A NonSmooth Contact Dynamics-based multi-domain solver
Code coupling (Xper) and application to fracture
DOI:
https://doi.org/10.13052/EJCM.19.389-417Keywords:
NonSmooth Contact Dynamics, frictional cohesive zone model, domain decomposition method, periodic media, fracture dynamics, heterogeneous mediaAbstract
This paper presents a micromechanical modeling strategy for complex multibody interactions and the associated numerical framework. The strategy rests on a periodic multibody method in the framework of the NonSmooth Contact Dynamics approach of Moreau (1988) extended to classical domain decomposition problems. Many complex interactions can be taken into account: interactions between discrete elements, between discrete or rigid bodies, (quasistatic) contact or impact, friction or adhesion, decohesion (cracking), etc. The associated numerical platform, Xper, is composed of three independent libraries with Object Oriented Programming. The ability of this computational approach is illustrated by two examples of fracture in heterogeneous materials.
Downloads
References
Alart P., Barboteu M., Renouf M., « Parallel computational strategies for multicontact problems
: applications to cellular and granular media. », International Journal for Multiscale
Computational Engineering, vol. 1, p. 419-430, 2003.
Alart P., Curnier A., « A mixed formulation for frictional contact problems prone to newton
like solution methods », Computer Methods in Applied Mechanics and Engineering, vol.
, p. 353-375, 1991.
Alfano G., Crisfield M., « Finite element interface models for the delamination analysis of
laminated composites : mechanical and computational issues », International Journal for
Numerical Methods in Engineering, vol. 50, p. 1701-1736, 2001.
Azema E., Radjaï F., Peyroux R., Dubois F., Saussine G., « Vibrational dynamics of confined
granular materials », Physical Review E, vol. 74, n° 3, p. 031302, 2006.
Balourdet M., Bernaudat C., Basini V., Hourdequin N., « The PROMETRA program : Assessment
of mechanical properties of Zircaloy-4 fuel properties during a RIA. », Transactions of
the 15th International Conference on Structural Mechanics in Reactor Technology, Seoul,
Korea, p. II-485-492, August 15-20, 1999.
Camacho G., Ortiz M., « Computational modelling of impact damage in brittle materials »,
International Journal of Solids and Structures, vol. 33, p. 2899-2938, 1996.
Cazalis B., Bernaudat C., Yvon P., Desquines J., Poussard C., Averty X., « The PROMETRA
program : a reliable material database for highly irradiated Zircaloy-4, ZirloTM and M5TM
fuel claddings. », 18th International Conference on Structural Mechanics in Reactor Technology,
Beijing, China, p. 383-393, August 7-12, 2005. SMiRT18 - C02_1.
CECILL, More information on the web site : http ://www.cecill.info/index.en.html, 2005.
Chetouane B., Dubois F., Vinches M., Bohatier C., « NSCD discrete element method for modeling
masonry structures », International Journal for Numerical Methods in Engineering,
vol. 64, p. 65-94, 2005.
De Saxcé G., Feng Z.-Q., « New inequality and functional for contact with friction : the implicit
standard material approach », Mechanics of Structures and Machines, vol. 19, p. 301-325,
Dodds J., Lopez L., « Substructuring in linear and nonlinear analysis », International Journal
of Numerical Methods in Engineering, vol. 15, p. 583-597, 1980.
Dubois F., JeanM., « Une plateforme de développement dédiée à la modélisation des problèmes
d’interaction », in M. Potier-Ferry, M. Bonnet, A. Bignonnet (eds), 6ème colloque national
en calcul de structures, vol. 1, Giens, p. 111-118, 2003.
Dureisseix D., Farhat C., « A numerically scalable domain decomposition method for the solution
of frictionless contact problems », International Journal for Numerical Methods in
Engineering, vol. 50, p. 2643-2666, 2001.
Fremond M., « Adhérence des solides. », Journal de Mécanique Théorique et Appliquée, vol.
