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Three models of non periodic fibrous materials obtained by homogenization. (English) Zbl 0795.92006

After removing the following defaults: (1) interactions between fibres and medium are neglected, (2) fibres are considered dimensionless, appearing in known results of several other authors, the present author has developed a model for studying cardiac muscles. The fibres considered here are not periodically arranged but their orientation varies continuously in the material. He used homogeneization theory when there are too many fibres.

MSC:

92C10 Biomechanics
74L15 Biomechanical solid mechanics
92C30 Physiology (general)
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References:

[1] M. J. ARTS, 1978, A Mathematical Model of the Dynamics of the Left Ventricle, Thesis, University of Limburg, The Netherlands.
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[10] E. SANCHEZ-PALENCIA, 1980, Non Homogeneous Materials and Vibration Theory, Springer Verlag, Monographs in Physics, V, 127 Berlin. Zbl0432.70002 MR578345 · Zbl 0432.70002
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[12] D. D. STREETER, 1979, Gross Morphology and Fiber Geometry of the Heart, Handbook of Physiology, Vol. 1, Section 2, American Physiology Society, Bethesda, Maryland.
[13] L. TARTAR, 1977, Cours Peccot au Collège de France, unpublished.
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