Summary
We study a quasistatic frictionless viscoplastic contact problem with normal compliance and damage for elastic-visco-plastic bodies. The mechanical damage of the material, caused by excessive stress or strain, is described by a damage function whose evolution is modelled by a parabolic inclusion. We provide a variational formulation for the mechanical problem that has a unique solution. We then study a fully discrete scheme for the numerical solution of the problem and derive error estimates for the approximate solutions. Finally, we present some numerical results.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Burguera, M., Viaño, J.M. (1995): Numerical solving of frictionless contact problems in perfect plastic bodies, Comput. Methods Appl. Mech. Engrg. 121, 303–322
Chau, O., Fernández-Garcua, J.R., Han, W., Sofonea, M. (2002): A frictionless contact problem for elastic-viscoplastic materials with normal compliance and damage. Comput. Methods Appl. Mech. Engrg. 191, 5007–5026
Ciarlet, P.G. (1978): The finite element method for elliptic problems. North Holland, Amsterdam
Clément, P. (1975): Approximation by finite element functions using local regularization. Rev. Française Automat. Informat. Recherche Opérationnelle Sér. Rouge Anal. Numer. 9, no. R2, 77–84
Cristescu, N., Suliciu, I. (1982): Viscoplasticity. Martinus Nijhoff, The Hague
Fernández, J.R., Han, W., Sofonea, M., Viaño, J.M. (2001): Variational and numerical analysis of a frictionless contact problem for elastic-viscoplastic materials with internal state variables. Quart. J. Mech. Appl. Math. 54, 501–522
Fernández, J.R., Sofonea, M., Viaño, J.M. (2002): A frictionless contact problem for elastic-viscoplastic materials with normal compliance: numerical analysis and computational experiments. Numer. Math. 90, 689–719
Frémond, M., Kuttler, K.L., Nedjar, B., Shillor, M. (1998): One-dimensional models of damage. Adv. Math. Sci. Appl. 8, 541–570
Frémond, M., Kuttler, K. L., Shillor, M. (1998): Existence and uniqueness of solutions for a dynamic one-dimensional damage model. J. Math. Anal. Appl. 229, 271–294
Han, W., Sofonea, M. (2000): Numerical analysis of a frictionless contact problem for elastic-viscoplastic materials. Comput. Methods Appl. Mech. Engrg. 190, 179–191
Han, W., Shillor, M., Sofonea, M. (2001): Variational and numerical analysis of a quasistatic viscoelastic problem with normal compliance, friction and damage. J. Comput. Appl. Math. 137, 377–398
Ionescu, I.R., Sofonea, M. (1993): Functional and numerical methods in viscoplasticity. Oxford University Press, Oxford
Martins, J.T., Oden, J.T. (1987): Existence and uniqueness results for dynamic contact problems with nonlinear normal and friction interface laws. Nonlinear Anal. 11, 407–428
Rochdi, M., Shillor, M., Sofonea, M. (1998): Quasistatic viscoelastic contact with normal compliance and friction. J. Elasticity 51, 105–126
Rochdi, M., Shillor, M., Sofonea, M. (2000): Analysis of a quasistatic viscoelastic problem with friction and damage. Adv. Math. Sci. Appl. 10, 173–189
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Italia
About this paper
Cite this paper
Chau, O., Fernández, J.R., Han, W., Sofonea, M. (2003). Numerical analysis of a contact problem for elastic-visco-plastic materials with damage. In: Brezzi, F., Buffa, A., Corsaro, S., Murli, A. (eds) Numerical Mathematics and Advanced Applications. Springer, Milano. https://doi.org/10.1007/978-88-470-2089-4_31
Download citation
DOI: https://doi.org/10.1007/978-88-470-2089-4_31
Publisher Name: Springer, Milano
Print ISBN: 978-88-470-2167-9
Online ISBN: 978-88-470-2089-4
eBook Packages: Springer Book Archive