, n° 3, p. 383-407, 1987.
Glowinski R., Le Tallec P., « Augmented Lagrangian interpretation of the non-overlapping
Schartz alternating method », Domain Decomposition method SIAM, Philadelphia, USA,
p. 224-231, 1990.
Gravouil A., Combescure A., « A multi-time-step explicit-implicit method for non-linear structural
dynamics », International Journal for Numerical Methods in Engineering, vol. 50,
p. 199-225, 2001.
He M. Y., Hutchinson J. W., « Crack deflection at an interface between dissimilar elastic materials
», International Journal of Solids and Structures, vol. 25, p. 1053-1067, 1989.
Herry B., Valentin L. D., Combescure A., « An approch to the connection between subdomains
with non-matching meshes for transient mechanical analysis », International Journal for
Numerical Methods in Ingineering, vol. 55, p. 973-1003, 2002.
Iceta D., Alart P., Dureisseix D., « A multilevel domain decomposition solver suited to nonsmoooth
mechanical problems », in M. Bercovier, M. Gander, R. Kornhuber, O. Widlund
(eds), Lecture notes in Computational Science and Engineering, vol. 70, Springer Verlag,
p. 113-120, 2009.
Jean M., « The non-smooth contact dynamics method », Computer Methods in Applied Mechanics
and Engineering, vol. 177, p. 235-257, 1999.
Jean M., Acary V., Monerie Y., « Non-smooth contact dynamics approach of cohesive materials
», Phil. Trans. R. Soc. Lond., vol. A359, p. 2497-2518, 2001.
LMGC90, Web site : http ://www.lmgc.univ-montp2.fr/dubois/LMGC90/, 2009.
Magoules F., Roux F., « Lagrangian formulation of domain decomposition methods :A unified
theory », Applied Mathematical Modelling, vol. 30, p. 593-615, 2006.
Martin E., Peters P., Leguillon D., Quenisset J., « Conditions for matrix crack deflection at an
interface in ceramic matrix composites », Materials Science and Engineering, vol. A250,
p. 291-302, 1998.
Martin R. C., « The Liskov Substitution Principle », C++ Report, 1996.
Martin R. C., Agile Software Development. Principles, Patterns and Practices, Alan Apt Series,
Prentice Hall, Pearson Education, Inc. Upper Saddle Reaver, New Jersey 07458., 2003.
Meyer B., Object-Oriented Software Construction, second edn, Prentice Hall PTR, 1997.
Michel J.-C., Suquet P., « An analytical and numerical study of the overall behaviour of metalmarix
composites », Modelling Simulation in Materials Science and Engineering, vol. 2,
p. 637-658, 1994.
Moreau J.-J., « Unilateral contact and dry friction in finite freedom dynamics », in J.-J.Moreau,
P. Panagiotopoulos (eds), Non Smooth Mechanics and Applications, vol. 302 of CISM -
Courses and Lectures, Springer, Vienna, p. 1-82, 1988.
Nineb S., Alart P., Dureisseix D., « Domain decomposition approach for non-smooth discrete
problems, example of a tensegrity structure », Computers and Structures, vol. 85, p. 499-
, 2007.
OrtizM., Stainier L., « The variational formulation of viscoplastic constitutive updates », Computer
methods in applied mechanics and engineering, vol. 171, p. 419-444, 1999.
PELICANS,Web site : https ://gforge.irsn.fr/gf/project/pelicans/, 2009.
Pelissou C., Baccou J., Monerie Y., Perales F., « Determination of the size of the representative
volume element for random quasi-bittle composites », International Journal of Solids and
Structures, 2009. In Press.
Perales F., Bourgeois S., Chrysochoos A., Monerie Y., « Two field multibody method for periodic
homogenization in fracture mechanics of nonlinear heterogeneous materials », Engineering
Fracture Mechanics, vol. 75, p. 3378-3398, 2008.
