Change of Constitutive Relations due to Interaction Between Strain-Gradient Effect and Material Gradation

[+] Author and Article Information
Youn-Sha Chan

Department of Computer and Mathematical Sciences,  University of Houston—Downtown, One Main Street, Houston, TX 77002

Glaucio H. Paulino

Department of Civil and Environmental Engineering,  University of Illinois, 2209 Newmark Laboratory, 205 North Mathews Avenue, Urbana, IL 61801

Albert C. Fannjiang

Department of Mathematics,  University of California, Davis, CA 95616

To get Eq. 11, one needs to specify the director field in the interior as well, namely, it has to be divergence free. If one allows non-divergence-free director field, then it is possible to have λ and G standing out of the partial derivative in the terms of 10 and still representing surface energy.

J. Appl. Mech 73(5), 871-875 (Jul 14, 2005) (5 pages) doi:10.1115/1.2041658 History: Received October 04, 2002; Revised July 14, 2005

For classical elasticity, the constitutive equations (Hooke’s law) have the same functional form for both homogeneous and nonhomogeneous materials. However, for strain-gradient elasticity, such is not the case. This paper shows that for strain-gradient elasticity with volumetric and surface energy (Casal’s continuum), extra terms appear in the constitutive equations which are associated with the interaction between the material gradation and the nonlocal effect of strain gradient. The corresponding governing partial differential equations are derived and their solutions are discussed.

Copyright © 2006 by American Society of Mechanical Engineers
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