A numerical study of strain localization in elasto-thermo-viscoplastic materials using radial basis function networks

Computers, Materials and Continua

Volumn 5, Issue 2, 2007, Pages 129-150

  Le, P ^a   Mai Duy, N ^a   Tran Cong, T ^a   Baker, G ^a  

^a UNIVERSITY OF SOUTHERN QUEENSLAND   (Australia)

Author keywords

Imperfection; RBFN; Shear band; Shear band formation; Strain localization

Indexed keywords

COMPUTER SIMULATION; HYDRODYNAMICS; MAPPING; NUMERICAL METHODS; STRAIN HARDENING; VISCOELASTICITY;

PLASTIC HEATING; SHEAR BAND; SHEAR BAND FORMATION; STRAIN LOCALIZATION;

RADIAL BASIS FUNCTION NETWORKS;

EID: 34249027256     PISSN: 15462218     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (32)

1. Atluri, S.; Shen, S. (2002): The meshless local Petrov-Galerkin (MLPG) method:A simple & less-costly alternative to the finite element and the boundary element methods. CMES: Computer Modeling in Engineering & Sciences, vol. 3, pp. 11-51.
2. Atluri, S. N.; Zhu, T. (1998): A new meshless local Petrov-Galerkin (MLPG) approach in computational mechanics. Comput. Mech., vol. 22, pp. 117-127.
3. Batra, R. C.; Kim, C. H. (1991): Effect of thermal conductivity on the initiation, growth and bandwidth of adiabatic shear bands. International Journal of Engineering Science, vol. 29, pp. 949-960.
4. Batra, R. C.; Zhang, G. M. (2004): Analysis of adiabatic shear bands in elasto-thermoviscoplastic materials by Modified Smooth-Particle Hydrodynamics (SPH) method. Journal of Computational Physics, vol. 201, pp. 172-190.
5. Bayliss, A.; Belytschko, T.; Kulkarni, M.; Lott-Crumpler, D. A. (1994): On the dynamics and the role of imperfections for localization in thermo-viscoplastic materials. Modelling and Simulation in Materials Science and Engineering, vol. 2, pp. 941-964.
6. Hairer, E.; Norsett, S.; Wanner, G. (1987): Solving Ordinary Differential Equations I. Nonstiff Problems. Springer-Verlag.
7. Hairer, E.; Wanner, G. (1996): Solving Ordinary Differential Equations II. Stiff and Differential-Algebraic Problems. Springer-Verlag.
8. Han, Z.; Atluri, S. (2004): A meshless local Petrov-Galerkin (MLPG) approach for 3-diemensional elasto-dynamics. CMC: Computers, Materials and Continua, vol. 1, pp. 129-140.
9. Han, Z. D.; Atluri, S. N. (2003): Trully Meshless Local Petrov-Galerkin (MLPG) Solutions of Traction & Displacement BIEs. CMES: Computer Modeling in Engineering & Sciences, vol. 4, no. 6, pp. 665-678.
10. Han, Z. D.; Liu, H. T.; Rajendran, A. M.; Atluri, S. N. (2006): The Applications of Meshless Local Petrov-Galerkin (MLPG) Approaches in High-Speed Impact, Penetration and Perforation Problems. CMES: Computer Modeling in Engineering & Sciences, vol. 14, no. 2, pp. 119-128.
11. Han, Z. D.; Rajendran, A. M.; Atluri, S. N. (2005): Meshless Local Petrov-Galerkin (MLPG) Approaches for Solving Nonlinear Problems with Large Deformations and Rotations. CMES: Computer Modeling in Engineering & Sciences, vol. 10, no. 1, pp. 1-12.
12. Kansa, E. J. (1990) : Multiquadrics - a scattered data approximation scheme with applications to computational fluid dynamics - II. Solutions to parabolic, hyperbolic and elliptic partial differential equations. Computers & Mathematics with Applications, vol. 19, pp. 147-161.
13. Kansa, E. J.; Power, H.; Fasshauer, G. E.; Ling, L. (2004): A volumetric integral radial basis function method for time-dependent partial differential equations: I formulation. Engineering Analysis with Boundary Elements, vol. 28, pp. 1191-1206.
