Saccomandi, Giuseppe; Beatty, Millard F. Universal relations for fiber-reinforced elastic materials. (English) Zbl 1032.74006 Math. Mech. Solids 7, No. 1, 95-110 (2002). From the summary: Two general universal relations for both compressible and incompressible, isotropic elastic materials reinforced by a single field of inextensible fibers are derived as components of an axial vector condition. The constitutive equations comprise a system of six scalar equations linear in four constraint and material response functions. It is known from the manifold method applied to this linear system that, in general, at least two universal relations exist. Hence, depending on the rank of a coefficient matrix, the two axial vector component equations comprise the complete set of universal relations for fiber-reinforced material. These equations are valid for all deformations, and they hold independently of balance equations and boundary conditions. The results are illustrated for a homogeneous simple shear with triaxial stretch of a material having various single fiber arrangements. Cited in 24 Documents MSC: 74A40 Random materials and composite materials 74E30 Composite and mixture properties Keywords:inextensible fibers; manifold method; axial vector component equations; homogeneous simple shear; triaxial stretch PDFBibTeX XMLCite \textit{G. Saccomandi} and \textit{M. F. Beatty}, Math. Mech. Solids 7, No. 1, 95--110 (2002; Zbl 1032.74006) Full Text: DOI References: [1] D’Ambrosio, P., ASCE Journal of Engineering Mechanics 121 pp 1041– (1995) [2] Kurashige, M., Journal of Applied Mathematics and Physics (ZAMP) 35 pp 822– (1985) · Zbl 0578.73042 [3] De Tommasi, D., Journal of Elasticity 45 pp 215– (1996) · Zbl 0883.73016 [4] Beatty, M. F., Journal of Elasticity 17 pp 113– (1987) · Zbl 0603.73010 [5] Pucci, E., Continuum Mechanics and Thermodynamics 9 pp 61– (1997) · Zbl 0873.73012 [6] Rivlin, R. S., Rendiconti di Matematica e delle sue Applicazioni 20 pp 35– (2000) [7] Hayes, M. A., Journal of Applied Mathematics and Physics (ZAMP) 17 pp 636– (1966) [8] Beatty, M. F., Acta Mechanica 80 pp 299– (1989) · Zbl 0703.73001 [9] Beatty, M. F., Principles of Engineering Mechanics. Volume 1: Kinematics - The Geometry of Motion (1986) · Zbl 0697.70001 [10] Pucci, E., Mathematics and Mechanics of Solids 1 pp 207– (1996) · Zbl 1001.74518 [11] Pucci, E., Contemporary Research in the Mechanics and Mathematics of Materials pp 176– (1996) [12] Saccomandi, G., Mathematics and Mechanics of Solids 2 pp 181– (1997) · Zbl 1001.74526 [13] Wineman, A., Journal of Elasticity 14 pp 97– (1984) · Zbl 0531.73008 [14] Beatty, M. F., Acta Mechanica 29 pp 119– (1978) · Zbl 0377.73019 [15] Beskos, D. E., Journal of Elasticity 2 pp 153– (1972) [16] Pipkin, A. C., Quarterly of Applied Mathematics 32 pp 253– (1974) · Zbl 0366.73041 [17] Pipkin, A. C., Quarterly Journal of Mechanics and Applied Mathematics 28 pp 271– (1975) · Zbl 0328.73037 [18] Pipkin, A. C., Journal of Applied Mechanics 38 pp 634– (1971) · Zbl 0234.73004 [19] Beskos, D. E., International Journal of Solids and Structures 9 pp 553– (1973) · Zbl 0263.73024 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.