zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Multiquadric method for the numerical solution of a biphasic mixture model. (English) Zbl 0910.76059
Summary: A computational algorithm based on the multiquadric method has been devised to solve the biphasic mixture model. The model includes a set of constitutive equations for the fluid flows through the solid phase, a set of momentum equations for stress-strain equilibrium, and continuity equations for the solid phase and the fluid phase. The numerical method does not require the generation of mesh as in the finite element method and hence gives high flexibility in applying the method to irregular geometry. Numerical examples are made to compute the solution of the confined compression problem which approximates the nonlinear response of soft hydrated tissues under external loadings.

MSC:
76M25Other numerical methods (fluid mechanics)
76T99Two-phase and multiphase flows
76Z05Physiological flows
WorldCat.org
Full Text: DOI
References:
[1] Spilker, R. L.; Suh, J. K.: Formulation and evaluation of a finite element model for the biphasic model of hydrated soft tissues. Comp. struct. 35, 425-439 (1990) · Zbl 0727.73061
[2] Suh, J. K.; Spilker, R. L.; Holmes, M. H.: A penalty finite element analysis for nonlinear mechanics of biphasic hydrated soft tissues under large deformation. Int. J. Num. meth. 32, 1411-1439 (1991) · Zbl 0763.73057
[3] Torzilli, P. A.; Mow, V. C.: On the fundamental fluid transport mechanisms through normal and pathological articular cartilage. Biomech. 9, 541-552 (1976)
[4] Mow, V. C.: The role of lubrication in biomechanical joints. ASME J. Lubr. technol. Trans. 91, 320-329 (1969)
[5] Simon, B. R.; Wu, J. S. S.; Carlton, M. W.; Evans, J. H.; Kazarian, L. E.: Structural models for human spinal motion segments based on a poroelastic view of the intervertebral disk. ASME J. Biomech. eng. 107, 327-335 (1985)
[6] Salzetein, R. A.; Pollack, S. R.; Mak, A. F. T.; Petron, N.; Brankov, G.: Electromechanical potentials in cortical bone, part 1: A continuum approach. Biomech. 20, 681-692 (1987)
[7] Taber, L. A.; Yang, M.; Keller, B. B.; Clark, E. B.: A poroelastic model for the trabecular embryonic heart. Advances in bioengineering, 623 (1992)
[8] Kenyon, D. E.: A mathematical model of water flux through aortic tissue. Bull. math. Biol. 41, 79-90 (1979)
[9] Oomens, C. W. J.; Vancampen, D. H.; Grootenboer, H. J.: A mixture approach to the mechanics of skin. Biomech. 20, 877-885 (1982)
[10] Mak, A. F. T.; Huang, L.; Wang, Q.: A biphasic poroelastic analysis of the flow dependent subcutaneous tissue pressure and compaction due to epidermal loadings: issues in pressure core. ASME J. Biomech. eng. 116, 421-429 (1994)
[11] Wayne, J. S.; Woo, S. L. Y.; Kwan, M.: Finite element analysis of repaired articular surfaces. Eng. medicine 205, 155-162 (1992)
[12] Hon, Y. C.; Huang, D. T.; Lu, M. W.; Mak, A. F. T.; Xue, W. M.: A new penalty formulation for the numerical solution of biphasic mixture model. J. neural, parallel & scientific computations 4, 465-474 (1996)
[13] Hardy, R. L.: Multiquadric equations of topography and other irregular surfaces. Geophys. res. 176, 1905-1915 (1971)
[14] Franke, R.: Scattered data interpolation: test of some methods. Math. comput. 38, 181-200 (1982) · Zbl 0476.65005
[15] Kansa, E. J.: Multiquadrics--a scattered data approximation scheme with applications to computational fluid dynamics--II. Solution to parabolic, hyperbolic and elliptic partial differential equations. Computers math. Applic. 19, 147-161 (1990) · Zbl 0850.76048
[16] Mow, V. C.; Holmes, M. H.; Lai, W. M.: Fluid transport and mechanical properties of articular cartilage: A review. Biomech. 17, 377-394 (1984)
[17] Tarwater, A. E.: A parameter study of Hardy’s multiquadric method for scattered data interpolation. Ucrl-54670 (Sept. 1985)
[18] Madych, W. R.: Miscellaneous error bounds for multiquadric and related interpolators. Computers math. Applic. 24, 121-138 (1992) · Zbl 0766.41003
[19] Golberg, M. A.; Chen, C. S.: On a method of atkinson for evaluating domain integrals in the boundary element method. Appl. math. Comput. 60, 125-138 (1994) · Zbl 0797.65090
[20] Bogomonly, A.: Fundamental solutions method for elliptic boundary value problems. SIAM J. Numer. anal. 22, 644-669 (1985) · Zbl 0579.65121
[21] Cheng, R. S. C.: Delta-trigonomeric and spline methods using the single-layer potential representation. Ph.d. thesis (1987)