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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 73
PROCEEDINGS OF THE EIGHTH INTERNATIONAL CONFERENCE ON CIVIL AND STRUCTURAL ENGINEERING COMPUTING
Edited by: B.H.V. Topping
Paper 123

Implicit Integration of Elastoplastic Constitutive Equations of Interface Element

F. Cai and K. Ugai

Department of Civil Engineering, Gunma University, Kiryu, Japan

Full Bibliographic Reference for this paper
F. Cai, K. Ugai, "Implicit Integration of Elastoplastic Constitutive Equations of Interface Element", in B.H.V. Topping, (Editor), "Proceedings of the Eighth International Conference on Civil and Structural Engineering Computing", Civil-Comp Press, Stirlingshire, UK, Paper 123, 2001. doi:10.4203/ccp.73.123
Keywords: interface element, constitutive equation, stress integration, elastoplastic, soil-structure.

Summary
The concept on isoparametric interface element has been described[1]. For two-dimensional problems, the interface element with four or six nodes is fully compatible with four and eight-node isoparametric solid elements, and for the three- dimensional problems, the interface element with eight or sixteen nodes is fully compatible with eight and twenty nodes isoparametric solid elements. The interface stresses are characterized with one normal stress, , and two shear stresses, , and, . The normal and shear stresses are related with the constitutive matrix to the normal and tangential relative displacements of the interface element. An elastoplastic constitutive equation is used herein. The formulation of the constitutive behaviour was based on the plasticity theory. The Mohr-Coulomb criterion is used to define the yield function and plastic potential function of interface element.

In any numerical scheme employed for the analysis of elastoplastic problems it eventually becomes necessary to integrate the constitutive equations governing material behaviour. Several widely used update rules for the integration of elastoplastic constitutive equations fall within the implicit integration algorithms. The implicit integration algorithm is firstly used for the integration of elastoplastic constitutive equations of interface element in this paper. Some complexity is introduced by the presence of the second derivatives of the plastic potential in the implicit integration algorithm, and frequently that term is omitted for simplicity[2]. However, it is indicated in this paper that the omission of that term results in the convergence difficulty when the shear stress in the interface element is small for the three-dimensional interface element. The second derivatives of the plastic potential are obtained for the elastoplastic constitutive equations of interface element. The value of the entry of the second derivatives of the plastic potential increases with the decrease in the shear stress of the interface element, and dramatically increases when the shear stress is smaller a certain value. It is obvious that the second derivatives of the plastic potential cannot be neglected when the shear stress is smaller than a certain value. This is because the value of this item, which is induced by the second derivatives of the plastic potential, is in the same order of the flexibility matrix of the interface element, in the implicit integration algorithm. The small shear stress in the interface element appears usually in the soil-structure interaction analysis, especially near the ground surface, where the normal stress in the interface element is usually small. If the structure is laterally loaded, the depth, where the shear stress in the interface element is small, is increased with the increase in the lateral load applied to the structure.

The proposed implicit integration of elastoplastic constitutive equations of interface element is confirmed with a benchmark, i.e., the pile-section loaded laterally in a soil. The numerical results are consistent well with the analytical solutions of the elastic behaviour[3] and the plastic limit pressure on the pile-section[4]. The numerical results of flexible piles in landslides show that the proposed implicit integration algorithm is robust and faithful under three-dimensional situation even when the constitutive equations of interface element are considered with non-regular yield surfaces and non-associative flow.

References
1
G. Beer, "An isoparametric joint/interface element for finite element analysis", International Journal for Numerical Methods in Engineering, 21, 585-600, 1985. doi:10.1002/nme.1620210402
2
O.C. Zienkiewicz, R.L. Tayor, "The finite element method", 4th Edition, McGraw-Hill, London, 1989.
3
F. Baguelin, R. Frank, Y.H. Said, "Theoretical study of lateral reaction mechanism of piles", Geotechnique, 27(3), 405-434, 1977.
4
M.F. Randolph, G.T. Houlsby, "The limiting pressure on a circular pile loaded laterally in cohesive soil", Geotechnique, 34(4), 613-623, 1984.

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