic collapse, International Journal for Numerical and Analytical Methods in Geomechanics 6 pp 129– (1982) · Zbl 0475.73086
[8] Guo, Triangular composite finite elements, International Journal for Numerical Methods in Engineering 47 pp 287– (2000) · Zbl 0985.74068
[9] Thoutireddy, Tetrahedral composite finite elements, International Journal for Numerical Methods in Engineering 53 pp 1337– (2002) · Zbl 1112.74544
[10] De Souza Neto, F-bar-based linear triangles and tetrahedra for finite strain analysis of nearly incompressible solids. Part I: formulation and benchmarking, International Journal for Numerical Methods in Engineering 62 pp 353– (2005) · Zbl 1179.74159
[11] Elguedj, B-bar and F-bar projection methods for nearly incompressible linear and non-linear elasticity and plasticity using high-order NURBS elements, Computational Methods in Applied Mechanics and Engineering 197 pp 2732– (2008)
[12] Bonet, A simple averaged nodal pressure tetrahedral element for incompressible and nearly incompressible dynamic explicit applications, Communications in Numerical Methods in Engineering 14 pp 437– (1998) · Zbl 0906.73060
[13] Bonet, Stability and comparison of different linear tetrahedral formulations for nearly incompressible explicit dynamic applications, International Journal for Numerical Methods in Engineering 50 pp 119– (2001) · Zbl 1082.74547
[14] Joldes GR, Wittek A, Miller K. Improved linear tetrahedral elements for surgical simulations. Proceedings of MICCAI, Copenhagen, vol. 1, 2006; 54-65.
[15] Detournay C, Dzik E. Nodal mixed discretization for tetrahedral elements. Proceedings of the 4th International FLAC Symposium on Numerical Modeling in Geomechanics (Hart and Varona edn), Madrid, 2006; Paper 07-02.
[16] Dohrmann, Node-based uniform strain elements for three-node triangular and four-node tetrahedral meshes, International Journal for Numerical Methods in Engineering 47 pp 1549– (2000) · Zbl 0989.74067
[17] Bonet, An averaged nodal deformation gradient linear tetrahedral element for large strain explicit dynamic applications, Communications in Numerical Methods in Engineering 17 pp 551– (2001) · Zbl 1154.74307
[18] Puso, A stabilized nodally integrated tetrahedral, International Journal for Numerical Methods in Engineering 67 pp 841– (2006) · Zbl 1113.74075
[19] Digonnet H, Coupez T. Object-oriented programming for ’fast-and-easy’ development of parallel applications in forming processes simulation. Proceedings of the 2nd MIT Conference on Computational Fluid and Solid Mechanics, Boston, 2003.
[20] Digonnet H, Silva L, Coupez T. Cimlib: a fully parallel application for numerical simulations based on components assembly. Proceedings of NUMIFORM 2007, Porto, 2007.
[21] Coupez, Parallel meshing and remeshing by repartioning, Applied Mathematical Modelling 25 pp 153– (2000) · Zbl 1076.74551
[22] Simo, Computational Inelasticity (1991)
[23] Gratacos, An integration scheme for Prandtl-Reuss elastoplastic constitutive equations, International Journal for Numerical Methods in Engineering 33 pp 943– (1992) · Zbl 0760.73063
[24] Hallquist O. LS-Dyna3D Theoretical Manual, Livermore Software Technology, 1998.
[25] Hibbitt, ABAQUS/Explicit User’s Manual Version 6.3 (2002)
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