Solution parallelization of softening plasticity problems

Ya. M. Klebanov ; I. E. Adeyanov

Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 2 (2011), pp. 89-100.

Résumé

Parallelization of deformation-damage coupling boundary value problem solution is considered. In definition the equations of the strength we used the principle of equivalence of deformations in a real and relatively undamaged structures. Principle of real and hypothetical undamaged structure strain equivalence is applied. An iterative procedure, which feature is successive solutions of plasticity and damage problems at each iteration step, is proposed. The approach to parallelization of softening plasticity boundary value problem solution is based on the conception of generalized nonlinear structural models and on the method of decomposition.

Détail

Keywords: parallelization, generalized model, softening plasticity, boundary value problem, nonlocal plastic strain.
Mots-clés : structure, decomposition

Bibliographie

[1] Klebanov I. M., Davydov A. N., A non-linear domain decomposition method, http://ansys.net/collection/746

[2] Klebanov I. M., Davydov A. N., “A parallel computational method in steady power-law creep”, Int. J. Num. Methods Eng., 50:8 (2001), 1825–1840 | DOI | Zbl

[3] Yagawa G., Yoshioka A., Soneda S., “A parallel finite element method with a supercomputer network”, Comput. Struct., 47:3 (1993), 407–418 | DOI | Zbl

[4] Asta M., Fischera R., Labartab J., Manza H., “Run-time parallelization of large FEM analyses with PERMAS”, Adv. Eng. Soft., 29:3–6 (1998), 241–248 | DOI

[5] Aifantis E. C., “On the role of gradients in the localization of deformation and fracture”, Int. J. Eng. Sci., 30:10 (1992), 1279–1300 | DOI

[6] Lemaître J., A course on Damage Mechanics, Springer, Berlin, 1996, 228 pp. | Zbl

[7] Shu J. Y., Barlow C. Y., “Strain gradient effects on microscopic strain field in a metal matrix composite”, Int. J. Plast., 16:5 (2000), 563–591 | DOI | Zbl

[8] Geers M. G. D., de Borst R., Peerlings R. H. J., “Validation and internal length scale determination for a gradient damage model: application to short glass-fibre-reinforced polypropylene”, Int. J. Solids Struct., 36:17 (1999), 2557–2584 | DOI

[9] Nygårds M., Gudmundson P., “Numerical investigation of the effect of non-local plasticity on surface roughening in metals”, Eur. J. Mech., A, Solids, 23:5 (2004), 753–762 | DOI | Zbl

[10] Baaser H., Tvergaard V., “A new algorithmic approach treating nonlocal effects at finite rate-independent deformation using the Rousselier damage model”, Comput. Methods Appl. Mech. Eng., 192:1–2 (2003), 107–124 | DOI | Zbl

[11] Botta A. S., Venturini W. S., Benallal A., “BEM applied to damage models emphasizing localization and associated regularization techniques”, Eng. Anal. Bound. Elem., 29:8 (2005), 814–827 | DOI | Zbl

[12] Kachanov L.M., Theory of creep, Fizmatgiz, Moscow, 1960, 390 pp.

[13] Boyle J. T., Spence J., Stress analysis for creep, Butterworth, London, 1983, 284 pp.

[14] Klebanov Ya. M., Samarin Yu. P., “Nested power dissipation surface in forces and displacements space for the steady creep of heterogeneous and anisotropic bodies”, Mekhanika Tverdogo Tela, 1997, no. 6, 121–125

[15] Klebanov Ya. M., Davydov A. N., “Parallel solution of nonlinear problems with an arbitrary deformation diagram”, Vestn. Samar. Gos. Tekhn. Un-ta. Ser. Tekhn. Nauki, 2000, no. 10, 21–25

[16] de Borst R., Pamin J., Geers M. G. D., “On coupled gradient-dependent plasticity and damage theories with a view to localization analysis”, Eur. J. Mech., A, Solids, 18:6 (1999), 939–962 | DOI | Zbl