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Saint-Venant end effects in antiplane shear for functionally graded linearly elastic materials. (English) Zbl 1060.74023

Summary: We investigate the influence of material inhomogeneity on the decay of Saint-Venant end effects in linear isotropic elasticity. The work is motivated by recent research activity on functionally graded materials (FGMs) i.e., materials with continuously varying properties tailored to satisfy specific engineering applications. In the framework of antiplane shear deformations of a semi-infinite strip, the mathematical issues involve the effects of spatial inhomogeneity on the decay rates of solutions to a Dirichlet boundary value problem for a second-order linear elliptic partial differential equation with variable coefficients. In previous work, the variable coefficient (the shear modulus) was assumed to be strictly positive on the closed semi-infinite strip. We relax this assumption to allow for the shear modulus to be zero on either long side of the strip. Thus, the results are applicable to FGMs that are graded continuously from zero shear modulus at one side of the strip. Lower bounds for the rate of decay of end effects are obtained, which allow for assessing the influence of material inhomogeneity. The results are illustrated using several specific material models.

MSC:

74G50 Saint-Venant’s principle
74B05 Classical linear elasticity
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[1] Scalpato, M. R., J. Elasticity 48 pp 145– (1997) · Zbl 0912.73010
[2] Chan, A. M., J. Elasticity 51 pp 227– (1998) · Zbl 0941.74007
[3] Horgan, C. O., Arch. Rational Mech. Anal. 124 pp 227– (1993) · Zbl 0819.35014
[4] Flavin, J. N., Proceedings of IUTAM Symposium on Anisotropy, Inhomogeneity and Nonlinearity in Solid Mechanics pp 339– (1995)
[5] Horgan, C. O., Quarterly of Applied Mathematics
[6] Horgan, C. O., in Advances in Applied Mechanics pp 179– (1983)
[7] Horgan, C. O., Applied Mechanics Reviews 42 pp 295– (1989)
[8] Horgan, C. O., Applied Mechanics Reviews 49 pp 101– (1996)
[9] Erdogan, F., Composites Engineering 5 pp 753– (1995)
[10] Pindera, M.-J., Special issue of Composites Part B: Engineering 28 (1997)
[11] Horgan, C. O., SIAM Review 37 pp 53– (1995) · Zbl 0824.73018
[12] Flavin, J. N., Qualitative Estimates for Partial Differential Equations (1996) · Zbl 0862.35001
[13] Aboudi, J., Composites: Part B 30 pp 777– (1999)
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