A stabilized P1/P1 finite element for the mechanical analysis of solid metals
Source abstract
Abstract
The aim of this paper is to propose a stabilized finite element P1/ P1 and to show that it is well suited for the finite-strain analysis of solid metals in the context of large von Mises elasto-viscoplastic or elasto-plastic transformations. The first part of this paper is dedicated to the finite element formulation which is detailed for an elasto-viscoplastic model problem. Then, a new stabilized formulation is proposed for the pressure solution. In the last part, examples are presented to show the relevance of the finite element P1/ P1 developed.
Source: openaire · Quality: candidate unverified · Source record ↗
Research context
OpenAlex topics: Metal Forming Simulation Techniques · Elasticity and Material Modeling · Advanced Numerical Methods in Computational Mathematics
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
References (33)
Show source-provided references
1. Reddy JN, Gartling DK (2000) The finite element method in heat transfer and fluid dynamics. CRC Press
2. Zienkiewicz ZO, Taylor RL (1990) La méthode des éléments finis. AFNOR technique
3. Hughes TJR (2000) The finite element method. Dover, New York
4. Belytschko T, Ong JSJ, Liu WK, Kennedy JM (1984) Hourglass control in linear and nonlinear problems. Comput Methods Appl Mech Eng 43:251–27610.1016/0045-7825(84)90067-7 ↗
5. Simo JC, Rifai MS (1990) A class of mixed assumed strain methods and the method of incompatible modes. Int J Numer Methods Eng 29:1595–163810.1002/nme.1620290802 ↗
6. Kasper EP, Taylor RL (2000) A mixed-enhanced strain method. Part I: geometrically linear problems. Comput Struct 75:237–25010.1016/S0045-7949(99)00134-0 ↗
7. Kasper EP, Taylor RL (2000) A mixed-enhanced strain method. Part II: geometrically nonlinear problems. Comput Struct 75:251–26010.1016/S0045-7949(99)00135-2 ↗
8. Elguedj T, Bazilevs Y, Calo V, Hughes T (2008) B-bar and F-bar projection methods for nearly incompressible linear and non-linear elasticity and plasticity using higher-order nurbs elements. Comput Methods Appl Mech Eng 197:2732–276210.1016/j.cma.2008.01.012 ↗
9. Brezzi F, Fortin M (1991) Mixed and hybrid finite elements methods. Springer series in computational mathematics. Springer, New York10.1007/978-1-4612-3172-1 ↗
10. Al Akhrass D, Bruchon J, Drapier S, Fayolle S (2014) Integrating a logarithmic-strain based hyperelastic formulation into a three-field mixed finite element formulation to deal with incompressibility in finite-strain elastoplasticity. Finite Elem Anal Des 86:61–7010.1016/j.finel.2014.04.004 ↗
11. Bathe KJ (1996) Finite element procedure. Prentice Hall
12. Babuška I (1973) The finite element method with Lagrangien multipliers. Numer Math 20:179–19210.1007/BF01436561 ↗
13. Brezzi F (1974) On the existence, uniqueness and approximation of saddle-point problems arising from Lagrangian multipliers, RAIRO, . Anal Numer R2:129–151
14. Ern A, Guermond J-L (2004) Theory and practice of finite elements. Springer Series in Applied Mathematical Sciences, vol 159. Springer, New York10.1007/978-1-4757-4355-5 ↗
15. Boffi D, Brezzi F, Fortin M (2008) Finite elements for the Stokes problem - Mixed finite elements, compatibility conditions, and applications - Lecture notes in mathematics, vol 1939, pp 45–10010.1007/978-3-540-78319-0_2 ↗
16. Duvaut G, Lions J-L (1972) Les équations en mécanique et en physique, Dunod, Paris. in french
17. Agelet de Saracibar C, Chiumenti M, Valverde Q, Cervera M (2006) On the orthogonal subgrid scale pressure stabilization of finite deformation J2 plasticity. Comput Methods Appl Mech Eng 195:1224–125110.1016/j.cma.2005.04.007 ↗
18. Agelet, de Saracibar C, Chiumenti M, Cervera M, Dialami N, Seret A (2014) Computational modeling and sub-grid scale stabilization of incompressibility and convection in the numerical simulation of friction stir welding processes. Arch Comput Meth Eng 21:3–3710.1007/s11831-014-9094-z ↗
19. Cervera M, Chiumenti M, Benedetti L, Codina R (2015) Mixed stabilized finite element methods in nonlinear solid mechanics. Part III: Compressible and incompressible plasticity. Comput Methods Appl Mech Eng 285:752–77510.1016/j.cma.2014.11.040 ↗
20. Belytschko T, Liu WK, Moran B (2000) Nonlinear finite elements for continua and structures. Wiley
21. Wagoner RH, Chenot J-L (2001) Metal forming analysis. Cambridge University Press10.1017/CBO9781139087070 ↗
22. Sani RL, Gresho PM, Lee RL, Griffiths DF (1981) The cause cure of the spurious pressures generated by certain FEM solutions of the incompressible Navier-Stokes equations - I. Int J Numer Methods Fluids 1(1):17–4310.1002/fld.1650010104 ↗
23. Sani RL, Gresho PM, Lee RL, Griffiths DF, Engelman M (1981) The cause cure of the spurious pressures generated by certain FEM solutions of the incompressible Navier-Stokes equations - II. Int J Numer Methods Fluids 1(2):171–20410.1002/fld.1650010206 ↗
24. Roger P (1988) Simple C0 approximations for the computation of incompressible flows. Comput Methods Appl Mech Eng 68:205–22710.1016/0045-7825(88)90116-8 ↗
25. SYSWELD User’s manual (2014) ESI Group
26. Brezzi F, Pitkaranta J (1984) On the stabilization of finite element approximations of the stokes equations. In: Hackbush W. (ed) Efficient solutions of elliptic systems. Notes on numerical fluid mechanics, vol 10, Braunschweig, Wiesbaden10.1007/978-3-663-14169-3_2 ↗
27. Marchal JM, Crochet MJ (1987) A new mixed finite element for calculating viscoelastic flow. J Non-Newtonian Fluid Mech 26:77–11410.1016/0377-0257(87)85048-6 ↗
28. Brooks AN, Hughes TJR (1982) Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations. Comput Methods Appl Mech Eng 32:199–25910.1016/0045-7825(82)90071-8 ↗
29. Feulvarch E, Bergheau JM, Leblond JB (2009) An implicit finite element algorithm for the simulation of diffusion with phase changes in solids. Int J Numer Methods Eng 78:1492–151210.1002/nme.2537 ↗
30. Avriel M (2003) Nonlinear programming: analysis and methods. Dover. ISBN 0-486-43227-0
31. Cottier E, Anglade P, Brosse A, Feulvarch E Fast 3D simulation of a single-pass steel girth weld. Mechanics and Industry, in press10.1051/meca/2015074 ↗
32. Karlsson L, Lindgren LE (1991) Modeling of casting, welding and advanced solidification processes V:187–202
33. Feulvarch E, Robin V, Bergheau JM (2011) Thermometallurgical and mechanical modelling of welding application to multipass dissimilar metal girth welds. Sci Technol Weld Join 16:221–23110.1179/1362171811Y.0000000008 ↗