NDLI: Numerical modeling of micro- and macro-behavior of viscoelastic porous materials

Content Provider	Springer Nature Link
Author	Huang, Y. Mogilevskaya, S. G. Crouch, S. L.
Copyright Year	2007
Abstract	This paper presents a numerical method for solving the two-dimensional problem of a polygonal linear viscoelastic domain containing an arbitrary number of non-overlapping circular holes of arbitrary sizes. The solution of the problem is based on the use of the correspondence principle. The governing equation for the problem in the Laplace domain is a complex hypersingular boundary integral equation written in terms of the unknown transformed displacements on the boundaries of the holes and the exterior boundaries of the finite body. No specific physical model is involved in the governing equation, which means that the method is capable of handling a variety of viscoelastic models. A truncated complex Fourier series with coefficients dependent on the transform parameter is used to approximate the unknown transformed displacements on the boundaries of the holes. A truncated complex series of Chebyshev polynomials with coefficients dependent on the transform parameter is used to approximate the unknown transformed displacements on the straight boundaries of the finite body. A system of linear algebraic equations is formed using the overspecification method. The viscoelastic stresses and displacements are calculated through the viscoelastic analogs of the Kolosov–Muskhelishvili potentials, and an analytical inverse Laplace transform is used to provide the time domain solution. Using the concept of representative volume, the effective viscoelastic properties of an equivalent homogeneous material are then found directly from the corresponding constitutive equations for the average field values.Several examples are given to demonstrate the accuracy of the method. The results for the stresses and displacements are compared with the numerical solutions obtained by commercial finite element software (ANSYS). The results for the effective properties are compared with those obtained with the self-consistent and Mori–Tanaka schemes.
Starting Page	797
Ending Page	816
Page Count	20
File Format	PDF
ISSN	01787675
Journal	Computational Mechanics
Volume Number	41
Issue Number	6
e-ISSN	14320924
Language	English
Publisher	Springer-Verlag
Publisher Date	2007-03-07
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Viscoelasticity Porous material Representative volume Correspondence principle Effective properties Circular holes Mechanics, Fluids, Thermodynamics Computational Science and Engineering Numerical and Computational Methods in Engineering Theoretical and Applied Mechanics
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Ocean Engineering Computational Theory and Mathematics Mechanical Engineering Computational Mechanics Computational Mathematics

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