14. Li, S.; Liu, W. C. (2000): Numerical simulation of Strain localization in inelastic solids using mesh-free method. Internationaljournal for Numerical Methods in Engineering, vol. 48, pp. 1285-1309.
15. Ling, L.; Trummer, M. R. (2004): Multi-quadratic collocation method with integral formulation for boundary layer problems. Computers & Mathematics with Applications, vol. 48, pp. 927-941.
16. Ling, L.; Trummer, M. R. (2006): Adaptive multiquadratic collocation for boundary layer problems. Journal of Computational and Applied Mathematics, vol. 188, pp. 265-282.
17. Madych, W. R.; Nelson, S. A. (1990): Multivariate interpolation and conditionally positive definite functions, II. Mathematics of Computation, vol. 54, pp. 211-230.
18. Mai-Cao, L.; Tran-Cong, T. (2005): A meshless IRBFN-based method for transient problems. CMES: Computer Modeling in Engineering & Sciences, vol. 7, pp. 149-171.
19. Mai-Duy, N. (2005): Solving high order ordinary differential equations with radial basis function networks. International Journal for Numerical Methods in Engineering, vol. 62, pp. 824-852.
20. Mai-Duy, N.; Tanner, R. I. (2005): Solving high order partial differential equations with indirect radial basis function networks. International Journal for Numerical Methods in Engineering, vol. 63, pp. 1636-1654.
21. Mai-Duy, N.; Tran-Cong, T. (2001): Numerical solution of differential equations using multiquadric radial basic function networks. Neural Networks, vol. 14, pp. 185-199.
22. Mai-Duy, N.; Tran-Cong, T. (2003): Approximation of function and its derivatives using radial basis function networks. Applied Mathematical Modeling, vol. 27, pp. 197-220.
23. Mai-Duy, N.; Tran-Cong, T. (2005): An efficient indirect RBFN-based method for numerical solution of PDEs. Numerical Methods for Partial Differetial Equations, vol. 21, pp. 770-790.
24. Mai-Duy, N.; Tran-Cong, T. (2006): Solving biharmonic problems with scattered-point discretization using indirect radial-basis-function networks. Engineering Analysis with Boundary Elements, vol. 30, pp. 77-87.
25. Molinari, A.; Clifton, R. J. (1987): Analytical characterization of shear localization in thermoviscoplastic materials. Journal of Applied Mechanics, vol. 54, pp. 806-812.
26. Rice, J. R.; Rudnicki, J. W. (1980): A note on some features of the theory of localization of deformation. International Journal for Solids Strucrures, vol. 16, pp. 597-605.
27. Sherif, R. A.; Shawki, T. G. (1992): The role of heat conduction during the post-localization regime in dynamic viscoplasticity. Plastic flow and Creep, ASME, vol. AMD-Vol. 135/MD-Vol. 31, pp. 159-173.
28. Tang, T.; Trummer, M. R. (1996): Boundary layer resolving pseudospectral methods for singular pertubation problems. SIAM Journal of Scientific Computing, vol. 17, pp. 430-438.
29. Walter, J. W. (1992): Numerical experiments on adiabatic shear band formation in one dimension. International Journal of Plasticity, vol. 8, pp. 657-693.
30. Wright, T. W. (1990): Adiabatic shear bands. Journal of Applied Mechanics, vol. 43, pp. S196-S200.
31. Wright, T. W. (2002): The physics and mathematics of adiabatic shear bands. Cambridge University Press.
32. Wright, T. W.; Walter, J. W. (1987): On stress collapse in adiabatic shear bands. Journal of Mechanics and Physics of Solids, vol. 35, pp. 701-720.