In this paper we give lower bounds for the spatial decay of the solutions for anti-plane shear deformations in the case of isotropic inhomogeneous elastic materials. We first consider the case when the shear modulus only depends on the lateral direction. By means of the logarithmic convexity arguments we obtain the required estimates. Some pictures illustrate our results. We also study the general inhomogeneity. We give some lower bounds whenever shear modulus satisfies several requirements.
ScalpatoMRHorganCO. Saint-Venant decay rate for an isotropic inhomogeneous linearly elastic solid in anti-plane shear. J Elasticity1997; 48: 145–166.
2.
ChanAMHorganCO. End effects in anti-plane shear for an inhomogeneous isotropic linearly elastic semi-infinite strip. J Elasticity1998; 51: 227–242.
3.
HorganCOPayneLE. On the asymptotic behavior of solutions of linear second-order boundary value problems on a semi-infinite strip. Arch Rat Mech Anal1993; 124: 277–303.
4.
HorganCOQuintanillaR. Saint-Venant end effects in antiplane shear for functionally graded linearly elastic materials. Math Mech Solids2001; 6: 115–132.
5.
HorganCOQuintanillaR. Spatial decay of transient end effects in functionally graded heat conducting materials. Q Appl Math2001; 59: 529–542.
6.
BorrelliAHorganCOPatriaMC. Exponential decay of end effects in anti-plane shear for functionally graded piezoelectric materials. Proc R Soc Lond A2004; 460: 1193–1212.
7.
LeseduarteMCQuintanillaR. Saint-Venant decay rates for a non-homogeneous isotropic mixture of elastic solids in anti-plane shear. Int J Solids Structures2005; 42: 2977–3000.
8.
LeseduarteMCQuintanillaR. Saint-Venant decay rates for an anisotropic and non-homogeneous mixture of elastic solids in anti-plane shear. Int J Solids Structures2008; 45: 1697–1712.
