Abstract
Based on the non-smooth nonlinear equations method for modeling three-dimensional elastic frictional contact problems (hereafter called NNEM), the extension to elastoplastic case in which the material nonlinearity is also involved is presented in this paper. Two approaches which combine two methods for solving elastoplastic problem with NNEM are proposed. A Numerical example is given to demonstrate the validation of the approaches.
Similar content being viewed by others
References
Chen GQ, Chen WJ, Feng EM (1994) The convergence of the mathematical programming method for the contact problem and it’s necessary improvement. Comput Struct Mech Appl 11(4): 374–379 (in Chinese)
Chen GQ, Chen WJ, Feng EM (1995) The nonlinear complementary programming method for the three dimensional contact problem. Sci China A 25(11): 1181–1190, (in Chinese)
Chen WJ, Chen GQ, Feng EM (1996) Variational principle with nonlinear complementarity for three-dimensional contact. proble Numer Method &, Sci China A (English edition) 3(5):528–539
Christensen P, Klarbring A, Pang J, Stromberg N (1998) Formulation and comparison of algorithm for frictional contact problems. Int J Numer Methods Eng 42:145–173
Christensen P (2002) A nonsmooth Newton method for elastoplastic problems. Comput Methods Appl Eng 191:1189–1219
Christensen P (2002) A semi-smooth Newton method for elasto-plastic contact problems. Int J Solids Struct 39:2323–2341
Conry T, Seireg A (1971) A mathematical programming method for design of elastic bodies in contact. J Appl Mech Trans ASME 2:387–392
Hung N, Sarce G (1980) Frictionless contact of elastic bodies by finite element method and mathematical programming technique. Comput Struct 11:55–67
Ju S, Stone J, Rowlands R (1995) A new symmetric contact element stiffness matrix for frictional contact problems. Comput Struct 52(2):289–310
Klarbring A (1986) A mathematical programming approach to three-dimensional contact problems with friction. Comput Methods Appl Mech Eng 58:175–200
Klarbring A (1999) Contact, friction, discrete mechanical structures and mathematical programming. In: Wriggers P., Panagiotopoulos P (eds) New developments in contact problems. Springer, Wien NY
Leung A, Chen G, Chen W (1998) Smoothing Newton method for solving two and three-dimensional frictional contact problems. Int J Numer Methods Eng 41:1001–1027
Li XW, Chen WJ (2000) Nonsmooth method for three-dimensional frictional contact problem. J Comput Struct Mech Appl 17:179–182 (in Chinese)
Pietrzak G, Curnier A (1999) Large deformation frictional contact mechanics: continuum formulation and augmented Lagrangian treatment. Comput Methods Appl Mech Eng 177:351–381
Qi LQ, Sun J (1993) A nonsmooth version of Newton’s method. Math Prog 58:353–367
Simo J, Laursen T (1992) Augmented Lagrangian treatment of contact problems involving friction. Comput Struct 42(1):97–116
Zhang HW, Zhong WX, Gu YX (2001) A new method for solution to 3-D elastic-plastic frictional contact problems. Appl Math Mech 22(7):673–681 (in Chinese)
Zhang HW, He SY, Li XS, Wriggers P(2004) A new algorithm for numerical solution of 3D elastoplastic contact problems with orthotropic friction law. Comput Mech 34(1):1–14
Zhong WX (1985) Parametric variational principle and parametric quadratic programming method for elastic contact problem. Comput Struct Mech Appl 2(1):1–9 (in Chinese)
Zhong WX, Sun SM (1988) A finite element method for elasto-plastic structure and contact parametric quadratic programming. Int J Numer Methods Eng 26(6):2723–2738
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Hu, Z.Q., Soh, AK., Chen, W.J. et al. Non-smooth Nonlinear Equations Methods for Solving 3D Elastoplastic Frictional Contact Problems. Comput Mech 39, 849–858 (2007). https://doi.org/10.1007/s00466-006-0074-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00466-006-0074-5