zbMATH — the first resource for mathematics

A simple average nodal pressure tetrahedral element for incompressible and nearly incompressible dynamic explicit applications. (English) Zbl 0906.73060
Summary: We present a linear tetrahedron element that can be used in explicit dynamics applications involving nearly incompressible materials or incompressible materials modelled using a penalty formulation. The element prevents volumetric locking by defining nodal volumes and evaluating average nodal pressures in terms of these volumes. Two well-known examples relating to the impact of elastoplastic bars are used to demonstrate the ability of the element to model large isochoric strains without locking.

74S05 Finite element methods applied to problems in solid mechanics
74M20 Impact in solid mechanics
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
74H99 Dynamical problems in solid mechanics
Full Text: DOI
[1] Goudreau, Recent developments in large scale Lagrangian hydrocodes, Comput. Methods Appl. Mech. Eng. 33 (1982) · Zbl 0493.73072 · doi:10.1016/0045-7825(82)90129-3
[2] Belytschko, On computational methods for crash-worthiness, Comput. Struct. 42 (1992) · doi:10.1016/0045-7949(92)90211-H
[3] Hallquist, LS-DYNA3D Theoretical Manual (1991)
[4] M. Kleinberger Application of finite element techniques to the study of cervical spine mechanics 1993
[5] A. J. Burton Explicit large strain dynamic finite element analysis with applications to human body impact problems 1996
[6] Weatherill, Efficient three-dimensional Delaunay triangulation with automatic point creation and imposed boundary constraints, Int. j. num. methods eng. 37 pp 2005– (1996) · Zbl 0806.76073 · doi:10.1002/nme.1620371203
[7] Hughes, A new finite element formulation for computational fluid dynamics V. Circumventing the Babuska-Brezzi condition, Comput. Methods Appl. Mech. Eng. 59 pp 85– (1986) · Zbl 0622.76077 · doi:10.1016/0045-7825(86)90025-3
[8] Zienkiewicz, Incompressibility without tears - How to avoid the restrictions of the mixed formulation, Int. j. numer. methods eng. 32 pp 1189– (1991) · Zbl 0756.76056 · doi:10.1002/nme.1620320603
[9] Bell, Suitability of 3-dimensional finite elements for modelling material incompressibility using exact integration, Commun. numer. methods eng. 9 (1993) · Zbl 0817.73059 · doi:10.1002/cnm.1640090405
[10] Simo, Variational and projection methods for the volume constraint in finite deformation elasto-plasticity, Comput. Methods Appl. Mech. Eng. 51 pp 117– (1985) · Zbl 0554.73036 · doi:10.1016/0045-7825(85)90033-7
[11] Bonet, Nonlinear Continuum Mechanics for Finite Element Analysis (1997) · Zbl 0891.73001
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.