Perales F.,Monerie Y., Chrysochoos A., « Nonsmooth fracture dynamics of functionally graded
materials », in J. Cirne, R. Dormeval, et al. (eds), 8th International Conference on Mehanical
and Physical Behaviour ofMaterials under Dynamic Loading, vol. 134, EURODYMAT,
Journal de Physique IV, Dijon, France, p. 367-372, sep, 2006.
Raous M., Cangémi L., Cocu M., « A consistent model coupling adhesion, friction and unilateral
contact », Computer Methods in Applied Mechanics and Engineering, vol. 177, n° 3–4,
p. 383-399, 1999.
Raous M., Monerie Y., « Unilateral contact, friction and adhesion : 3D crack in composite
material », in J. Martins, M. Monteiro Marques (eds), 3d Contact Mechanics International
Symposium, Collection Solid Mechanics and its Applications, Kluwer, Peniche (Portugal),
p. 333-346, 17-21 june, 2001.
Raous M., Monerie Y., « Unilateral contact, friction and adhesion : 3D cracks in composite
materials », in J. Martins, M. M. Marques (eds), Collection Solid Mechanics and its Applications,
Contact Mechanics, Kluwer, vol. 302 of CISM - Courses and Lectures, p. 333-346,
Renouf M., Optimisation numérique et calcul parallèle pour l’étude des milieux divisés bi- et
tridimensionnels, PhD thesis, Université Montpellier II, 2004.
RenoufM., Bonamy D., Dubois F., Alart P., « Steady surface flows in rotating drum : Numerical
Simulation », Physics of Fluids, vol. 17, p. 103303, 2005.
Siegmund T., Fleck N. A., Needleman A., « Dynamic crack growth across an interface », International
Journal of Fracture, vol. 85, p. 381-402, 1997.
Stainier L., Dubois F., Peyroux R., « MatLib, une bibliothèque portable de modèles constitutifs
pour la mécanique non-linéaire des solides : concepts et implémentation », in M. Potier-
Ferry, M. Bonnet, A. Bignonnet (eds), 6ème Colloque National en Calcul des Structures,
vol. 3, Giens, p. 25-32, 2003.
Tvergaard V., « Effect of fibre debonding in a whisker-reinforced metal. », Materials Science
and Engineering, vol. A125, p. 203-213, 1990.
Vincent P.-G.,Modélisation micromécanique de la croissance et de la percolation de pores sous
pression dans une matrice céramique à haute température, PhD thesis, Université d’Aix
Marseille 1 - Provence, 2007. http ://tel.archives-ouvertes.fr/tel-00492215/fr/.
Xu G., Bower A. F., Ortiz M., « The influence of crack trapping on the toughness of fiber
reinforced composites. », Journal of the Mechanics and Physics of Solids, vol. 46, n° 10,
p. 1815-1833, 1998.
Xu X.-P., Needleman A., « Numerical simulations of fast crack growth in brittle solids », Journal
of Mechanics and Physics of Solids, vol. 42, n° 9, p. 1397-1434, 1994.
Yamanaka S., Yamada K., Kurosaki K., Uno M., Takeda K., Anada H., Matsuda T., Kobayashi
S., « Thermal properties of zirconium hydride. », Journal of Nuclear Materials, vol. 294,
p. 94-98, 2001.
Yamanaka S., Yoshioka K., Uno M., Katsura M., Anada H., Matsuda T., Kobayashi S., « Thermal
and mechanical properties of zirconium hydride. », Journal of Alloys and Compounds,
vol. 293–295, p. 23-29, 1999.
Yang Q., Stainier L., Ortiz M., « A variational formulation of the coupled thermo-mechanical
boundary-value problem for general dissipative solids », Journal of Mechanics and Physics
of Solids, vol. 54, p. 401-424, 2006.
Zavattieri P. D., Raghuram P. V., Espinosa H. D., « A computational model of ceramic microstructures
subjected to multi-axial dynamic loading. », Journal of the Mechanics and
Physics of Solids, vol. 49, p. 27-68, 2001.