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Partition of unity-based discontinuous elements for interface phenomena: computational issues. (English) Zbl 1058.74082
Summary: We study numerically the performance of partition of unity-based discontinuous elements. In particular, we show that conventional interface elements and partition of unity-based discontinuous elements share the same structure of stiffness matrix governing the interface behaviour and, under specific circumstances, the same shortcomings (i.e. oscillations in traction profile). The effect of various integration schemes on the interface contribution is studied through the analysis of a linearly elastic notched beam. Further, an eigenvalue analysis of the partition of unity-based discontinuous element is conducted to gain more insight into its mechanical behaviour.

MSC:
74S05 Finite element methods applied to problems in solid mechanics
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
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[1] Goodman, A model for the mechanics of jointed rocks, Journal of the Soil Mechanics and Foundations Division 94 pp 637– (1968)
[2] Saouma, A review of fracture mechanics applied to concrete dams, International Journal of Dam Engineering 1 (1) pp 41– (1990)
[3] Alfano, Finite element interface models for the delamination analysis of laminated composites: mechanical and computational issues, International Journal for Numerical Methods in Engineering 50 (7) pp 1701– (2001) · Zbl 1011.74066
[4] Bittencourt, Quasi-automatic simulation of crack propagation for 2D LEFM problems, Engineering Fracture Mechanics 52 (2) pp 321– (1996)
[5] Simo, An analysis of strong discontinuities induced by strain-softening in rate-independent inelastic solids, Computational Mechanics 12 pp 277– (1993) · Zbl 0783.73024
[6] Melenk, The partition of unity finite element method: basic theory and applications, Computer Methods in Applied Mechanics and Engineering 139 (1-4) pp 289– (1996) · Zbl 0881.65099
[7] Duarte, H-p clouds-an h-p meshless method, Numerical Methods for Partial Differential Equations 12 (6) pp 673– (1996) · Zbl 0869.65069
[8] Moës, A finite element method for crack growth without remeshing, International Journal for Numerical Methods in Engineering 46 (1) pp 131– (1999) · Zbl 0955.74066
[9] Wells, A new method for modelling cohesive cracks using finite elements, International Journal for Numerical Methods in Engineering 50 (12) pp 2667– (2001) · Zbl 1013.74074
[10] Simone, From continuous to discontinuous failure in a gradient-enhanced continuum damage model, Computer Methods in Applied Mechanics and Engineering 192 (41-42) pp 4581– (2003)
[11] Remmers, A cohesive segments method for the simulation of crack growth, Computational Mechanics 31 (1-2) pp 69– (2003) · Zbl 1038.74679
[12] Schellekens, On the numerical integration of interface elements, International Journal for Numerical Methods in Engineering 36 pp 43– (1993) · Zbl 0825.73840
[13] Oden, A new cloud-based hp finite element method, Computer Methods in Applied Mechanics and Engineering 153 (1-2) pp 117– (1998) · Zbl 0956.74062
[14] Rots JG Computational modeling of concrete fracture 1988
[15] Remmers, Solids, Structures and Coupled Problems in Engineering, Proceedings of the Second European Conference on Computational Mechanics 2 pp 906– (2001)
[16] Rots, Computer Aided Analysis and Design of Concrete Structures pp 909– (1990)
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