ASME Journal of Applied Mechanics, Vol. 73, No. 5, pp. 871-875, 2006
Y.-S.
Chan
Department of Computer and Mathematical Sciences, University of Houston—Downtown, One Main Street, Houston, TX 77002
G.H. Paulino
Department of Civil and Environmental Engineering, University of Illinois at Urbana-Champaign, Newmark Laboratory, 205 North Mathews Avenue, IL 61801, U.S.A.
A.C. Fannjiang
Department of Mathematics, University of California,Davis, CA 95616, U.S.A.
Abstract
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.
Key words: constitutive equations,
strain-gradient elasticity, material gradation, partial differential equations,
high-order continuum theory, multiscale theory