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Finite element analysis of seepage in viscoelastic media. (English) Zbl 0531.73055

Summary: R. S. Sandhu and E. L. Wilson presented ”Finite element analysis of seepage in elastic media” [J. Eng. Mech. Div. ASCE 95, No.EM3, 641-652 (1969)], by which complex problems in engineering can be solved. In this paper, it is extended to the case of viscoelastic media. If the soil skeleton is regarded as viscoelastic media, the stress-strain relation will be changed with time, which increases the complexity of problems. By making use of the finite-element method to solve such problems, the linear stress-strain increment relation is considered in every preselective interval of time. The linear proportional constant here is called ”equivalent elastic tensor”. On the basis of the equivalent elastic tensor, this paper deduces the formulation for solving problems in viscoelastic media.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
74S99 Numerical and other methods in solid mechanics
74L10 Soil and rock mechanics
76S05 Flows in porous media; filtration; seepage
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References:

[1] Sandhy, R. S. and Edward L. Wilson, Finite element analysis of seepage in elastic media, J. Eng. Mech. Div. ASCE, Vol. 95, No. EM3, June, (1969), 641–652.
[2] Jin Wen-lu, and Wu Gan-qing, Solution of three-dimensional consolidation and secondary time-effect problems of clay and its application, China Civil Engineering Journal, Vol. 15, No. 2, (June 1982). (in Chinese)
[3] Yin Zong-ze, Principle and Calculation in Soil Technique, Part I. Water Conservang Publishing House, (1979), 225. (in Chinese)
[4] Gurtin, M. E., Variational principles for linear elastodynamics, Archives for Rational Mechanics and Analysis, Vol. 16, (1964), 34–50. · Zbl 0124.40001
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