Summary
A new class of materials called Implicit Standard Materials is proposed. It allows to generalize Fenchel’s inequality, and then to recover normality law for non standard behaviour, in particular for unilateral contact with dry friction and granular materials. In terms of finite element method, an algorithm based on the non linear mathematical programming is used to solve every step of the incremental problem. The numerical applications show the convergence of the method. The significative sensitivity of the solution to the non associativity of the soil flow rule can be quotted.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Ladeveze P., 1985, Sur une famille d’algorithmes en mécanique des structures, Comptes-rendu, Académie des Sciences-Paris. 300. Serie II, n°2, 41–44, 1985.
De Saxcé G., 1992a, The variational inequations for the problem of unilateral contact with friction, Proc. 2ème Congrès National Belge de Mécanique Théorique et Appliquée.
De Saxcé G., Feng Z.Q., 1991. New Inequation and Functional for Contact with Friction: the Implicit Standard material Approach. Mech. of Structures and Machines., Vol. 19, N°3.
De Saxcé G., 1992b, Une généralisation de l’inégalité de Fenchel et ses applications aux lois constitutives, C.R. Acad. Sci. Paris, t. 314, Série II.
Rudnicki J. and Rice J.R., 1975. Conditions for the localization of deformation in pressure-sensitive dilatant materials, J. Mech. Phys. Solid., Vol. 23, pp. 371–390.
De Saxcé G., Bousshine L., 1993, On the extension of limit analysis theorems to the non associated flow rules in soils and to the contact with Coulomb’s friction, Proc. XI, Polish Conference on Computer Methods Mechanics. Vol. 2. pp. 815–822. Kilce (Poland), mai 11–14.
Murtagh B.A.. Sanders M.A.. Minos 5.1 User’s guide. Technical Rapport Sol 83–20R.
De Saxcé G., Berga A., Bousshine L., 1992a. The Implicit Standard Material Approach for Non Associated Plasticity in Soil Mechanics, Proc. Int. Cong. on Num. Meth. in Eng. and Appi. Sciences, Vol. 1, pp. 585–594, Conception (Chile), 16–20 november.
De Saxcé G., Berga A., 1994, Elastoplastique Finite Element Analysis of Soil Problems with Implicit Standard Material Constitutive Laws, Revur Européenne des éléments finis, Vol. 3. N° 2.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1995 Springer Science+Business Media New York
About this chapter
Cite this chapter
Bousshine, L., de Saxcé, G. (1995). Modelization by Finite Elements of Cutting and Punching Problems Using an Algorithm Based on the Implicit Standard Materials, Applied to the Friction. In: Raous, M., Jean, M., Moreau, J.J. (eds) Contact Mechanics. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-1983-6_18
Download citation
DOI: https://doi.org/10.1007/978-1-4615-1983-6_18
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4613-5817-6
Online ISBN: 978-1-4615-1983-6
eBook Packages: Springer Book Archive