Title: A constitutive formulation to elastic media having different Young's moduli and Poisson's values in tension and compression

Authors: Zhi-Ming Ye, Benqi Guo, Huanran Yu

Addresses: Department of Civil Engineering, Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200444, PR China. ' Department of Mathematics, University of Manitoba, Winnipeg R3T 2N2, Canada. ' Department of Mechanics, Lanzhou University, Lanzhou, Gansu 730000, PR China

Abstract: This paper presents a new formulation of constitutive equations to different Young|s moduli in tension and in compression. Historically, the theories of different Young|s moduli gave the characteristics of the same Poisson|s values in tension and in compression although the Young|s moduli are different in tension and in compression. This could lead to incompatibility between the normal stress and the shear stress in the unit element. In order to overcome this incompatibility, it is necessary to use the theory of fundamental continuum mechanics to modify the material constitutive relationship, to ensure any assumptions made in deriving the basic equations are consistent.

Keywords: constitutive equations; elastic mechanics; Young|s modulus; Poisson|s ratio; tension; compression; normal stress; shear stress; continuum mechanics; mathematical modelling.

DOI: 10.1504/IJMIC.2007.014944

International Journal of Modelling, Identification and Control, 2007 Vol.2 No.3, pp.188 - 194

Available online: 20 Aug 2007 *

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